Summary Microeconomics: Consumer and Firms

Chapter 1: Introduction Microeconomics

Microeconomics

Microeconomics is the branch of economics that studies the specific choices made by consumers and producers. This framework of thoughts is used to approach the study of markets.

Macroeconomics, in contrast to microeconomics, is a study of economics that looks at the world from a wider perspective and looks at a more complex model of consumers and firms.

We want to be able to create precise models with exact numbers and therefore mathematics and graphs are incorporated in the study of microeconomics. When relationships in a model are discovered we want to know why the relationships exist.

When we understand the behavior of consumers and producers we can predict how various policies change the incentives of the behavior of consumers and producers.

There are different tools to examine and explain why economic entities behave as they do. We always start the analysis with theories and models. Data from previous years are used to test the theory. One can also gain information from essays written by economists about a theory.

The book

In this book we will first take a look at how a transaction will affect the consumer and producer involved. Both the consumer and producer side will be explained more specific.

Then the book will take a closer look at the market supply. We will look at different ways of producers to supply output to markets. Different forms of market competition will be discussed, like perfect competition and monopoly. Last of all the book will focus on data.

Microeconomics has evolved into an empirical study. This means that not only theory is used but that they use more data analysis and experiments to explore phenomena.

Chapter 2: Supply and demand

The market

Producers all over the world offer a large number and variety of goods. Consumers can choose from this large basket of goods. How do producers know which products to sell and how do consumers decide which goods to buy? To answer these questions we use a simple supply and demand model of the market. A market is referred to as the specific products being bought and sold, a particular location and a point in time.

There are four basic assumptions to the supply and demand model:

• Focus on a single market

In this single market producers are represented by supply and consumers are represented by demand.

• All goods sold in the market are identical

We assume that all goods bought and sold in the market are homogeneous. This means that the consumer is as happy with one good as with another good. Commodities are products traded in markets in which consumers view different varieties of the goods as essentially interchangeable.

• All goods sold in the market sell for the same price, and everyone has the same information

This means that everybody knows everything about the transactions; there are no deals or discounts for particular buyers.

• There are many producers and consumers in the market

There is no specific consumer or producer that has a noticeable impact on things that happen in the market.

Demand

There are several factors that influence the demand:

• Price. This is the most important factor.

• The number of consumers. When there are more people in a market, the quantity people desire of a good is higher.

• Consumer income or wealth. When a consumer becomes richer he will buy more goods.

• Consumer tastes. When the taste of consumers changes this will have an effect on the amount of the goods being bought.

• Price of other goods.
  Substitutes are goods that can be used in place of another good. When the price of a substitute is lower than the price of the initial good, consumers will buy the substitute.
  A complement is a good that is purchased and used in combination with another good. When the price of a complement falls, people want to buy more of that good and thus they will also buy more of the initial good.

We will simplify the relationship and will look at how the amount consumers demand will change when only a goods' price changes, all other factors determining demand being the same. From this relation we can draw a demand curve. The demand curve is downward sloping.

The demand curve for tomatoes, for instance, is given by the equation:

Q = 1,000 – 200P

Where Q is the quantity demanded (pounds) and P is the price (dollars). From this equation we can see that a $1 increase in the price leads to a 200 pound decline in the quantity demanded. This leads to the following demand curve:

Economists often use the demand equation in the form of the price as a function of quantity because this is easier to work with. This equation is called the inverse demand curve. The inverse demand curve can be found by solving for P:

Q = 1,000 – 200P

200P + Q = 1,000

200P = 1,000 – Q

P = 5 – 0.05Q

In this new equation one can clearly see that consumers are not willing to pay a price greater than 5 because in that case Q is zero. This price level is called the demand choke price.

When a factor other than the price, that affects demand, changes, then the demand curve will shift. For instance, when there is an outbreak of salmonella and people think that tomatoes contain this salmonella, then people will buy fewer tomatoes. At a given price they will buy fewer tomatoes than before and therefore the demand curve will shift to the left, to D2.

When scientists tell people that tomatoes are good for your health then people will buy more tomatoes than before. As a result the demand curve will shift to the right, to D3. Economists call it a change in demand when the demand curve shifts left or right due to a change in a factor other than the price.

If only the price changes then we have a movement along the demand curve and economists call this a change in quantity demanded.

Why do economists primarily look at the price and not at other factors that affect demand?

• The price is the most important factor.

• It is easy to change prices. This is useful when the market has to respond to shocks.

• The price is the only factor that also has a direct effect on the other side of the market, the supply. The price is seen as the element that bounds supply and demand.

Supply

There are several factors that determine supply:

• Price. Similar as with demand, the price is the most important determinant of supply.

• Suppliers’ cost of production. Changes in input prices and technology will change the suppliers’ production costs. This will affect the quantity supplied to the market. Also changes in production technology (the process used to make, distribute and sell) will change the suppliers’ production costs.

• The number of sellers. When there are more producers offering the product then the quantity supplied will be higher.

• Sellers’ outside options. A producer can produce different goods in different markets. When a producer’s view about doing business in other markets changes this can affect the quantity he is willing to supply in the initial market.

Just as we have a demand curve we also have a supply curve. The supply curve is upward sloping and shows the relationship between the quantity supplied and the price. The supply curve for tomatoes can for instance be given by:

Q = 200P – 200

Where Q is the quantity supplied (pounds) and P is the price (dollars). From this equation we can see that for every $1 increase in the price, the quantity supplied will increase by 200. Economists often use the inverse supply curve, where the price is a function of quantity. In this case the inverse supply curve is:

Q = 200P – 200

200P = Q + 200

P = 0.005Q + 1

From this inverse supply equation one can see that no producer is willing to supply at a price of $1 because this is the price when the quantity is zero. This price is called the supply choke price.

The supply of tomatoes is given by the line S1 in the graph on the next page.

When there is a change in a factor other than the price then the supply curve will shift. For instance, when a producer buys a machine that can harvest tomatoes faster, then the quantity supplied will increase. This will shift the supply curve to the right, to S2. If there is for instance a period of drought, then the quantity of tomatoes a producer can supply decreases. This will shift the supply curve left, to S3. These shifts of the supply curve are called changes in supply.

When the price changes then there will be no shift of the supply curve but instead there will be a movement along the supply curve. This is called a change in quantity supplied.

The equilibrium

We will now combine the demand and supply curve by drawing them in the same graph. We will look at the same curves as before:

Demand: Q = 1,000 – 200P

Supply: Q = 200P – 200

The point where the supply and demand curves cross is called the market equilibrium. The equilibrium is given by point E. The price and quantity associated with this equilibrium are given by P_e and Q_e.

To calculate the exact equilibrium price and quantity we have to use the equations of the demand and supply. We find the values by solving Q^D = Q^S:

Q^D = Q^S

1,000 – 200P = 200P – 200

1,200 = 400P

P_e = 3

To find the equilibrium quantity we can fill in P_e in the demand or supply curve:

Q_e = 1,000 – 200 x 3 = 400

It can be that the current price is not equal to the equilibrium price.

• Current price > P_e. In this case there is an excess quantity supplied, which is called a surplus. To reduce this surplus, producers need to attract more buyers. They do this by lowering their price. When the price falls the demand will rise until the market reaches its market equilibrium.

• Current price < P_e. This is the contrary of the case before; there is more demand than supply. This is called a shortage. Buyers who cannot find a good will bid up prices and as a result producers will raise their prices. When prices rise, quantity demand will decrease and quantity supplied will increase until the market reaches its equilibrium E.

We will again take a look at the case when the demand of tomatoes changes due to tomatoes being a source of salmonella. This will shift the demand curve in/left. How does this change the equilibrium? Suppose that due to this change the new demand curve will become: Q = 500 – 200P. We can find the equilibrium values with the same method as before:

Q^D = Q^S

500 – 200P = 200P – 200

400P = 700

P_e = 1.75

From this follows that Q_e = 500 – 200 x 1.75 = 150

We can see that the equilibrium price has fallen from $3 to $1.75 and that the equilibrium quantity has fallen from 400 to 150. So the equilibrium has shifted to the left.

Now we will take a look how the equilibrium changes when supply changes. When the supply increases, this will shift the supply curve out/to the right. Suppose that the new supply curve is given by Q = 200P + 200. We can calculate the equilibrium values:

Q^D = Q^S

1,000 – 200P = 200P + 200

400P = 800

P_e = 2

From this follows that Q_e = 1,000 – 200 x 2 = 600.

We can see that the equilibrium price has fallen from $3 to $2 but the equilibrium quantity has risen from 400 to 600. This means that the equilibrium has shifted to the right.

An overview:

The size of the price and quantity changes depends on whether the demand and supply curves are flatter or steeper than the normal curves.

• Demand curve shift with a flatter supply curve: a shift of the demand curve to the right will result in a small increase in the equilibrium price and a large increase in the equilibrium quantity.

• Demand curve shift with a steeper supply curve: a shift of the demand curve to the right will result in a large increase in the equilibrium price and a small increase in the equilibrium quantity.

• Supply curve shift with a flatter demand curve: a shift of the supply curve to the right will result in a small decrease in equilibrium price and a large increase in equilibrium quantity.

• Supply curve shift with a steeper demand curve: a shift of the supply curve to the right will result in a large decrease in equilibrium price and a small increase in the equilibrium quantity.

When both curves shift at the same time, we will know with certainty the direction of change of either the equilibrium price or quantity, but never both.

Price elasticity

The slope of a curve determines whether it is steep or flat. A steep demand curve means that consumers are not very sensitive to changes in the price; their demand will not change much in response to a change in the price.

Elasticity is the ratio of percentage change in one value to the percentage change in another value. With the price elasticity of demand we refer to the percentage change in quantity demanded resulting from a 1% change in the price.

It is important to understand that the slope of a curve is not the same as the elasticity of it. Using the slope of a curve to measure price responsiveness does not always lead to a correct answer. To eliminate unit problems and make magnitudes across markets comparable, we use elasticities.

Price elasticity of demand = % change in quantity demanded / % change in price

In short: E^D = %ΔQ^D / %ΔP

Price elasticity of supply = % change in quantity supplied / % change in price

In short: E^S = %ΔQ^S / %ΔP

When a demand curve is very price sensitive, a small change in the price will have a large change in the quantity demanded. This means that the numerator of the equation is relatively large and the denominator is relatively small.

The change in demand has the opposite change compared to the price. So when the change in price is positive, the change in demand is negative. This results in a large but negative elasticity. Markets with a less price sensitive demand curve have elasticities that are small.

When it is easy for consumers to switch between products or markets, they will be more sensitive to price changes. This means that the price elasticity of demand will be relatively large.

Economists use special terms for specific elasticity magnitudes:

• Elastic: A price elasticity with an absolute value greater than 1.

• Inelastic: A price elasticity with an absolute value less than 1.

• Unit elastic: A price elasticity with an absolute value of 1.

• Perfectly inelastic: A price elasticity that is equal to zero. This means that when the price changes this has no effect on the quantity demanded or supplied.

• Perfectly elastic: A price elasticity that is infinite. This means that a change in the price leads to an infinite change in the quantity demanded or supplied.

In the calculation of the elasticity we use the change in quantity: %ΔQ. We can rewrite this term into ΔQ/Q. We can now put this new term into the equation:

E = %ΔQ / %ΔP= (ΔQ/Q) / (ΔP/P) = (ΔQ/ΔP) x (P/Q) = (1/slope) x (P/Q)

In this formula ‘’slope’’ refers to the slope of the demand curve.

The P/Q ratio falls when we move down along the demand curve. This reduces the magnitude of the price elasticity of demand. When the demand curve intersects the vertical axis the elasticity will be - ∞. When the curve intersects the horizontal axis the elasticity will be zero.

When we move along the supply curve P/Q will fall. When the supply curve intersects the vertical axis the elasticity will be + ∞. Unlike the demand curve, the elasticity of supply can never be equal to zero because the supply curve will never intersect the horizontal axis.

We discussed that at a point where the price elasticity is zero then demand and supply are perfectly inelastic. But how will the demand and supply curves look when they are perfectly inelastic or perfectly elastic at all points?

A perfectly inelastic curve is vertical because a change in the price will have no effect on the quantity. A perfectly elastic curve is horizontal because a change in the price will lead to an infinitely large change in the quantity.

There is a relationship between the expenditures of a consumer and the price elasticity of demand. To understand this relationship we have to recognize that:

Total expenditures = total revenue = P x Q

Expenditures rise with an increase in the price if the demand is inelastic and they decrease with prices if demand is elastic. If the demand is unit elastic then a change in the price has no effect on the expenditures.

In the next graph one can see the relationship between the price and the total amount of expenditures. Point B represents the maximum expenditures point.

Besides price elasticities we can also calculate the income elasticity of demand. This is the percentage change in quantity demanded associated with a 1% change in consumer income.

E^D_I = %ΔQ^D / %ΔI = (ΔQ^D / ΔI) x (I / Q^D)

This formula describes how sensitive demand is to changes in income.

Several different goods are:

• An inferior good is a good for which the quantity demanded decreases when income rises. This means that the good has a negative income elasticity. Examples are bus tickets and youth hostels.

• A normal good is a good for which quantity demand rises when income rises. This means that the good has a positive income elasticity. Most goods fit into this category.

• A luxury good is a good with an income elasticity greater than 1. These goods are a subcategory of normal goods. Examples are a butler and yachts.

The cross-price elasticity of demand is the ratio of the percentage change in the quantity demanded of one good associated with a 1% change in the price of another good.

E^D_XY = %ΔQ^D_X / %ΔP_Y = (ΔQ^D_X / ΔP_Y) X (P_Y / Q^D_X)

To avoid confusion between the cross-price elasticity of demand and the price elasticity of demand we discussed before, we use another term for the latter. We will use the term own-price elasticity of demand.

Chapter 3: Market analysis

Consumer and producer surplus

To better understand the market we will take a look at a way to measure the benefit for consumers and producers as a result of a certain policy.

Consumer surplus is the difference between the price consumers would be willing to pay for a good or service and the amount they actually have to pay. This is usually measured as an amount of money. The total consumer surplus is the area under the demand curve and above the market price. The height of this triangle is the difference between the market price and the demand choke price.

When the demand curve becomes more elastic, flatter, then the consumer surplus will decrease. This is because the difference between the demand choke price and the market price is smaller now.

The equation to calculate the CS triangle is:

CS = 0.5 x base x height = 0.5 x quantity sold x (demand choke price – actual market price)

Producer surplus is the difference between the price at which producers are willing to sell their good or service and the price they actually receive. The producer surplus is the area above the supply curve and below the price. The height of this triangle is the difference between the market price and the supply choke price.

PS = 0.5 x base x height = 0.5 x quantity sold x (actual market price – supply choke price)

When there is a change in the market resulting in a shift of the demand or supply curve, then the CS and PS will change. What happens, for instance, when manufacturing costs increase and therefore shift the supply curve to the left?

Before the shift of the supply curve, the equilibrium quantity and price are Q₁ and P₁. In this case:

CS = A + B + C + D (triangle under demand curve but above market price)

PS = E + F + G (triangle above supply curve but under market price)

Due to the shift of S1 to S2, the new equilibrium quantity and price will become Q₂ and P₂. The new CS and PS are:

CS = A

PS = B + E

The loss in PS is F + G but there is also a shift from CS to PS represented by area B. The loss in CS is C + D.

One can do a similar analysis for an inward shift of the demand curve. This results in a lower equilibrium price and quantity leading to a reduction of producer surplus. The change in consumer surplus is ambiguous and similar to the change in PS in the case above; the inward shift leads to a lower consumer surplus but there is also a transfer from PC to CS which increases the consumer surplus.

Price regulations

A price ceiling is a regulation that sets the highest price that can be paid legally for a good or service. At certain times in the past there have been price ceilings for specific goods. We will now take a look at the effect of a price ceiling on the market.

Before the price ceiling, the market is in equilibrium with P_e and Q_e. Then:

CS = A + B + C

PS = D + E + F

Assume that a price ceiling of P_c is put in place. As a result, demand will be higher than the supply and thus there will be a shortage of Q_D – Q_s. One can see this in the graph on the next page.

The new CS and PS will be:

CS = A + B + D

PS = F

The PC has reduced because of the fall in the price. The area D transfers from producers to consumers and the net gain to consumers is area D – C. The area C + E is the deadweight loss (DWL) created by the price ceiling. The deadweight loss is defined as the reduction in total surplus that occurs as a result of a market inefficiency.

DWL = 0.5 x (Q_e – Q_S) x (P’ – P_c)

The magnitude of the deadweight loss of a price ceiling depends on the elasticities of the demand and supply. When supply and demand are relatively inelastic, the transfer from PS to CS is much larger than the DWL. When supply and demand are relatively elastic, the transfer from PS to CS is much smaller than the DWL.

Usually price ceilings are set below the equilibrium price. In case the price ceiling is set above the equilibrium price we speak of a non binding price ceiling.

Besides price ceilings there are also other types of price regulations, like a price floor. This is a price regulation that sets the lowest price that can be paid legally for a good or service.

Assume that a price floor of P_f is put in place.

As a result, supply will be higher than demand and thus there will be a surplus of Q_S – Q_D.

The new CS and PS will be:

CS = A

PS = B + D + F

The area B is transferred from consumers to producers. The net gain to producers is equal to B – E. The DWL created by the price floor is C + E.

DWL = 0.5 x (Q_e – Q_D) x (P_f – P’)

Price floors are usually set above the equilibrium price. When it is set below the equilibrium price we call it a non binding price floor.

Quantity regulations

Besides price regulations, a government can also choose to impose quantity regulations.

A quota is a regulation that sets the quantity of a good or service provided. The government uses a quota to force firms to produce a certain amount of a good or to limit the amount of goods produced. It is more often used as the latter than the former. A country can also limit imports by establishing a quota.

The establishment of a maximum quota has an effect on the supply curve. The supply curve will have the same form as the original one from the y axis until the point of the quota, but from the point of the quota quantity the supply curve will be a vertical line at that quantity.

As a result of the quota, consumer surplus will decrease and producer surplus will increase. As we saw before with price regulations, quantity regulations will also create a deadweight loss.

It is hard for a government to let firms produce a minimum amount of a good that firms do not want to produce. In this case it is possible that the government itself can produce the good. For example, governments often offer education. The direct government provision of goods and services has an effect on the market.

When the government decides to offer education the supply for total education will increase and therefore shifts out/to the right. This results in a lower equilibrium price and a higher equilibrium quantity. The new total quantity has increased less than the total amount offered by the government and therefore it must be that private education has decreased. This decline in quantity supplied by the private schools is known as the crowding out effect.

Taxes

Governments use taxes on many different things and through different ways. When the government imposes a tax, this will have an effect on the market. We will look at the market of movie tickets. In the graph on the next page one can see that:

CS = A + B + C

PS = D + E + F

Suppose the government imposes a tax of 0.5 per movie ticket. The supply curve will shift inward due to this tax. The equilibrium quantity will decrease to Q₂, buyers will pay P_b and sellers will receive P_s. The areas B and D form together the tax revenue, it is a transfer from consumers and producers to the government.

After the tax:

CS = A

PS = F

C + E is the deadweight loss of the tax. The magnitude of the DWL is primarily determined by how large the change in quantity is due to introducing the tax.

Imposing a large tax is much worse for the market than imposing a small tax. When a large tax is imposed, the tax wedge between the price consumers pay and the price producers receive increases. Although the tax revenue for the government increases, a large tax creates a much larger DWL.

When a tax is imposed on the price of tickets, suppliers are not the only ones that bear the burden of the tax; also consumers bear the burden. The tax incidence is who actually pays the burden of a tax. It is unaffected by whether the seller or buyer has to pay the tax.

P_s = P_b - tax

This equation shows that it does not matter whether you subtract the tax from what the supplier receives or add the tax to what the buyer pays.

The elasticities of supply and demand determine whether consumers or producers bear the burden of the tax.

Share born by consumer = E^S/ (E^S+ Ι E^D Ι )

Share born by producers = Ι E^DΙ / (E^S+ Ι E^D Ι )

In this formula Ι E^D Ι and Ι E^S Ι stand for the absolute value of the elasticities. When the price elasticity of supply (E^S) is infinite, the consumers’ share is 1 and thus consumers bear the whole burden. When Ι E^D Ι is infinite, the consumers’ share of the tax burden is zero and thus suppliers bear the whole burden.

Subsidies

A subsidy is a payment by the government to a buyer or seller of a good or service. It is the exact opposite of a tax and therefore we can treat it as a negative tax. Due to the subsidy, the price the buyer pays is lower than the price the supplier receives.

P_b + subsidy = P_s

When the government imposes a subsidy, the supply curve will shift out/right.

The CS and PS after imposing the subsidy will be:

CS = A + B + C + F + G + H

PS = B + C + D + F + G + J

The cost of the subsidy for the government is: B + C + D + E + F + G + H + I.

The DWL is E + I.

In this case we see that parts of CS and PS areas overlap because both sides are getting more surplus than before. The costs associated with the subsidy are larger than the sum of the benefits to producers and consumers.

Chapter 4: Consumer behavior

Utility

Every decision a consumer makes is partly based on its preferences. Every day they have to make choices about what to buy and what not. We assume that all consumers’ decisions about what they should or should not buy share four properties:

• Completeness and rank-ability. This means that consumers can compare the different goods they consider to buy. Economists use the term consumption bundle: a set of goods or services a consumer considers purchasing. A consumer is able to choose between two or more available consumption bundles.

• For most goods, more is better than less. In general, consumers think that more of a good is always better.

• Transitivity. This means that when a consumer prefers bundle 1 over bundle 2 and 2 over 3, than he must also prefer 1 over 3.

• The more a consumer has of a particular good, the less he is willing to give up of something else to get even more of that good. Consumers like variety. You may want to pay a high price for a certain good that you do not have. But the more you have of that good, the less you are willing to pay.

Utility is a measure of how satisfied a consumer is. The utility function shows the relationship between what consumers consume and their level of well-being. So it shows the utility level of a consumer.

An important thing related to the utility function is the marginal utility. This is the additional utility a consumer receives from an additional unit of a good or service. The marginal utility is calculated with the following formula:

MU = Δ Utility / Δ units of the good

The utility functions help us to determine which bundle we prefer but we cannot determine how much more we prefer a specific bundle over another bundle. It is also not possible to compare the utility function of one consumer with the utility function of another consumer.

Indifference curves

To better understand utility we take the special case in which a consumer is indifferent between bundles of goods. This means that the consumer derives the same utility level from each of the consumption bundles.

If we combine all these bundles with the same utility, we can derive the indifference curve. For each level of utility, there is a different indifference curve. In the graph on the previous page one can see some indifference curves for different utility levels between two goods.

To go to a higher utility level one must shift to an indifference curve more to the right/up.

The four assumptions we have made about consumer preferences lead to characteristics of indifference curves:

• We can draw indifference curves. Completeness and rank-ability imply that we can always draw indifference curves.

• We can figure out which indifference curves have higher utility levels and why they slope downward. The assumption ‘’the more is better’’ tells us that we can determine which curve represents the highest utility. It also implies that the curve can never slope upward.

• Indifference curves never cross.

• Indifference curves are convex to the origin. They will bend into the origin.

The slope of the indifference curve is called the marginal rate of substitution (MRS). It is the rate at which a consumer is willing to trade off one good (the good on the horizontal axis, X) for another good (the good on the vertical axis, Y) and still be left equally well off.

MRS_XY = - (ΔY / ΔX)

Because the slope of the indifference is negative, we use the negative of it to make the MRS a positive number.

We can also use marginal utilities to calculate the MRS:

MRS_XY = MU_goodX / MU_goodY

The shape of the indifference curve can tell us something about consumers’ utility functions.

• When the curve is steep, consumers are willing to give up a high quantity of Y to get another unit of X.

• When the curve is flat, consumers are willing to give up a lot of X to get another unit of Y.

• When the curve is relatively straight, the goods are likely to be highly substitutable. Meaning that when you move to another point on the curve it does not change the MRS much.

• When the curve is much curved, the goods are likely to be complementary.

We will look at the extreme case of substitutes and complements;

• A perfect substitute is a good that a consumer can trade for another good, in fixed units, and receive the same level of utility. The indifference curves of two goods that are perfect substitutes are straight lines. The MRS of these indifference curves is constant.

• A perfect complement is a good whose utility level depends on it being used in a fixed proportion with another good. The indifference curves of two goods that are complements are L-shaped. The consumer’s utility can only rise when the consumer has more of both goods. The MRS is zero on the horizontal parts and infinite on the vertical parts.

In the next graph one can see an example of indifference curves of perfect substitutes and perfect complements.

In most cases, the indifference curves of one consumer have the same shape. However, it can be that a consumer has indifference curves with different shapes. This can for instance be because the consumer views the goods as substitutes at low utility levels and as complements at high utility levels.

The budget constraint

To better understand the behavior of the consumer we will take a look at the interactions between utility, income and prices. We will focus on a simple model with only two goods. We make the following assumptions:

• Each good has a fixed price and any consumer can buy as much of a good as he wants.

• The amount of consumer’s income is fixed.

• The consumer cannot save or borrow.

When we incorporate income and prices into the model of consumer behavior we get a budget constraint. This is a curve that describes the entire set of consumption bundles a consumer can purchase when spending all its income. The mathematical formula for it is:

Income = P_X Q_X + P_Y Q_Y

This shows that the total expenditures on good X and Y are equal to the total income of the consumer. Below is a graph with an example of a budget constraint.

A feasible bundle is a bundle that the consumer is able to purchase with his income. It lies on or below the consumer’s budget constraint.

An infeasible bundle is a bundle that the consumer cannot afford with his income. It lies to the right and above the consumer’s budget constraint.

We can rewrite the equation of the budget constraint into:

Q_Y = (income / P_Y) – (P_X / P_y) Q_X

From this formula we can see that the slope of the budget constraint is determined by the prices of the two goods.

Slope = - P_X / P_Y

A change in the price or income will have an effect on the position of the budget constraint. If the price of good X increases, consumers will buy less of good X. Similar happens when price of good Y increases, consumption of good Y will fall. When the income of the consumer falls, the entire budget constraint will shift inwards. The marked areas represent the loss of feasible bundles.

In all the cases we have discussed so far the budget constraints were straight lines. However, there are some cases in which the budget constraint is kinked.

• Quantity discounts

A company can offer a discount for a specific amount of a good. When there is a discount for good Y, the budget constraint will look like:

The marked area represents the combination of good X and good Y that he can afford under the new budget constraint that he could not have purchased before.

• Quantity limits

When there is a limit on how much a consumer can consume the budget constraint will also show a kink. Assume that there is a limit on good Y, then the budget constraint will look like:

The marked area represents the combination of good X and good Y that the consumer first was able to afford but under the new budget constraint this area is infeasible for him.

Consumption

The optimal consumption bundle of a consumer is found where the budget constraint and the indifference curve are tangent.

The consumers can afford the bundles of point A, B, C and D. He cannot afford the bundle represented by point E because it lies outside its budget. The consumer will choose point A over point B, C and D because it lies on a higher utility curve. Thus point A is the utility maximizing point of the consumer.

We can express this theory of utility maximization mathematically:

Slope of indifference curve = slope of budget constraint

- MRS_XY= - MU_X/ MU_Y= - P_X/ P_Y

MU_X/ MU_Y= P_X/ P_Yor MU_X/ P_X= MU_Y/ P_Y

This leads to the theory that even if two consumers have very different preferences between two goods, they will still have the same ratio of marginal utilities for the two goods. This is because utility maximization implies that MRS equals the ratio of the prices.

We argued before that indifference curves can never cross but in fact they can. The indifference curves of 1 consumer can never cross but the different indifferent curves of two consumers (A and B) can.

So far we assumed that the consumer wants to spend some income on both goods. This is referred to as an interior solution; a utility maximizing bundle that contains positive quantities of both goods.

Sometimes a consumer wants to spend all his income on just one good. This is called a corner solution, it is a utility-maximizing bundle located at the corner of the budget constraint. This will graphically look like:

The consumer can afford the bundle at point A and B but it will choose A, because it lies on a higher utility function. In this case the consumer only buys one good and that point A lies in the corner.

So far we used the utility maximization approach; the consumer chooses the highest utility level given its budget constraint. However, we can also use the expenditure maximization approach; the consumer first sets the utility level and then looks for the appropriate budget constraint.

Chapter 5: Demand: a closer look

Changes in income

The income effect is the change in a consumer’s consumption choice that results from a change in the purchasing power of the consumer’s income. When we examine this we have to hold all other factors constant. We especially assume that the preferences of the consumer and the prices of the goods stay the same.

The effect of the income change on the consumption choice depends on what kind of goods you are dealing with;

• A normal good is a good for which consumption rises when income rises.

Assume a case in which both goods are normal. An increase in income will shift the budget constraint outward to BC₂.

Both goods are normal and thus the quantity of both goods will increase when income rises. The new utility maximizing bundle is at point B.

• An inferior good is a good for which consumption decreases when income rises.

Assume a case in which one good is normal, good X, and the other good is inferior, good Y. An increase in income will again lead to an outward shift of the budget constraint to BC₂.

Good X is a normal good and the quantity of it will thus rise when income rises, but the quantity of good Y will decrease because it is an inferior good.

We can further distinguish between different goods by looking at differences between the income elasticities. The income elasticity is given by:

E^D_I = %ΔQ^D / %ΔI = (ΔQ^D / ΔI) x (I / Q^D)

We can now distinguish between two types of goods:

• A necessity good is a good for which the income elasticity is between 0 and 1. This means that the quantity consumed of this good rises with income, but at a slow rate.

• A luxury good is a good with an income elasticity greater than 1. The fraction of income spent on these kinds of goods increases when income rises.

We have learned that t he utility maximizing points are located where the budget constraint is tangent to the utility function. If we draw a line starting in the origin, through all these utility maximizing points we get the income expansion path. It is an upward sloping line for two normal goods and it can be negative sloping when one good is inferior and the other is normal. The curve can be straight or can have curves.

Although the income expansion path is a useful tool to examine consumer behavior, it has two weaknesses:

• A graph has only two axes and therefore it is only possible to look at two goods at a time.

• From the expansion path we cannot directly see what the corresponding income is at each point.

Because of these weaknesses it is useful to derive a graph in which consumer’s income is plotted against the quantity of a good consumed. The curve that we obtain from this is called the Engel curve. An example of an Engel curve:

This curve shows the quantity of a good consumed at each income level. We put the quantity of the good consumed on the horizontal axis and the consumer’s income on the vertical axis. The Engel curve is usually a curve with a lot of curves.

Changes in the price

So far we analyzed how a consumer’s behavior changes when income changes, holding prices and preferences constant. We will no look at what happens to consumers' behavior when prices change, holding income, preferences and the prices of other goods constant. This analysis will tell us exactly where a demand curve comes from.

To get to a consumer’s individual demand curve we first start with looking at the utility maximizing consumption bundle of a good for a specific price. We obtain the specific quantity demanded that goes with this price.

We can repeat this step for different prices thus leading to multiple quantity-price points. These points together form the individual demand curve of that specific good.

The individual demand curve will shift when there are changes in the consumer’s preferences, income or the prices of other goods. If for instance a consumer’s preference for a specific good decreases, this consumer will buy less of that good. This leads to an inward shift of the demand curve.

Substitution and income effects

The change of a goods' price has two effects on an individual’s demand:

• Substitution effect: The change in a consumer’s consumption choice (quantity demanded) resulting from a change in the relative prices of two goods. When the price of one good is relatively cheap compared to the price of the other good, then consumers will buy more of the relatively cheaper good.

• Income effect: The change in a consumer’s consumption choice (quantity demanded) resulting from a change in the purchasing power of the consumer’s income. When the price of a good changes, the purchasing power of the consumer has changed. With the purchasing power we refer to the amount of goods the consumer can buy with a given dollar-level of expenditure.

Every change in quantity demanded due to a price change can be decomposed into these two effects. However, it is hard to distinguish between the income and substitution effect. The overall change in quantity demanded is called the total effect.

Total effect = Substitution effect + Income effect

We will first take a closer look at the substitution effect. The bundle the consumer consumes after the price change must provide him with the same utility as he received before. So the new bundle must be on the initial indifference curve U₁.

When the relative prices of a good change the budget constraint shifts. We assume here that those new relative prices are captured in the new budget constraint BC_2. We now have a problem because there is no tangency point between U₁ and BC₂. See the graph on the next page.

However, there is a tangency point with the budget constraint BC’, which is parallel to the consumer’s new budget constraint BC₂. This new tangency point of is point A’. The change from bundle A to A’ is the substitution effect.

The size of the substitution effect depends on how curved the indifference curve is. A highly curved indifference curve means that the MRS changes fast along the curve. A flat indifference curve means that the MRS does not change fast along the curve. A flat indifference curve results in a larger substitution effect than a highly curved indifference curve.

We will now take a closer look at the income effect. The income effect is the change in quantity resulting from a change in purchasing power after the price change. Before the price change, all bundles above BC₁ were infeasible. After the price change only bundles above BC₂ are infeasible.

When relative prices decrease, the consumer’s income left to spend on other goods will increase. The consumer can now afford a larger bundle than before, giving him a higher level of utility. The change from bundle A’ to B is the income effect.

The size of the income effect depends on the quantity of each good a consumer purchases before the price change. The more the consumer was spending on the good before the price change, the greater the effect on the consumer’s budget. When the price of a good that the consumer purchases a lot decreases, he will have a higher income left for other goods to purchase.

This graph shows the backward-bending labor supply:

The income effect is dominant for wages above ω*. In this case the curve will be a backward-bending supply curve. This is because laborers then choose to consume more leisure and work fewer hours. The substitution effect is dominant when the wage is below ω*. The supply curve is then upward sloping.

So far we looked at the income and substitution effect between two normal goods. What will happen when one of the goods is inferior? When the budget constraint changes due to price changes, the consumer changes its preferences for the inferior good. This leads to a shift in his utility curve to U₂.

A giffen good is a good for which the price and quantity demanded are positively related. The demand curves of giffen goods are upward sloping. The more expensive the good is, the higher the quantity demanded.

The substitution effect of a giffen good is smaller than the reduction in desired quantity caused by the income effect. When the relative price of the giffen good decreases this leads to a decrease in quantity demanded. Therefore, the total effect on quantity demanded of the giffen good will be negative.

Complements and substitutes

We will now focus on the effects of a change in a goods' price on the quantity demanded of the other goods.

A characteristic of substitutes is that when the quantity demanded of one good rises, the price of the other good will rise. Thus the quantity of a good moves in the same direction as the price of the other good. Goods can be better substituted when they are more alike.

When the price of a substitute rises, the demand rises. For instance, when the price of good Y doubles, the consumer’s budget constraint will move inwards. This leads to the new budget constraint BC₂.

As a result of this shift in the BC, the consumer will change his utility function. When we look at the new utility maximizing point we see that the quantity of good Y has fallen and that the quantity of good X has risen.

Complements are goods that are purchased in combination with another good. In this case, the quantity demanded of a good moves in the opposite direction as the price of the other good. When the price of a complement rises, the demand falls.

On the next page one can see graph describing this situation.

When the price of good Y rises, the consumer’s budget constraint will shift inward from BC₁ to BC₂. The consumer’s utility function will change due to this, to U₂. When we look at the new utility maximizing point we see that the demand for both goods X and Y has fallen.

Market demand

It is more useful to know the combined demand of all consumers instead of one consumer’s demand. The market demand is the sum of all the individual demand curves. So the market quantity at a specific price is the sum of all the individual demands at that price.

There are a few things we can notice about the market demand curve:

• It will always be to the right of any individual demand curve because all consumers’ demands combined must at least be as much as the demand of that individual.

• The slope of the curve will always be flat or flatter than the individual demand curve.

• When the price is so high that only one consumer wants the good, then the individual demand curve lies directly on top of the market demand curve at that price.

Assume we have the following two individual demand curves:

Q₁ = 5 – 0.05P and Q₂ = 13 – 0.25P

We find the market demand curve by adding these two curves:

Q_m = (5 – 0.05P) + (13 – 0.25P) = 18 – 0.3P

One important thing to note is that you also have to look at the demand choke price of both individuals.

Chapter 6: Producer behavior

The basics

Production is the process by which a person, company, government, or non-profit agency creates a good or service that others are willing to pay for.

Production can have many forms. Some producers make final goods; goods that are bought by the consumer. Other producers make intermediate goods; goods that are inputs used to produce another good.

To build a simple model we first have to introduce the production function. This is a mathematical relationship that describes how much output can be made from different combinations of inputs.

In practice, production is a very complicated process. To better understand the production behavior model we will make the following assumptions:

• The firm produces a single good.

This is because if the firm sells many products it is very complicated to determine the decisions it makes about each product.

• The firm has already chosen which product to produce.

We will only look at how it can be done most efficiently.

• The firm’s goal is to minimize the cost of producing whatever quantity it chooses to make.

In practice most firms act this way so it is reasonable to assume that this is the same in our model. Besides that, cost minimization is necessary if a firm wants to maximize its profits. However, sometimes in real life there are limits to firm’s abilities to minimize costs.

• The firm uses only two inputs in making its product: capital and labor.

Labor refers to all human resources and capital refers to buildings, machinery and raw materials needed for the production of the product. In the model, all different kinds of labor and capital are named under one single label.

• In the short run, a firm can choose to employ as much or as little labor as it wants, but it cannot rapidly change how much capital it uses. In the long run, the firm can freely choose the amounts of labor and capital it employs.

This is because it takes time to put capital into use.

• The more inputs the firm uses, the more output it makes.

It is logical that the more labor and capital input the firm uses, the more output can be produced.

• A firm’s production exhibits diminishing marginal returns to labor and capital.

This means that each additional worker generates less output than the one before, keeping the amount of capital constant. The same holds for output, keeping the labor amount constant. Therefore it is more productive to use a combination of labor and capital in your production instead of labor or capital alone.

• The firm can buy as many capital or labor inputs as it wants at fixed prices.

Before we assumed that consumers could buy as much as they wanted at a fixed price. Similar we can assume that producers can buy as many capital and labor as they want at a fixed price.

• If there is a well-functioning capital market (banks and investors), the firm does not have a budget constraint.

The firm will be able to obtain enough resources to acquire the labor and capital needed as long as they can make profits. When the firm does not have the necessary cash, it can raise funds by issuing stock or by borrowing. Investors are willing to finance as long as there are expected profits.

A firm has to turn the capital and labor units into output. Which combination of inputs can be used for an amount of output is described by the production function:

Q = f (K,L)

A production function can take two forms:

• It can take for instance the form Q = αK + βL. In this form the inputs are separated.

• Or it can take the form Q = K^αL^1-α. In this form the inputs are multiplied together. It is known as the Cobb-Douglas production function. α has a value between 0 and 1. This is the most common production function used by economists.

The short run

The short run is easier to understand than the long run so therefore we start with the short run analysis.

We will work with the following Cobb-Douglas production function:

Q = K^0.5L^0.5

Because in the short run capital is fixed we get the following function with a fixed amount of capital (Ǩ) of 4 units: Q = f (Ǩ, L).= K^0.5L^0.5 = 4^0.5L^0.5 = 2L^0.5. With this production function, a firm that uses zero units of labor will produce zero units of output.

The marginal product is the additional output that a firm can produce by using an additional unit of an input, holding use of the other input constant. Capital is fixed in the short run so therefore we will only look at the marginal product of labor.

The marginal product of labor (MP_L) is the change in quantity (ΔQ) resulting from a one-unit change in labor inputs (ΔL):

MP_L = ΔQ / ΔL

The diminishing marginal product is the reduction in the extra output obtained from adding more and more units of input. As a firm hires additional units of a given input, the marginal product of that input falls.

Because of the diminishing marginal product of labor, the production function curve is flatter at higher quantities of labor. The curve is upward sloping because an increase in labor increases output. As we move along the curve the slope becomes flatter. One can see an example of a short-run production function on the next page.

One thing to note is that diminishing marginal returns do not have to occur the entire time, they just need to occur eventually.

Besides plotting output against labor, we can also plot the marginal product of labor against labor. The slope of the short run production function is ΔQ / ΔL and therefore the MP_L is the slope of the production function at any given level. The slope of the production function declines when we move along the curve. This leads to a downward sloping marginal product curve;

We can rewrite the equation for the marginal product of labor:

MP_L = ΔQ / ΔL = (f (Ǩ, L + ΔL) – f (Ǩ,L)) / ΔL

If we apply this for our short run production function 2L^0.5, we get:

MP_L = (2 (L + ΔL)^0.5 - 2L^0.5) / ΔL

The average product is the quantity of output produced per unit of input. It is calculated by dividing the total quantity output by the number of inputs used to produce that quantity. The average product of labor falls as labor inputs increase.

AP_L = Q / L

The long run

In the long run firms can also change their level of capital input. This has two important benefits:

• The firm might be able to decrease the incentive of the diminishing marginal product. When capital was fixed, the firm was limited in production due to diminishing marginal product. Capital can make each unit of labor more productive.

• Producers can have the ability to substitute capital for labor and vice versa. The production methods of firms can be more flexible and they can better respond to changes in relative prices of capital and labor.

Because now both labor and capital inputs can be chosen we have the Cobb-Douglas production function: Q = f (K,L) = K^0.5L^0.5. For any given level of capital, labor has a diminishing marginal product.

Cost-minimization problem

One assumption we made about the production behavior is that the firm’s goal is cost-minimization. Cost-minimization is a firm’s goal of producing a specific quantity of output at minimum cost. They cannot just minimize cost by refusing the quantity they want to produce.

The firm uses isoquants to solve its constrained minimization problem. An isoquant is a curve representing all the combinations of inputs that allow a firm to make a particular quantity of output. It shows the quantity constraint the firm faces. An example of isoquants:

The more the isoquant is from the origin, the higher the corresponding output level. As we also saw with indifference curves, the isoquants can never cross and are convex to the origin.

The negative of the slope of the isoquant is called the marginal rate of technical substitution (MRTS_XY). It is the rate at which the firms can trade input X for input Y, holding output constant. In other words, it is the quantity change in X that is necessary to keep output constant when the input Y changes.

The total change in quantity must equal zero:

ΔQ = MP_L x ΔL + MP_K x ΔK = 0

We can rearrange this formula to get the slope of the isoquant:

MRTS_LK = - ΔK / ΔL = MP_L / MP_K

The MRTS gives you the relative products of capital and labor at any point. The MRS and MRTS are closely tied together; they are both about marginal trade offs.

How easily firms can substitute one input for another tells us something about how curved the isoquant is. When the inputs are close substitutes (see graph a), the MRTS_LK does not change much along the curve. This means that the isoquant is relatively straight.

When inputs are not close substitutes (see graph b), the MRTS_LK varies greatly along the curve. This means that the isoquant is relatively curved.

The isoquants for the extreme cases of perfect substitutes and perfect complements look different. The isoquants for perfect substitutes are straight lines and the isoquants for perfect complements are L-shaped right angles.

The slope, MRTS_LK, of the isoquant for perfect substitutes does not change along the curve.

So far we have talked about the quantity and input choices of a firm but we have not yet discussed the cost choices. A key concept in this is the firm’s isocost line.

The isocost line is a curve that shows all of the input combinations that yield the same cost. Isocost lines are straight downward sloping lines. See the graph on the next page for some examples of isocost lines.

When we move further from the origin, the isocost lines represent a higher level of costs. The mathematical expression for the isocost line is:

C = RK + WL

With:

• R is the price per unit of capital, the rental rate. Can also be considered the user cost of capital.

• K is the number of capital units

• W is the price per unit of labor, the wage.

• L is the number of capital units

We can rewrite this equation into:

K = (C/R) – (W/R) L

From this new equation one can see that the slope of the isocost line is – W/R.

When relative prices change this will have an effect on the isocost line. When for instance the price of labor increases, the slope of the isocost line will increase. This means that the isocost line will become steeper than before. This is an example of such a change:

The isocost line rotates. We can see in the graph that the intersect with the vertical axis, capital, remains the same but that the intersect with the horizontal axis, labor, has moved to the left. So less labor units are used now because of the increased price of labor.

If the price of capital changes, the slope will decrease and the isocost line will become flatter. The curve rotates in the opposite direction than with a labor price increase.

To minimize its cost, a firm must choose the capital and labor inputs to minimize the expenditures. The firm will come to a conclusion about how to optimally produce the quantity by looking at graphs. We will look at the combined graph of isoquants and isocost lines.

The firm wants to produce the quantity Q = Q. The cost-minimizing point is where the isoquant is tangent to the isocost line. In this graph both point A and B are possible combinations for the firm. However, the cost-minimizing point is represented by point B because this point lies on a lower isocost line.

This point implies that the slope of the isocost line must be equal to the slope of the isoquant:

- W/R = - MP_L / MP_K or W/R = MP_L / MP_K

We can rearrange this condition into:

MP_K / R = MP_L / W

When input prices change, this will lead to a change in the cost-minimizing point. Assume for instance that the price of labor becomes relatively more expensive. This will lead to a shift in the isocost line, it will become steeper. The cost-minimization point will shift in the direction of capital, with a lower labor to capital ratio than before.

The contrary happens if capital becomes relatively more expensive. Then the isocost line becomes flatter. This leads to a cost-minimizing point more to the direction of labor, with a higher labor to capital ratio than before.

Returns to scale

Returns to scale is a change in the amount of output in response to a proportional increase or decrease in all of the inputs.

A production function is said to have constant returns to scale if changing the amount of capital and labor by some multiple changes the quantity of output by exactly that same multiple. The Cobb-Douglas production function, Q = K^0.5L^0.5, we use has constant returns to scale.

We speak of increasing returns to scale if we have a production function for which changing all inputs by some multiple changes output more than that multiple.

Finally, we have decreasing returns to scale. We speak of this when we have a production function for which changing all inputs by some multiple changes output less than that multiple.

We have to note that there is a difference between marginal products and returns to scale. Marginal products refer to changes in only one input while holding the other input constant. Returns to scale refers to changes in all inputs at the same time.

There are some aspects of production technology that determine the returns to scale of a production function. In some ways, it is just natural for a production function to have constant returns to scale.

Some influences that can lead to increasing returns to scale:

• Fixed costs

A fixed cost is an input cost that does not vary with the amount of output. These costs are even present when output is zero. These costs will remain the same no matter what quantity is produced. So the firm is able to double its output without doubling its inputs.

• Learning by doing

Learning by doing is the process by which a firm becomes more efficient at production as it produces more output. So when the firm will produce more and more of a good it will become more efficient in production. Because of this increased efficiency, the firm is able to double its output without doubling its inputs.

An influence that can lead to decreasing returns to scale is regulatory burden. In some businesses there are a lot of rules and regulations that a firm has to cope with when it wants to expand. These rules and regulations lead to higher costs when expanding. Therefore the fraction increase in inputs must be higher than the wanted fraction increase in output.

Change in technology

Economists have found data where the output rises over time while the amount of inputs has not changed. This change in output must be due to total factor productivity growth, also called technological change.

Total factor productivity growth is referred to as an improvement in technology that changes the firm’s production function such that more output is obtained from the same amount of inputs.

To adjust the production function for technological change, we have to assume that the technological change (A) is a constant that multiplies output:

Q = A f (K, L)

This adjustment of the production function does not affect the isocost lines. However, it does change the isoquants because a higher level of output is achieved with the same level of inputs. A high value of A shifts the isoquants toward the origin.

A durable good is a good that has a long service life.

Expansion path and total cost

The expansion path is the curve that illustrates how the optimal mix of inputs varies with total output. The expansion path starts from the origin and goes through all the cost minimizing points.

The expansion path can be a straight or a curved line.

We can plot the total cost from the isocost line and the output quantity from the isoquants located along the expansion path. If we do this we get the total cost curve. This curve shows a firm’s cost of producing particular quantities.

Chapter 7: Different types of costs

Opportunity costs

Accounting costs are the direct cost of operating a business, including costs for raw materials.

Opportunity cost is the value of what a producer gives up by using an input. If the firm uses the input for one thing it gives up the ability to use it for something else.

The sum of accounting and opportunity cost is called the economic cost. This is the cost where economists pay attention to.

Decisions are based on economic costs so it is important to see the difference between accounting and economic costs. The firm should consider its economic profit instead of its accounting profit.

Economic profit is a firm’s total revenue minus its economic costs.

Accounting profit is a firm’s total revenue minus its accounting costs.

Sunk costs

We saw before that firms can have fixed costs, costs a firm always has independent of a firm’s output. Some examples are rent, insurance, license fees and advertising expenses. The firm can recover some of these fixed costs by selling or renting these items to other firms. These types of fixed costs are called avoidable because the firm can take action so that it does not have to pay them.

Some fixed costs, however, are not avoidable. These costs are called sunk costs. A sunk cost is a cost that, once paid, can never be recovered by the firm. The difference between fixed and sunk costs is crucial to the decision making of the firm.

Whether the firm’s capital can be used by another firm is a very important determinant of sunk costs. Specific capital is capital that cannot be used outside of its original application.

Once the sunk costs are paid they should not affect the current and future production decisions. They should not affect the relative costs.

When you want to open a new business you know that there will be some potential benefits but you also know that there will be costs. These benefits are called operating revenue, and these costs are called operating costs.

The decision between staying and shutting down only depends on whether a firm’s operating revenues exceed its operating costs. It does not depend on the sunk costs.

When firms, by mistake, do use sunk costs to affect their forward-looking decision, they commit sunk cost fallacy. As a firm you want to avoid fallacies like this.

Cost curves

When analyzing costs we can distinguish between fixed costs (FC) and variable costs. Variable costs (VC) are the costs of inputs that vary with the quantity of the firm’s output. When a firm wants to make more output it needs more input for this. The payment for that input is counted as a variable cost.

The total cost (TC) is the sum of a firm’s fixed and variable costs:

TC = FC + VC

When a firm is unable to determine how much of an input it purchases when output varies, the input costs are fixed. If a firm can easily adjust the level of input used as output varies, the input costs are variable. The key factor in determining the flexibility of input factors is the time span over which the cost analysis is relevant; the time horizon.

Many costs are fixed over short time periods because it is impossible for the firm to adjust input levels in short periods. Firms have a greater flexibility to change inputs over longer time horizons. In these long time spans, costs are variable. There are no long-run fixed costs.

Another factor that can affect the flexibility of input factors is the presence of active capital rental and resale markets. The presence of these markets allows firms to pay for the input just when it is needed to make more output.

A last example of a factor is the labor contract. Some contracts of laborers require a specific amount being paid to the workers regardless of the output. These labor costs are fixed costs. You can also have a contract where the loan is a proportion of the output produced by the firm. In that case the labor costs are variable costs.

To better understand all the different kinds of costs we use cost curves. A cost curve is a mathematical relationship between a firm’s production costs and its output. The cost curves for FC, VC and TC take the following form:

The fixed costs do not change and therefore its cost curve is a horizontal line. The VC cost line is an upward sloping line because the variable costs increase when output increases. The TC cost curve is a sum of the FC and VC cost curves.

Marginal and average costs

We will now introduce two other costs that play a role in the production: average cost and marginal cost.

The average fixed cost (AFC) is a firm’s fixed cost per unit of output.

AFC = FC/Q

The average variable cost (AVC) is a firm’s variable cost per unit of output.

AVC = VC/Q

The average total cost (ATC) is a firm’s total cost per unit of output.

ATC = TC/Q

ATC = AFC + AVC

The AFC, AVC and ATC cost curves have the following form:

The ATC curve is U-shaped and is separated from the AVC by the value of the AFC.

The other cost concept that plays a key role in the production is the marginal cost. The marginal cost is the additional cost of producing an additional unit of output.

MC = ΔTC/ΔQ

Fixed costs do not affect the marginal cost and therefore the marginal cost can also be defined as:

MC = ΔVC/ΔQ

The MC cost curve is, just like the ATC curve, U-shaped. Marginal cost decreases in the begin and then increases at higher levels of output. The marginal cost is the cost that matters to a firm in decision making.

There is a direct relationship between average and marginal cost. When MC is less than AC, producing an additional output will reduce the average cost. This is because the cost of an extra unit is less than the average cost of making all the units before.

This means that if the MC curve is below the AC curve, the AC must be falling. The AC curve will be falling until the point where it is equal to the MC. From that point on the MC will be larger than the AC and thus the AC curve will be rising.

The marginal cost curve crosses the average total cost curve and the average variable cost curve at their minimum points.

On the next page one can see this in a graphical way.

Different cost curves

In the long run a firm has more flexibility in shifting input levels due to changes in output. This is because capital fixed in the short run and flexible in the long run. This leads to the fact that costs are more flexible in the long run.

A firm’s short-run total cost curve is the mathematical representation of a firm’s total cost of producing different quantities of output at a fixed level of capital. Just as with the cost curves before we can draw an expansion path through all the cost-minimizing points.

The expansion path for the short run will be a horizontal line at K=Ǩ; the fixed level of capital. The long run expansion path is the same as the one we saw before; there are no fixed levels of inputs.

When we compare total cost curves in the short and long run we see that for every quantity the total cost curve in the short run is higher than the total cost curve in the long run. However, there is one point where the curves touch each other. This is the point where capital is at the cost minimizing capital level.

We can also compare average total cost curves in the short and long run. The short run average total cost is higher than the long run average total cost. This means that the U-shaped average total cost curve of the long run is wider than the one of the short one. We can see this in the following graph:

One can see that the ATC curve for the short run lies inside the ATC curve for the long run.

Just as the total and average cost curves differ between the short and long run, so do marginal cost curves. The short run MC curves are steep upward sloping curves and go through the minimum points of the corresponding ATC curves.

The long run MC curve will intersect with the short run MC curve at the points at which labor is cost minimizing. It will also intersect the long run ATC curve at its minimum point. The long run MC curve is much flatter than the short run MC curve.

The production process

Just as we have returns to scale we also have economies of scale. Economies of scale are when the total costs rise at a slower rate than output rises. This means that when output doubles, costs are less than doubled. This also implies that the long run ATC falls as output grows and thus the long run ATC is downward sloping.

Dis economies of scale are when total cost rise at a faster rate than output rises. This means that when output doubles, the costs are more than doubled.

Constant economies of scale are when total cost rise at the same rate as output rises. This means that when output doubles, the costs are also doubled.

Although returns to scale and economies to scale are related, they are not the same. Returns to scale are about the change in output when inputs are increased by a factor. This imposes constant input ratios. Economies of scale are about costs and output and it does not impose constant input ratios as returns to scale does.

Economies of scope indicate how the costs of a firm change when they make more than one product. It exists when a producer can simultaneously produce multiple products at a lower cost than if the firm made each product separately. We can use a formula called SCOPE to compare economies of scope.

SCOPE = (TC(Q₁,0) + TC(0,Q₂) – TC(Q₁, Q₂)) / TC(Q₁, Q₂)

Where:

• TC(Q₁,0) stands for the total cost of single-production 1.

• TC(0,Q₂) stands for the total cost of single-production 2.

• TC(Q₁, Q₂) stands for the total cost of joint production.

If SCOPE > 0, the total cost of joint production is less than making the goods separately. In that case there are economies of scope. The larger SCOPE, the larger the cost saving from making multiple products.

If SCOPE < 0, it is cheaper to produce Q₁ and Q₂ separately. In this case there are dis economies of scope; the simultaneous production of multiple products at a higher cost than if a firm made each product separately.

Chapter 8: A competitive market

Market structures

In this chapter we will primarily focus on perfect competition. Perfect competition is a market with many firms producing identical products and no barriers to entry. We will analyze how firms behave in perfect competition to maximize their profits.

To understand how firms behave we have to look at the competitive environment in which it operates, also called the market structure. We can distinguish between four different types of markets; perfect competition, monopolistic competition, oligopoly and monopoly.

On basis of the following three characteristics we can make a distinction between those four markets:

• Number of firms. The more firms in the market, the more competitive it is.

• Whether the consumer cares which company made the good. The more distinguishable a product is, the more competitive the market is.

• Barriers to entry. The easier it is to entry the market, the more competitive it is.

A truly perfect competition is rare in practice but in theory it is very useful to explain some things. Therefore we will first focus on this type of market.

As we stated before, a market of perfect competition must have many firms, identical products and no barriers to entry. There must be many firms so that the effect of a change in price of output of one firm has a very small impact on the market equilibrium.

With identical products we mean that the consumer must view all goods as perfect substitutes; that the consumers do not care which producer made the good. Finally it is very important that there are no barriers to entry; that firms can come and leave when they want.

There are several reasons why we use a perfect competitive market for the study of market behavior:

• A perfectly competitive firm is a price taker; it takes the price as given. It must sell at the price that is dictated by supply and demand forces in the market. They only have to decide about how to maximize profits at their wanted quantity.

• There are some perfectly competitive markets in the real world so it is useful to know how such markets work.

• Many markets are close to perfectly competitive and learning how a perfectly competitive market works helps us to understand how these markets work.

• Perfectly competitive markets are the most efficient markets there are. Economists use these markets to compare the efficiency of other markets.

Profit maximization

We almost always assume that firms choose their actions to maximize profits. Profit is the difference between a firm’s revenue and its total cost. The firm chooses an output level at which the profit is the highest. The mathematical equation for profit (π), with total revenue (TR) is:

π = TR – TC

Just as we have marginal cost we also have marginal revenue. Marginal revenue is the additional revenue from selling one additional unit of output.

MR = ΔTR/ΔQ

In a perfectly competitive market, marginal revenue is equal to the market price;

MR=P

The marginal revenue curve is a horizontal line at the height of the market price. Firms are price takers in a perfectly competitive market and therefore the price will not change. If the output increases by one unit, the revenue increases by the marginal revenue which in this case is equal to the price. This leads to a total revenue curve that is a straight line.

When the market price is less than the marginal cost, it is not profitable for a firm to make the extra unit of output. The profit-maximizing level in a perfectly competitive market is found where the marginal revenue equals marginal cost:

MR = P = MC

Point A is the profit-maximizing point for the firm. The firm should increase production as long as MR = P > MC. It should decrease production if MR = P < MC. The fact that the marginal revenue is equal to the price of a firm in a perfect competition makes the output decision relatively easy for the firm.

There are exceptions of firms where the main goal is not to maximize profits. This can be because the CEO is acting in self-interest and not in the interest of the firm. However, the perfect competition market pushes firms to maximize profits so we can assume that in the end all firms will maximize profits.

We can rewrite the profit equation:

π = TR – TC = (P x Q) – (ATC x Q) = (P – ATC) x Q

Now we have rewritten the profit equation we can determine the profit in a graph with ATC, MR and MC curves. We find the profit-maximizing quantity, Q*, where MR=MC. If we go down from the profit-maximizing point to the ATC curve, we find the corresponding ATC* level.

The shaded area in the graph on the next page is the profit to the firm. In this case π > 0 because P > ATC*. When P = ATC*, the firm will make zero profit. When P < ATC*, the firm will make a loss.

When a firm makes zero profit it has to decide whether it is better to operate at a loss or to shut down and not producing anything. This depends on the revenues and costs of a firm.

When the firm decides to shut down it has some costs. We can calculate the ‘profit’ of shutting down with the following formula:

π_{shut down} = TR – TC = TR – (FC + VC) = 0 – (FC + 0) = - FC

So the cost of shutting down is equal to FC.

When the firm decides to operate at a loss it will make some revenue but it also has to pay fixed and variable costs. The profits of operating at a loss are:

π_operate = TR – TC = TR – FC – VC

We can also look at the difference between the profit of shutting down and the profit of operating at a loss;

π_operate - π_{shut down} = TR – FC – VC – (- FC) = TR – VC

From this we can conclude that in the short-run a firm should:

• Operate as long as TR > VC

• Shut down if TR < VC

Fixed costs do not affect the decision because they have to be paid whether the firm operates or not.

We can rewrite the rules above in terms of the market price, P, and average variable cost, AVC*:

• Operate as longs as P > AVC*

• Shut down if P < AVC*

These last rules apply to all firms in all industries in any type of market structure.

The short run

Now we have determined the profit-maximizing point of a perfectly competitive firm we can derive the short-run supply curve for that firm. The supply curve shows the supply at each price. The short-run supply curve must be the marginal cost curve because the firm chooses to produce where P = MC.

The short-run supply curve is the proportion of the marginal cost curve above the AVC because a firm will only operate when P > AVC. Otherwise it shuts down and the quantity supplied is then zero.

We know now the individual short-run supply curve of a firm. The combined decisions of all the firms together form the industry supply curve. The industry supply curve is the horizontal sum of all the individual firms’ supply curves. This curve shows that output increases when the price increases.

The intersection of the industry supply curve and the market demand curve gives us the equilibrium price and quantity. Demand is in the short-run equal to MR. The firm maximizes profits at Q*. For all the units of Q* the MC < P. Therefore, the firm earns a markup for each of these units.

Adding up all the price-marginal cost markups gives us the producer surplus of the firm. In the graph this is the area below the demand curve and above the MC curve.

We can also calculate the producer surplus by subtracting variable costs from total revenue.

PS = TR – VC

The rectangle P X Q* is the total revenue for the firm and the rectangle AVC* x Q* is the variable cost for the firm. To find the producer surplus we have to subtract the variable cost rectangle from the total revenue rectangle. This leads to the shaded area in the graph; the rectangle with height (P – AVC*) and length Q*.

Profit and producer surplus are closely related but they are not the same. A firm can operate while making less than zero profit but it will never operate with a producer surplus that is less than zero. This is because that would mean that each unit costs more to produce than it sells for.

The industry producer surplus is the surplus for the entire industry. It is represented by the shaded area in the graph; the area below the market price but above the short-run supply curve.

The long run

The long-run supply curve is different from the short-run supply curve. In the short run, a firm produces where its short-run marginal cost equals the market price. In the long run, a firm produces where its long-run marginal cost equals the market price. The long-run supply curve is the proportion of the MC curve that is above the average total cost curve. Remind that in the long run LATC = LAVC because there are no fixed costs.

Another difference between the long and short run is that in the short run the number of firms is fixed while in the long run firms can freely enter and exit the market. Firms may leave or enter due to changes in profitability.

Free entry is the ability of a firm to enter an industry without encountering legal or technical barriers. It does not mean that the firm is also free in monetary sense; the firm may need to pay some start up costs. When there is free entry in an industry, the market price will fall until it equals the minimum average total cost.

Free entry has an effect on the industry supply curve. When firms enter the market the short-run supply curve will shift outward from S₁ to S₂.

This leads to a reduction in the market price from P₁ to P₂. New entrants will keep pushing down the price. This will continue until the market price is equal to the minimum average total cost. At that point there will be no profits and firms are then indifferent between entering the industry and staying out. This will stop the entry of firms and then the market is in long-run competitive equilibrium.

If the market price is below the minimum average total cost firms will not enter the market because they would earn negative profits. Firms that are already in the market make negative profits. If there is free exit, firms may shut down and leave the industry. Free exit is the ability of a firm to exit an industry without encountering legal or technical barriers.

The exit of firms shifts the industry supply curve inward. This leads to an increase in the market price. Exit continues until the market price is equal to the minimum average total cost. At that point firms will stop exiting the market.

One thing to note is that the long-run industry supply curve is horizontal at the long-run minimum average total cost, while the short-run industry supply curve is upward sloping.

In reality, it can take a long time to get to the long-run equilibrium.

Suppose that we are in a long-run equilibrium and that suddenly the demand increases due to a change in consumers’ taste. This change shifts the demand curve outward/to the right. The short-run response to this is an increase in the equilibrium output and price.

The price is now above the minimum average total cost and there is a positive profit. The positive profit will attract firms and therefore firms will enter the market. The increase in supply shifts the supply curve outward. This raises output and decreases the market price.

This entry continues until the market price is equal to the minimum average total cost. In the end the price will be unchanged but the output has risen. In the graphs beneath we can see the industry adjustments of price and quantity over time due to the change in demand:

Now suppose that the costs of all firms in the industry will decrease. This will lead to lower MC for all firms resulting in higher supply for each firm. Due to this the industry short-run supply curve will shift out. The minimum average cost curve will shift down. The original price will be above a firm’s average total cost.

When supply shifts out, the market price will fall and quantity will increase. This continues until the market price is equal to the new LATC. In this case the price drop is permanent. Quantity has increased:

So far we assumed that the industry is a constant-cots industry. This is an industry whose firms’ total costs do not change with total industry output.

However, this may not always be the case. It can also be an increasing-cost industry. That is an industry whose firms’ total cost increase with increases in industry output. This means that when output increases, the average total cost of the firm also increases.

Decreasing-cost industries are industries whose firms’ total cost decrease with increase in industry output. This means that when output increases, the average total cost of the firm decreases. It might be due to increasing returns to scale.

Economics profits

In our analysis we assumed that all firms have the same cost functions. However, this is not very realistic. Each firm faces for instant different prices for inputs. The efficient producers in an industry earn a special return called economic rent. Economic rents are returns to specialized inputs above what firms paid for them.

Firms with higher costs only produce when the market price is high. Because firms have different cost curves, they also have other profit-maximizing outputs. The more the MC curve is located to the left, the higher the marginal cost of the firm. Higher cost firms produce less than low-cost firms. This indicates a negative relationship between a firm’s costs and its size.

In a perfect competitive market where firms have different costs, the long-run market price is equal to the minimum average total cost of the highest cost firm in the industry. That firm has minimum average total costs that are above the market price and thus makes zero producer surplus and zero profit. The other firms in the market have minimum average total costs below the market price and thus make a profit.

Note that economic profit and economic rent are not the same. Economic rent is included in the opportunity cost for inputs that earn them, and economic profit measures inputs’ opportunity costs.

Chapter 9: Market power

Sources

We will now look at a situation in which a firm has some influence on the price of its products. If a firm has this ability it is said to have market power. The most extreme version of market power is a monopoly. A monopoly is a market served by only one firm. The sole supplier and thus price setter of this market is called the monopolist.

In some markets there are only a few firms operating. These firms all have substantial market power. Firms with market power can earn producer surplus and profit in a way that is impossible for competitive firms.

Barriers to entry are factors that prevent entry into markets with large producer surpluses that come from market power.

There are several factors that create a barrier to entry:

• A natural monopoly is a market in which it is efficient for a single firm to produce the entire industry output. A natural monopoly is a barrier to entry. The cost curve of a natural monopoly exhibits economies of scale. This means that the LATC is always downward sloping for the firm. The larger the quantity produced, the lower the ATC. It is most efficient that the single firm produces the entire industry supply.

It is hard for new firms to enter in this monopoly because the new firm has to pay some start up costs. The incumbent firm does not face these costs and thus has a cost advantage.

• A second barrier to entry is the presence of consumer switching costs. This means that the consumer has to give up something to switch to the product of a competitor. The consumer can have, for instance, privileges by the incumbent and it gives up these privileges if he switches to another producer. This gives the incumbent firm market power and makes entry for new firms difficult. Switching costs can also come from technology differences.

The most extreme switching costs exist with a network good. A network good is a good whose value to each consumer increases with the number of other consumers consuming the product. In this way each consumer creates a benefit for all the other consumers consuming it. These network goods and economies of scale form together a very strong barrier to entry.

• Even if two goods are substitutes, consumers can have a specific preference for one of the goods. They would even be willing to pay a premium for it. This imperfect substitutability across varieties of products is called product differentiation. This prevents new firms from entering the market and thus creates a barrier to entry.

• Absolute cost advantages or control of key inputs is another barrier to entry. If the firm has control over a key input it has a special input that other firms do not have. This control over the input allows the firm to have lower cost than the cost of competitors. It is difficult for other firms to take some production away from this low-cost producing firm.

• Government regulation is the final barrier to entry. A government can have regulations that make it impossible for new firms to enter the market.

Marginal revenue

Even if a firm is not a monopolist, it almost always has some form of market power. Its demand curve can slope downward, just as the monopolist’s demand curve.

Two other common types of market structure are:

• Oligopoly: A market structure in which a few competitors operate.

• Monopolistic competition: A market structure with a large number of firms selling differentiated products.

In these two types of markets, the demand curve that a firm faces depends on the supply decisions of all other firms. We will now analyze how firms in these two markets behave.

A firm with market power faces a downward sloping demand curve and thus it can only sell more by reducing the price. This means that the marginal revenue will decrease as output rises. Total revenue will first increase and then decrease. We will see that firms with market power will restrict output to keep prices high. One important thing to note is that the firm cannot charge different prices to different consumers.

For a perfectly competitive firm we saw that MR = P. This does not hold for a firm with market power, the MR is not equal to the price.

The firm’s revenue at P₁ and Q₁ is equal to the area A + B. When the firm decides to increase its output from Q₁ to Q₂, the price will fall from P₁ to P₂.

The new revenue will equal area B + C. The firm’s marginal revenue is equal to area;

MR = (B + C) – (A + B) = C – A

We can compute a formula for the firm’s marginal cost:

MR = P + (ΔP/ΔQ) x Q

Before we learned that the inverse demand curve is P = a – bQ. We also saw that for any linear demand curve of this form with constants a and b, that ΔP/ΔQ= -b. If we substitute these two things into our MR equation we come to an expression for the marginal revenue for each demand curve.

MR = (a – bQ) + (-b)Q = a – 2bQ

The only difference between the demand and the marginal revenue curve is that with marginal revenue bQ is replaced with 2bQ. This means that the marginal revenue curve is twice as steep as the demand curve.

Profit maximization

When we look at profit maximizing for a firm with market power we base this on the same thing as with a perfect competitive firm. However, marginal revenue is not equal to the market price in this case. The firm with market power maximizes profit where;

MR = MC

If MR > MC, a firm can produce more and increase its profits. If MR < MC, a firm can reduce output and lose less revenue than it loses costs. This leads to an increase in profits.

If we have a demand curve and we want to show graphically where the profit-maximizing point is, we first have to derive the MR curve. The MR curve starts at the same place on the vertical axis as the demand curve but is twice as steep. This means that it will cross the horizontal axis at half the quantity of the demand intersection with the horizontal axis.

When we have derived the demand curve we can find the profit-maximizing point in the graph where MR = MC. If we go from this intersect up to the demand curve we can find the optimal price level. So the profit-maximizing price is P* and optimal quantity is Q*.

We will now provide a mathematical approach. Assume the demand curve is given by:

Q = 200 – 0.2 P

To find the marginal revenue curve we first have to derive the inverse demand curve and then multiply the slope by 2:

P = 1,000 – 5Q

MR = 1,000 – 2(5Q) = 1,000 – 10Q

Assume that the marginal cost for this firm is constant at 200. To find the optimal price and quantity we have to calculate MR=MC:

MR = MC

1,000 – 10Q = 200

Q* = 80

We can fill in this optimal quantity in the inverse demand curve to get the optimal price:

P* = 1,000 – 5 x 80 = 600

So this firm maximizes its profits at P* = 600 and Q* = 80.

We can rewrite the rule MR = MC into:

P – MC = - (1 / E^D) x P

or

(P – MC) / P = - (1 / E^D)

With this new formula we can better see the firm’s profit-maximizing markup. The markup is the percentage of the firm’s price that is greater than its marginal cost. It is the left hand side of the last equation above. E^D is the price elasticity of demand in this formula.

This formula shows that when demand is quite inelastic, consumers are not sensitive to changes in the price. This makes it easier for the firm to increase profits by raising the price.

This equation about the firm’s markup or level of market power has a special name: the Lerner index. The Lerner index has always a value between 0 and 1. The firm with the highest Lerner index has the highest market power.

When demand is perfectly elastic E^D = - ∞. In this case the Lerner index is zero, which means that the markup is also zero. On the contrary, when demand is perfectly inelastic, then E^D = 0. In this case the Lerner index and thus the markup is 1. This means that the product’s price is all markup. The corresponding profit-maximizing price will be infinitely high.

Market changes

We now know how firms with market power should maximize their profits. What we do not know yet is how they react to changes in the market. What will changes do to the profit-maximizing price and quantity?

• First we will look at what happens when marginal cost increase.

This increase will shift the MC curve up. We will use the same marginal revenue and demand curves as before. Suppose MC increases from 200(like in the situation used before) to 250. We can now calculate optimal output and price:

MR = MC

1,000 – 10Q = 250

Q* = 75

The optimal price will be: P = 1,000 – 5 x 75 = 625.

Before the change the optimal price and output where, P* = 600 and Q* = 80. We see that as a result of the increase in MC, P* has increased with 25 and Q* has fallen with 5 units. So price is higher and quantity is lower.

• Second we will look at a change in the demand.

Suppose the demand curve shifts outward due to an increase in the demand. This leads to the new inverse demand curve P = 1,400 – 5Q. So the new MR is:

MR = 1,400 – 2(5Q) = 1,400 – 10Q

We suppose that MC is equal to 200, like in the original case. Setting MR = MC gives us:

1,400 – 10Q = 200

Q* = 120

And P* = 1,400 – 5 x 120 = 800

The price has increased with 200, from 600 to 800. The quantity has increased with 40, from 80 to 120. So an outward shift in demand leads to an increase in both optimal price and quantity.

• Finally, we will look at the change in price sensitivity of consumers.

This change of the market will have a different kind of effect on the market than the two changes we saw before. A change in price sensitivity makes the demand curve flatter or steeper. Suppose that the demand becomes more price-sensitive. This leads to a flatter demand curve. Due to this also the MR curve changes. The new optimal price will be lower and the optimal output will be higher.

Consumer and producer surplus

Firms with market power charge a price that is above marginal cost and therefore it is beneficial for firms to have market power. We use producer and consumer surplus to measure this benefit.

Because the firm has market power, it can charge the price it wants. See the next graph. In this case the firm charges price P_m at quantity Q_m. However, the competition price and quantity are represented by P_c and Q_c.

CS (competition) = A + B + C

PS (competition) = 0

CS (market power) = triangle A = 0.5 x base x height = 0.5 x Q_m x (P – P_m)

PS (market power) = rectangle B = base x height = Q_m x (P_m – P_c)

DWL = triangle C = 0.5 x base x height = 0.5 x (Q_c – Q_m) x (P_m – P_c)

So consumer surplus decreases with B + C and producer surplus increases with B. The deadweight loss from the market power is equal to area C.

The size of the producer surplus depends on the elasticity of demand. If demand is less elastic, the demand curve is steep and the producer surplus will be relatively large. If demand is more elastic, the demand curve is flat and the producer surplus will be relatively small.

Government regulation

We have seen that market power creates a deadweight loss. Government intervention can be justified when the regulations can reduce the DWL. A government can intervene in markets in several ways:

• Direct price regulation

When governments think that there are firms with too much market power in the market they will sometimes directly regulate prices. The government allows the firm to operate but it will limit its pricing behavior. Suppose the firm produces at point m.

If the government sets a price cap equal to the firms marginal cost, LMC, then the firm will produce at the perfectly competitive price and quantity. Under this regulation:

CS expands from A to A + B + C

• Antitrust

A government can use an antitrust law. This is a law designed to promote competitive markets by restricting firms from behavior that may limit competition. Sometimes this prevents firms from merging with or acquiring other firms. Governments can investigate whether a firm is a fair monopolist in an industry.

The downside of this intervention is that there are large potential costs and uncertainties involved.

• Promoting monopoly: patents, licenses and copyrights

Instead of limiting market power, a government can also encourage monopolies. They can do this by using patents, licenses, copyrights, trademarks and other legal rights to exercise market power. A government can do this for instance for a medicine because it is very important that there is enough supply of it and that it is made correctly. A monopoly can be beneficial in such a case.

A patent can lead to innovation because other firms will need to come up with another technology. If the innovation market is large this can lead to big profits.

The downside of it is that it can lead to very high prices.

When a firm is rent-seeking it attempts to gain government-granted monopoly power and therefore additional producer surplus.

Chapter 14: The general equilibrium

General equilibrium effects

Now we will look at how one market affects other markets. The general equilibrium analysis is the study of market behavior that accounts for cross-market influences and is concerned with conditions present when all markets are simultaneously in equilibrium. General equilibrium holds when all market are in equilibrium. This analysis has two parts:

1. Part one describes the mechanisms of market interactions and how market changes affect the general equilibrium.

2. The second part explains whether an economy-wide market equilibrium is efficient or equitable.

The partial equilibrium analysis is the determination of the equilibrium in a particular market that assumes there are no cross-market spillovers. This analysis is more complicated.

To explain general equilibrium effects we use two industries; the corn and the wheat market.

We assume that there will be a renewable fuel mandate that increases the demand for corn. This shifts the demand curve out and out. This leads to a higher price for corn. Wheat is seen as a substitute good for corn. The increased price of corn leads to an increase in the demand of wheat, shifting the demand cure for wheat out. The shift in demand leads to a higher price of wheat.

Besides analyzing the demand side, we can also analyze the supply side of the market. When two markets use common inputs there are some spillovers between the markets. An increased corn demand leads to a decrease in the supply of wheat because farmers shift some of their production from wheat to corn.

This shifts the supply of wheat inward leading to a fall in quantity and a rise in price. The increase in wheat price has now its effect on the supply of corn. The corn supply will shift inward because the input price for corn has gone up due to the increased price of wheat.

We will now use some specific numbers. Again we will use the industries of corn and wheat. We assume the following:

For wheat: Q^S_w = P_w and Q^d_w = 20 – P_w + P_c

For corn: Q^S_c = P_c and Q^d_c = 20 – P_c + P_w

Corn and wheat are seen as substitutes of each other. Being a substitute of each other is a condition that must be satisfied to have cross-market effects. First we have to derive the partial equilibrium condition that supply must equal demand in both markets:

Q^S_w = Q^d_w

P_w = 20 – P_w + P_c = 10 + (P_c / 2)

We can do the same for corn, this gives:

P_c = 20 – P_c + P_w = 10 + (P_w / 2)

From these two equations we can see that each equilibrium price depends on the price of the other good. To find the price that satisfies both markets we have to substitute the formula

P_c = 10 + (P_w / 2) into P_w = 10 + (P_c / 2). This gives us:

P_w = 10 + ( (10 + (P_w / 2)) / 2)

P_w = 20

Now we know the price of wheat we can substitute it into the equation for the price of corn:

P_c = 10 + 20/2= 20

In this case the price of corn is equal to the price of wheat. This is because the supply and demand curves of the two markets are of the same shape. Note that this is a special case.

When both prices are known we can calculate demand and supply in both markets.

Q^s_w = 20 and Q^d_w = 20 – 20 + 20 = 20

Q^s_c = 20 and Q^d_c = 20 – 20 + 20 = 20

Since the equilibrium lies where Q^S = Q^d, the general equilibrium quantities for wheat and corn are 20.

We look at the case of the renewable fuels mandate. Demand for corn increases because of this by 12. This leads to the following demand curve:

Q^d_c = 32 – P_c + P_w

Now we have derived this new demand curve, we can follow the same steps as before. First we derive the partial equilibrium in both markets and then we can substitute the price of corn into the formula for the price of wheat. This leads to the following results:

P_w = 24 P_c = 28

Q^d_w = 24 Q^d_c = 28

Both wheat and corn prices have gone up in the new general equilibrium. Also the demand of both wheat and corn has gone up.

Social welfare

Economists use a social welfare function to try to think about the overall desirability of market outcomes. The social welfare function is a mathematical function that combines individual’s utility levels into a single measure of society’s total utility level. This makes it possible to compare outcomes of various markets. A common type of welfare function is:

W = u₁ + u₂ + … + u_N

Where W is the value of the social welfare function and all utility levels have the same weight.

The utilitarian social welfare function is a mathematical function that computes society’s welfare as the sum of every individual’s welfare. This function does not pay much attention to how utility is distributed among all individuals.

The Rawlsian social welfare function is a mathematical function that computes society’s welfare as the welfare of the worst-off individual. It calculates the welfare as the minimum of all utilities in society.

The equation for it is:

W = min (u₁, u₂, …, u_N)

This function is an extreme example of an egalitarian welfare function. Egalitarian is the belief that the ideal society is one in which each individual is equally well off.

Social welfare functions can be very useful but they are also very difficult to use. It is difficult to form a conclusion about the outcomes of the function. Because of this difficulty, economists use another tool; Pareto efficiency.

Pareto efficiency is an economic allocation of goods in which the goods cannot be reallocated without making at least one individual worse off. So no one can be made better off without making someone else worse off. It does not have to be fair and does not have to maximize social welfare. It can lead to large differences in utility functions between individuals.

Under a specific set of assumptions about the environment of the market, market outcomes are Pareto-efficient. Markets have a natural tendency to move to these efficient outcomes. In reality, however, we see that there are no markets for which all assumptions hold.

There are three basic conditions that must hold in an efficient economy:

1. Exchange efficiency. There must be a Pareto-efficient allocation of a set of goods across consumers. No one can be made better off without making someone else worse off.

2. Input efficiency. There must be a Pareto-efficient allocation of inputs across producers. Producing a higher quantity of one good means producing a smaller quantity of another good.

3. Output efficiency. There must be a mix of outputs that simultaneously supports exchange and input efficiency. This means that the mix of goods produced in an economy cannot change without making some consumer or producer worse off.

In the next three sub chapters we will take a closer look at these three conditions.

Exchange efficiency

A very useful tool for analyzing market efficiency is the Edgeworth box. The Edgeworth box is a graph of an economy with two economic actors and two goods. In an Edgeworth box we graph the indifference curves of two consumers X and Y of two goods A and B. It is in fact an indifference graph of person X with a rotated indifference curve of person Y. Below one can find an example of an Edgeworth box. The thicker lower and left line are from consumer X and the thinner upper and right line are from consumer Y.

The indifference curves of consumer 1 are represented by U_X and the indifference curves of consumer 2 are represented by U_Y. We can find allocation points where the indifference curves of consumer X and Y intersect.

Point A is an inefficient allocation because any point in the shaded area, including point B, will give both consumer X and Y higher utilities and thus makes them better off.

To find a Pareto-efficient allocation we need to find a point where there is no area between the indifference curves of consumer X and Y. Point C in the next graph is such a point. At this point, the indifference curves of consumer X and Y are tangent to each other.

Thus, at point C:

MRS_AB of consumer X = MRS_AB of consumer Y

This leads to the conclusion that Pareto efficiency in a market implies that:

MRS_AB of consumer X = MRS_AB of consumer Y = P_A / P_B

The consumption contract curve is a curve that shows all possible Pareto-efficient allocations of two goods across two consumers;

Input efficiency

An input can be used to make one product or another, but it cannot be used at the same time for the production of both goods. Therefore, the firm has to choose for which good it will use the input. The analysis of input efficiency is similar to the analysis of exchange efficiency.

The input efficiency allocation is where the isoquants of the producers are tangent to each other. Again we will use an Edgeworth box, but this time we use one about production.

We will look at the two products A and B with inputs labor and capital. The isoquants for good A are represented by Q_A and the isoquants for good B are represented by Q_B.

We can find the input efficient allocations where good A’s isoquant is tangent to good B’s isoquant. This is the case in points C, D and E. At these points:

MRTS_LK of good A = MRTS_LK of good B = MP_L^A / MP_K^A = MP_L^B / MP_K^B = W/R

Where W is the wage rate and R is the rental rate.

The product contract curve is a curve that shows all Pareto-efficient allocations of inputs across producers. It is a curve from origin to origin that goes through all the input efficient allocations.

Now we have the product contract curve we can draw a production possibilities frontier (PPF). This is a curve that connects all possible efficient output combinations of two goods. It shows all the output combinations of good A and B that are made when inputs are allocated efficiently. The next graph shows an example of a PPF.

The points C, D, E and F are all efficient allocations. Point G, however, is an inefficient allocation of inputs. All output that falls outside the PPF is inefficient.

Output efficiency

Output efficiency involves the choice of how many units of each good the economy should make. The PPF that we introduced shows how much output must be given up of one good to get one more unit of the other good. This is also called the marginal rate of transformation (MRT). The MRT is the slope of the PPF.

MRT_AB = MP_L^B / MP_L^A

Also MRT_AB = MP_K^B / MP_K^A

Therefore, it must be that for every point on the PPF it holds that:

MP_L^B / MP_L^A = MP_K^B / MP_K^A

This means that the ration of an input’s marginal product must be the same for all inputs on the PPF.

We find the output efficient allocation where the PPF is tangent to the indifference curve. So the slope of the PPF must me equal to the slope of the indifference curve. This implies that output efficiency requires that:

MRT = MRS

U_N and U_M represent two indifference curves.

Point M is an intersection point and not a tangency point and therefore it is an inefficient output allocation. The output combination at point N, which is located at the tangency point of the PPF and the indifference curve, is an efficient output allocation.

Welfare theorems

The first welfare theorem states that perfectly competitive markets, in general equilibrium, distribute resources in a Pareto-efficient way. A condition of this theorem is that producers and consumers take the price of inputs as given. It also relies on the assumptions of asymmetric information, externalities and public goods.

The second welfare theorem states that any given Pareto-efficient allocation in a perfectly competitive market is a general equilibrium outcome for some initial allocation. It means that any Pareto-efficient equilibrium is possible when choosing the right initial allocation of goods. However, it is not easy to achieve this.

The allocations of goods should have to be lump-sum transfers. A lump-sum transfer is a transfer to or from an individual for which the size is unaffected by the individual’s choices. In reality these lump-sum transfers are almost never used.