Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 3
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1 Economics 2 Spring 2018 rofessor Christina Romer rofessor David Romer SUGGESTED ANSWERS TO ROBLEM SET 3 1.a. A monopolist is the only seller of a good. As a result, it faces the downward-sloping market demand curve. Its marginal revenue curve is also downward sloping. This is true because when the monopolist tries to sell another unit, it not only affects the market price on that unit, but also on all of the units that it could have sold at the previous price. Like any firm, a monopolist maximizes its profits by producing where marginal revenue is equal to marginal cost. This occurs at quantity Q 1. The monopolist then sets the price of the good at 1, the price corresponding to Q 1 on the demand curve. 1 Q1 MC D MR Q b. If the market were competitive, it would produce where MC (which would be the supply curve) equals demand. The equilibrium price would be C and the MC equilibrium quantity would be Q C. The problem 1 states that the government sets a price ceiling ( ) C below C. The price ceiling affects the marginal revenue curve of the monopolist. Up to the point where the line at intersects the demand curve, the D monopolist can sell all it wants at the controlled price. Thus, its marginal revenue is constant and MR1, MR2 equal to. After the point where the line at Q1 Q2 QC Q intersects the demand curve, the monopolist s marginal revenue curve is its original downwardsloping one. This is true because beyond this point, to sell another unit the monopolist has to drop the price on all the previous units as well. The new marginal revenue curve (MR 2) is the light blue, discontinuous line. With the price ceiling in place, the monopolist chooses to produce at Q 2, which is where the new MR curve intersects the MC curve. It is possible that imposing a price ceiling on a monopolist could increase total welfare, but it is far from certain. For total welfare to rise, two things must be true. First, imposing the price ceiling must move the quantity produced and sold by the monopolist closer to the competitive outcome. That happens for the way we have drawn the price ceiling (Q 2 is greater than Q 1). If the price ceiling were set substantially lower, however, Q 2 could be less than Q 1. Second, even if Q 2 is closer to Q C, the price ceiling does not necessarily increase total welfare. The issue is that with the price ceiling, there will be a shortage of the good. It is likely that whatever alternative method used to allocate the good to consumers will result in some misallocation (which is not present at Q 1). Thus, for the price ceiling to increase total welfare, it must both move the quantity produced and sold closer to the competitive outcome and not cause too much misallocation among consumers. 2.a. The demand curve (D 1) is the private marginal benefit curve (MB 1). Assuming that there is no positive externality associated with construction, D 1 is also the social marginal benefit curve (SMB 1). The supply curve (S 1) is the private marginal cost curve (MC 1). When there is a negative externality, the social marginal cost curve (SMC 1) is above the private marginal cost
2 2 curve. The difference between the two curves is the external marginal cost associated with each level of consumption and production. It is the harm to people outside the market when another unit of construction is undertaken. The market equilibrium level of output is Q 1, which occurs where MB 1 and MC 1 intersect. This is the point where supply is equal to demand. The socially optimal level of output is Q*, which occurs where SMB 1 intersects SMC 1. The socially optimal level of construction is lower than the level chosen by the market. This occurs because the market participants do not consider the costs to society of the noise associated with construction. They choose to produce and consume where the private marginal cost is equal to the private marginal benefit. SMC1, MC1 a b c d External MC, MB1, SMB1 Q* Q1 Q b. The total social surplus when there is a negative externality is the total private surplus minus the external cost. The total private surplus is the area between the private marginal benefit curve (MB 1) and the private marginal cost curve (MC 1), up to whatever level is produced and consumed. The external cost is the area between the social marginal cost curve (SMC 1) and the private marginal cost curve (MC 1), again up to whatever level is produced and consumed. The welfare accounting is the following: Market Equilibrium (Q 1) Social Optimum (Q*) Total rivate Surplus a + b + d a + b External Cost b + c + d b Total Social Surplus a c a The accounting makes clear that the social surplus at the social optimum does indeed exceed the social surplus at the market equilibrium level of output. The difference between the two social surpluses, area c, is the deadweight loss associated with the externality. A simpler way to calculate the deadweight loss when there is an externality is to realize that the total social surplus is the area between the social marginal benefit curve (SMB 1) and the social marginal cost curve (SMC 1), up to whatever level is produced and consumed. Examining this area shows that the total social surplus at Q* is larger than the total social surplus at Q 1 by the area c. c. There are a variety of ways that society could try to deal with the negative externality. One obvious one is to impose a tax on construction. In principle, a tax set equal to the external marginal cost would serve to move the market equilibrium to the socially optimal level of construction. A benefit of the tax is that it achieves the optimal level of construction, but still
3 3 allows the production and consumption of the good to be allocated by price. One disadvantage is that, realistically, the amount of noise created by construction (and the costs that the noise imposes on neighbors) varies greatly across construction projects. As a result, a single tax level that applies to all construction activities would probably be greater than the external marginal cost for some types of construction (for example, projects that generate little noise or that are in places with few neighbors) and less than the external marginal cost for others (such as noisy projects in crowded areas). Another disadvantage is that a tax on construction does not create incentives for firms to actually try to generate less noise in the construction process. A related approach that might deal with this incentive problem would be for the government to fine construction firms for excessive noise. This would have the benefit of taxing the behavior that actually causes the externality, rather than all construction. It would lead firms to sort themselves the ones that can most easily reduce noise will be the ones that continue to produce. This would help get the desired noise reduction at the lowest possible cost. A disadvantage to this approach is that enforcement could be difficult. It would require many noise monitors to figure out which construction firms should be fined. Another approach would be for the government to regulate the construction industry so that it generates less noise or inconvenience. It could set rules about when construction can occur (say, only from 9 to 5) or that mandated quieter techniques. This approach would have the effect of raising the marginal cost of construction (and so, like the tax, it would shift back the supply curve and reduce the amount of construction). It could be more effective than the tax in getting firms to actually reduce noise. An obvious disadvantage is that the regulations might be excessive or ill-conceived. A rule that makes sense in a dense urban environment might just be wasteful in a more rural setting. Or, a rule that makes sense today might not make sense five years from now when new techniques have been discovered, but could nevertheless remain on the books. rivate negotiation might also be a solution. If the government made clear that neighbors of a construction site had the right to quiet and made it easier for neighbors to enforce those rights, then side payments between the construction firm and the neighbors could compensate the neighbors for the external effects. The side payments would make the construction firms feel the impact of their actions on the neighborhood. Thus, it could lead to both the socially optimal level of construction and give firms an incentive to generate less noise. A downside of this approach is that negotiations between all the affected parties could be very difficult. And, there will be an incentive for a few people to hold out so that they get a much larger payment than the others. There is no right answer to this question. The purpose is to get you to think about the many possible ways that society can deal with the problem of externalities. Most involve government intervention of some sort. Indeed, even private solutions require government to define the property rights and to provide an enforcement mechanism for private agreements. 3.a. For the United States to want to import some of the good, it must be the case that the world price ( W1) is below the price that would prevail if the U.S. were a closed economy. (The diagram is on the next page.) In this case, U.S. producers would choose to produce Q US, which is the quantity where the marginal cost of producing the good in the U.S. is equal to the world price. U.S. consumers would choose to consume Q US, which is the point on their demand curve corresponding to W1. The U.S. would import quantity Imports 1.
4 4 The problem states that the widespread use of subsidies by foreign governments to their producers reduces the world price of the good. This shows up in the diagram as a fall in W (from W1 to W2). Nothing happens to the supply curve of U.S. producers because the U.S. is not subsidizing its producers. Thus, their marginal costs are unchanged. The fall in the world price will cause U.S. producers to produce less (Q US S2 is less than Q US US ) and U.S. consumers to consume more (Q D2 is greater than Q US ). U.S. imports will rise (from Imports 1 to Imports 2) W1 W2 g a Q US US S2 Q b c d e f Q US US Q D2 S US D US Q Imports1 Imports2 b. The foreign subsidies that reduce the world price of the good will increase consumer surplus in the U.S. and reduce producer surplus. The welfare accounting is below. At W1 At W2 Consumer Surplus a + b a + b + c + d + e + f roducer Surplus c + g g Total Surplus a + b + c + g a + b + c + d + e + f + g Consumer surplus rises because U.S. consumers pay a lower price and consume more of the good. roducer surplus falls because U.S. producers produce less and receive a lower price. The total surplus clearly rises. The amount that U.S. consumers gain from the foreign subsidies is larger than what U.S. producers lose. From this analysis, you can see why American producers are complaining about the foreign subsidies, but American consumers are not. 4.a. We are thinking about the market for meat from the Australian perspective, so the domestic supply curve is S A, and the domestic demand curve is D A. For Australia to be a net exporter of meat, it must be the case that the world price of meat ( W) is above the level that would prevail if Australia were a closed economy. As always, it is helpful to realize that the price on the vertical axis is the price of meat relative to other prices in the economy. Here, since the only other good is machinery, the price on the vertical axis is the price of meat relative to the price of machinery. W S A D A A A Q D Q S Q Exports b. We can draw the usual C/CC diagram for Australia. The production possibilities curve (C) shows the combinations of meat and machinery that Australia can produce just using all of its resources. It is surely curved because the country will organize production according to comparative advantage. That is, the opportunity cost of producing meat or machinery will rise as
5 5 more is produced. There are terms of trade at which meat and machinery trade in the world market. Machinery This trade-off in the market depends on the world prices of the two goods. If we put meat on the horizontal axis (as in the diagram), then the terms of trade are the units of machinery per 1 unit of Slope = Meat/Machinery) meat, or, equivalently, the price of meat divided by the price of machinery. Where a line representing the terms of trade is just tangent to the C (point A) is the optimal combination of meat and C B A machinery that Australia can produce. It is the combination of the two goods that has the highest CC value in the world market. Australia can then trade Meat for any combination of goods along the tangent line representing the terms of trade because all of them cost the same in the world market. This line is thus the consumption possibilities curve (CC). The fact that Australia exports meat means that it does not consume all of the meat that it produces at point A. This implies that Australia chooses to consume at a point to the left of point A on the CC (such as point B). c. A rise in the world price of meat shows up in the supply and demand diagram for meat as a shift up in the world (relative) price line (from W1 to W2). This will result in a decline in the A amount of meat Australian consumers demand (from Q to Q A D2 ) and a rise in the amount of A meat Australian producers supply (from Q to Q A S2 ). Australia s meat exports will rise (from Exports 1 to Exports 2). In the C/CC diagram the rise in the world price of meat shows up as a steepening of the terms of trade line (its slope is Meat/ Machinery, and the world price of meat is now higher). The point of tangency with the C is now at point C, which has a larger quantity of meat and a smaller quantity of machinery. This result makes intuitive sense if the world price of meat rises, Australia will not want to just do what it was doing before. It will want to produce more of the good whose price has risen (and hence less of the good whose price has not changed). There is a new CC (CC 2), which is shown in light blue in the diagram. Notice that in the supply and demand diagram, at W2, Australians are consuming less meat then before. This tells us that the country is at a point like D on the new CC (which has less meat than at point B). Supply and Demand Diagram for Meat W2 W1 S A C/CC Diagram Machinery D CC2 D A C B A C CC1 A A Q D2 Q Q A A Q S2 Meat Exports1 Exports2
6 6 5. The demand curve for workers in fast food restaurants is derived from profit maximization on the part of the restaurants. It is the downward-sloping marginal revenue product of labor (MR L) curve because profit-maximizing firms want to hire labor up to the point where the MR L of another worker is just equal to the going wage. The supply curve of fast food workers is derived from utility maximization on the part of households. As discussed in class, the income and substitution effects of a wage change on labor supply go in opposite directions. However, as an empirical matter, the substitution effect is typically stronger than the income effect, so the labor supply curve is upward sloping. The equilibrium wage and level of employment of fastfood workers are determined by the intersection of the labor demand and labor supply curves in this market. a. Increasing awareness of nutrition that reduces the demand for fast food will shift the demand curve for fast food to the left (from D 1 to D 2). This will reduce the equilibrium price and quantity of fast food (from 1 to 2 and from Q 1 to Q 2). 1 2 D2 Q2 Q1 Q The MR L is the extra revenue generated by another worker. It is equal to the marginal (physical) product of another worker times the marginal revenue associated with selling one more unit of the good. Assuming that the market for fast food is competitive (as it likely is), the marginal revenue associated with selling one more unit is just the going market price for fast food. The fall in the price of fast food means that the MR L of fast food workers has fallen at every level of employment. Thus, this development will shift back the labor demand curve for fast food workers (from D 1 to D 2). As a result, the wage and employment of fast food workers will decrease (from w 1 to w 2 and from L 1 to L 2, respectively). w w1 w2 L2 L1 D2 L (Note: We have drawn D 2 as being asymmetrically below D 1. This is technically correct because the MR L is marginal product times price. Therefore, if we reduce the price, the new MR L is lower by a fixed proportion, not by a constant vertical distance. However, this is a technical point that it is fine not to worry about in Econ 2.) This problem illustrates the important point that a change in the demand for the product that labor produces will change the demand for labor.
7 7 b. New apps and video games that make leisure time more enjoyable will affect the marginal utility of leisure for a typical household at every level of leisure consumption. If we think of a typical household choosing between leisure and everything else that they like, a household maximizes its utility by setting the MU Leisure/ Leisure = MU Everything Else/ Everything Else. The increase in the MU Leisure implies that at the initial level of leisure consumption, the MU Leisure/ Leisure > MU Everything Else/ Everything Else. The household needs to consume more leisure (and so push down the MU Leisure) and less of everything else (and so push up the MU Everything Else). If the household is consuming more leisure at a given Leisure (which is the wage), this implies that they are supplying less labor to the market. Thus, the labor supply curve has shifted to the left (from S 1 to S 2). A shift back in labor supply will reduce the equilibrium level of employment (from L 1 to L 2) and raise the equilibrium wage (from w 1 to w 2). w w2 w1 S2 L2 L1 L c. The adoption of new fryers that increase the productivity of fast food workers will make workers able to produce more in a given amount of time. This will increase the marginal (physical) product of fast food workers the amount of fries produced by another worker will now be greater than before at every level of employment. This increase in the marginal (physical) product of labor will tend to increase the marginal revenue product of labor (which is marginal product times marginal revenue). The only complication is that the increase in productivity will tend to shift out the supply curve of fast food and hence lower the price. For a competitive industry, marginal revenue is just equal to the prevailing price of the good. Therefore, this reduction in the price will tend to lower the MR L. Theoretically, this negative effect on marginal revenue product could counteract the positive effect of the increase in the marginal product. However, the demand for fast food would have to be very inelastic for the shift out in supply to decrease price by as much or more than the marginal product of labor increased. For this reason, it is reasonable to suppose that the marginal revenue product of fast food workers will increase because of the new fryers. Since the demand curve for labor is the marginal revenue product of labor, the demand curve for fast food workers will shift out (from D 1 to D 2). The shift out in the demand curve will result in a rise in both the wage of fast food workers (from w 1 to w 2) and the level of employment (from L 1 to L 2). This problem illustrates the important point that technological progress and the addition of more capital is typically beneficial to workers. w w2 w1 L1 L2 D2 L (Note: As with a change in the price of the product, an increase in the M of labor will shift the MR L curve asymmetrically. This is true because it enters multiplicatively. Again, for simplicity, you may ignore this technicality.)
8 8 d. As shown in part (c), technological progress will tend to increase wages and employment in the industries where it occurs. In this problem, we are considering the effect of technological change elsewhere in the economy on the fast food industry. If wages are higher and more workers are working in other industries (and there was no unusual unemployment to start with), it must be the case that fewer workers are available to work in the fast food industry. This implies that the labor supply curve has shifted to the left (from S 1 to S 2). A shift back in labor supply will reduce the equilibrium level of employment (from L 1 to L 2) and raise the equilibrium wage (from w 1 to w 2). w w2 w1 L2 L1 S2 L
Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 3
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