Economics 2 Spring 2017 Professor Christina Romer Professor David Romer SUGGESTED ANSWERS TO PROBLEM SET 3 1.a. Both the consumption and production of higher education are likely to generate benefits for people ho are neither the consumers nor the producers of higher education. On the consumption side, hen people get a college education, they are likely to be more informed voters and more skilled orkers. It is certainly possible that more informed voters ill help to enact better policies that benefit all members of society. Likeise, it is possible that the presence of more skilled orkers ill encourage innovative firms to locate in an area, and innovative firms may generate ne technologies that benefit not just themselves but also other firms. On the production side, teaching undergraduates and training graduate students may lead to ne research findings that have little monetary benefit to universities, but have large benefits to society. For example, the discovery of the laser by university scientists led to many ne products and more efficient production techniques. b. The demand curve () is the private marginal benefit curve (PMB 1). When there is a positive externality, the social marginal benefit curve (SMB 1) is above the private marginal benefit curve (PMB 1). The difference beteen the to curves is the external marginal benefit associated ith each level of consumption and production. The supply curve () is the private marginal cost curve (PMC 1). Because there is no obvious negative externality related to the consumption and production of higher education, the social marginal cost (SMC 1) and private marginal cost (PMC 1) curves are the same. The market equilibrium level of output is Q 1, hich occurs here PMB 1 and PMC 1 intersect. This is the point here supply is equal to demand. The socially optimal level of output is Q*, hich occurs here SMB 1 intersects SMC 1. The socially optimal level of enrollment in institutions of higher education is greater than the level chosen by the market. This occurs because the market participants do not consider the benefits to society of higher education. They stop production and consumption here the private marginal benefit is equal to the private marginal cost. P External Marginal Benefit a b c d, PMC 1, SMC 1 SMB 1 Q 1 Q*, PMB 1 Q The total social surplus hen there is a positive externality is the sum of the total private surplus and the external benefits. The total private surplus is the area beteen the private marginal benefit curve (PMB 1) and the private marginal cost curve (PMC 1), up to hatever level is produced and consumed. The external benefits are the area beteen the social marginal benefit curve (SMB 1) and the private marginal benefit curve (PMB 1), again up to hatever level is produced and consumed. The elfare accounting is the folloing:
2 Market Equilibrium (Q 1) Social Optimum (Q*) Total Private Surplus a a d External Benefit b b + c + d Total Social Surplus a + b a + b + c There is an area of negative private surplus at the social optimum because e are pushing production into the range here the private marginal cost exceeds the private marginal benefit. 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 beteen the to social surpluses, area c, is the deadeight loss associated ith the externality. A simpler ay to calculate the deadeight loss hen there is an externality is to realize that the total social surplus is the area beteen the social marginal benefit curve (SMB 1) and the social marginal cost curve (SMC 1), up to hatever level is produced and consumed. Examining this area shos that the total social surplus at Q* is larger than the total social surplus at Q 1 by the area c. c. A subsidy is a negative tax; rather than taking money aay from people, the government gives them money. A subsidy paid directly to consumers ill shift the demand curve up by the amount of the subsidy (from to D 2). This is true because the amount that consumers ould be illing to pay for any quantity of higher education is no higher by the amount of the subsidy. If the subsidy is set exactly equal to the size of the external marginal benefit, then the ne demand curve (D 2) ill lie on top of the social marginal benefit curve (SMB 1). The market ill no choose to produce here the ne demand curve (D 2) crosses the supply curve (). This occurs at the socially optimal level of output (Q*). The subsidy has made consumers internalize P a External Marginal Benefit, Subsidy, PMC 1, SMC 1 b c d Q 1 Q* SMB 1, D 2, PMB 1 the externality. The government has made the people in the market feel the benefits that they are conferring on society by giving them money equal to those external benefits. Though not necessary for a complete anser, elfare analysis confirms that a subsidy ill indeed result in a elfare gain. The elfare accounting for a subsidy set equal to the external marginal benefit is the folloing: Q Market Equilibrium (Q 1) After the Subsidy (Q*) Total Private Surplus a a + b + c External Benefit b b + c + d Government Expenditure (b + c + d) Total Social Surplus a + b a + b + c A key effect of the subsidy is to increase the total private surplus. When the government gives people a subsidy, the area beteen the supply curve () and the relevant demand curve (D 2) gets larger. The amount that the government spends is just equal to the external benefits. But, because the private surplus is larger, the social surplus is larger (as before, by area c).
3 2.a. As described in lecture and in the textbook, marginal revenue for the first unit a monopolist sells is equal to price (since the additional revenue from selling the first unit is just the price of that unit). But for units after the first, marginal revenue is less than price, because the monopolist needs to cut its price to sell more, and so the price it receives on all units is loer. For the specific case of a linear demand curve, the (negative) slope of the marginal revenue curve is tice the (negative) slope of the demand curve. P P 1 ATC 1 Q 1 MR MC ATC D Q The firm maximizes profits by producing here marginal revenue equals marginal cost. Thus the profit-maximizing quantity to produce is Q 1. It then charges the point corresponding to this quantity on the demand curve, hich is P 1. Finally, e can see that at Q 1, price is greater than average total cost, and so profits are positive. They are equal to Q 1 times the difference beteen price and average total cost. This area is shon by the shaded rectangle in the diagram. b. If the marginal cost associated ith producing another unit rises by the same amount at all levels of production, there is a parallel upard shift of the marginal cost curve (from MC 1 to MC 2), and the P ATC 2 average total cost curve shifts up by the same ATC2 MC P2 amount as the marginal cost curve (from ATC 1 to 2 P1 MC ATC 2). The marginal revenue and marginal cost ATC1 1 ATC curves no intersect at a loer level of output. Thus 1 the quantity the monopolist produces falls (from Q 1 to Q 2). Since the demand curve slopes don and has MR not shifted, hen the monopolist cuts production, it 1 raises the price it charges (from P 1 to P 2). Finally, the fact that the monopolist s costs are higher means Q 2 Q 1 Q that the profits it is able to earn are loer. In the case shon in the diagram, the rise in costs is so large that profits sitch from positive (the grey rectangle) to negative (the pink rectangle). 3.a. When orkers ithin a country differ in ability, e cannot dra the PPC for a typical orker. Instead, e need to dra the PPC for the hole country. Because the opportunity cost of a good rises as more is produced, the PPC ill be curved. The opportunity cost of producing a good rises because e ill organize production so that the loest-opportunity-cost resources are used first, the next-loest second, and so on. Assuming that the U.S. is on average relatively better at book production than at shirt production, the curved PPC for the U.S. (ith shirts on the vertical axis and books on the horizontal axis) ill have a somehat short, fat shape. Since the orld price of a book is $60 and the orld price of a shirt is $30, the terms of trade in orld markets beteen books and shirts is 2 shirts for 1 book. Since in this example the only to goods are books and shirts, e can also say that the orld relative price of a book is the orld price of a book divided by the orld price of a shirt, or 2. This orld relative price defines a trade-off beteen the to goods in the orld market. In the orld market 1 book ill trade for 2 shirts.
4 A country ith rising opportunity costs ants to produce a good up to the point here the domestic opportunity cost of that good is equal to the orld relative price. At levels of production here the domestic opportunity cost is less than the orld relative price, the country can have more of the good by producing it domestically than by producing something else and trading for the good. Only hen the domestic opportunity cost is equal to the orld relative price can the country reap no more gains from specialization. In our diagram, the U.S. ants to produce here a line reflecting the orld relative price of 2 shirts per 1 book is just tangent to the PPC. This occurs at point A. This is the point here the domestic opportunity cost of a book is equal to the orld relative price of a book. At point A, the U.S. is producing quantity Q S of shirts and quantity Q B of books. Shirts Q S PPC Line reflecting orld relative price of 2 shirts per 1 book A Q B Notice that because of the high orld relative price of books and the somehat short, fat shape of the curved PPC, the U.S. ants to produce relatively fe shirts and relatively many books. This is because the U.S. has an opportunity cost for books that is loer than the orld relative price up to a high level of book production. In this sense the U.S. has a comparative advantage in book production: up to quite high levels of production, it is the lo-opportunitycost producer. b. The consumption possibilities curve ith trade (CPC) shos the combinations of shirts and books that the U.S. can purchase on orld markets hen it trades its domestic production at the prevailing orld relative price. In our diagram, the CPC ith trade is the line reflecting the orld relative price that is just tangent to the curved PPC. Shirts CPC ith trade The slope of the CPC is minus the orld relative price of the good on the horizontal axis. In our example, the orld relative price of a book is 2; 1 book ill purchase 2 shirts. Therefore, the slope of the CPC in our example is 2. The trade-off in the orld market does not vary ith production (so the CPC has a constant slope) because e assume that any one country is small relative to the rest of the orld. Therefore, changes in the quantity of a good either supplied or demanded by a country ill not affect the orld relative price. Q S PPC A Q B The position of the CPC is determined by the point of tangency ith the PPC. One ay to think about the point of tangency (point A in the diagram) is that it shos the feasible combination of domestic production of the to goods ith the highest value on the orld market. This domestic production combination is the endoment that the country brings to the orld market to trade at the orld relative price. The country can then trade for any other
5 combination of the to goods ith the same value in the orld market. Thus, the total value of every combination of books and shirts along the PPC is the value of the combination of books and shirts that the U.S. can produce that has the highest value on orld markets. c. A supply and demand diagram ith a orld relative price can capture the same decision reflected by the point of tangency beteen the curved PPC and the orld relative price line. Consider the market for books in the U.S. There is an upard sloping domestic supply curve (S ). Its upard slope reflects the fact that the opportunity cost of producing books rises in the U.S. as more are produced because orkers ithin the country differ in ability. There is a donard sloping domestic demand curve (D ) that shos that American consumers ant more books (from all sources) hen the relative price of books is loer than hen the relative price is higher. When there is a large orld market, e can think of there being an infinitely elastic orld demand for books at the prevailing orld relative price (P W). This just means that e can sell as many books as e could plausibly ant to foreigners ithout changing the orld relative price. Relative Price of P W S D Q D Q S Q of Exports The point of intersection beteen the orld relative price line and the American supply curve shos the quantity of books the U.S. ants to produce domestically (Q S ). This is the quantity of books that corresponds to point A in part (a). It is the quantity of books here the domestic opportunity cost of a book is equal to the orld relative price of a book. American consumers ant to consume here the orld relative price line intersects the domestic demand curve (Q D ). At this point, the marginal benefit of another book is just equal to the orld price. As e have dran the diagram, the quantity of books American producers supply is greater than the quantity of books American consumers ant to buy. Therefore, the U.S. ill export books. d. If the orld price of shirts falls to $20, hile the orld price of books remains at $60, this implies that the orld relative price of books has risen to 3. This means that on orld markets 1 book ill no trade for 3 shirts. The rise in the orld relative price of books ill make the U.S. ant to produce more books. This fact can be seen in both the PPC/relative price line diagram and the supply and demand diagram ith trade. In the PPC diagram, the rise in the orld relative price implies that the line representing the orld relative price has gotten steeper. It no has a slope of 3 instead of 2. The U.S. ants to produce any books for hich the domestic opportunity cost is loer than the trade-off in the orld market. Because the trade-off in the orld market has risen, the level of book production here domestic opportunity cost is equal to the trade-off in the orld market is no larger than before. The ne relative price line is no tangent to the PPC at point B, hich has a larger quantity of books than before (and a smaller quantity of shirts). The diagram is on the next page. In the supply and demand diagram ith trade, the rise in the orld relative price is represented by a shift up in the orld price line (from P 1 to P 2). The U.S. ants to produce here the ne orld relative price line intersects the supply curve. This occurs at quantity Q S2. The rise in the orld relative price increases domestic production and decreases domestic
6 consumption. The result is an increase in U.S. book exports (from Exports 1 to Exports 2). Shirts Line reflecting orld relative price of 3 shirts per 1 book Line reflecting orld relative price of 2 shirts per 1 book Relative Price of P W2 P W1 S PPC Q S1 Q S2 A B Q B1 Q B2 Q D2 Q D1 Exports 1 Q S1 Q S2 D Q of Exports 2 Note: The fall in the orld price of shirts as described as being the result of technological progress. If the technological progress occurred in the U.S. as ell as in the orld more generally, this ould change the U.S. PPC. In particular, it ould make the PPC somehat taller (the vertical intercept ould be higher than before). Notice, if e incorporated this change into our diagram, the impact of the price change ould be less obvious. The rise in the orld relative price of books ould tend to make the U.S. ant to produce more books. But, technological progress in the shirt industry ould tend to make the U.S. ant to produce more shirts (and therefore feer books). You could sho the same phenomenon in the supply and demand diagram for shirts (the good e import). The orld relative price of shirts has fallen. The technological progress (if it also occurred in the U.S.) ould shift don the S curve for shirts. The loer price makes the U.S. ant to produce feer shirts; the technological progress makes the U.S. ant to produce more. e. As usual, the subsidy to U.S. book producers ill shift the supply curve don by the amount of the subsidy: because producers receive a subsidy, the price they need to supply a given quantity is loer by the amount of the subsidy. Thus the supply curve shifts don from to S 2. Hoever, there is still a perfectly elastic demand curve for books from abroad at the prevailing orld price. As a result, the price of books does not change. Because the price of books is unchanged, the quantity of books American consumers buy is unchanged (at Q D ). Hoever, the quantity of books produced by American producers rises (from Q S1 to Q S2 ), and our exports rise (from Exports 1 to Exports 2). Relative Price of P W a d b c e h Q D i Exports 1 f Exports 2 g Q S1 Q S2 D S 2 Subsidy Q of
7 f. Consumer surplus is the area belo the demand curve and above the price, up to the quantity consumed. Because the price at hich consumers can buy books and the demand curve are unchanged, consumer surplus does not change it is area a both before and after the introduction of the subsidy. Producer surplus is the area above the supply curve and belo the price, up to the quantity produced. Since the supply curve shifts don and the price does not change, producer surplus rises from b+c+d to b+c+d+e+f+h+i. The government spends the amount of the subsidy on each unit produced in the U.S. Thus e can sho it as the difference beteen the to supply curves (hich is the amount of the subsidy per book) up to Q S2. This is h+i+e+f+g. Since there are no externalities in this market, one ould expect the subsidy to cause a deadeight loss. Intuitively, hen there is a subsidy, the U.S. is selling some books at the orld price even though the opportunity cost of producing them is greater than the orld price. Specifically, the deadeight loss is the area beteen the marginal cost of production (shon by S 1 ) and price from Q S1 to Q S2. This is area g in the diagram. The full elfare accounting is: Without a Subsidy With a Subsidy Consumer Surplus a a Producer Surplus b+c+d b+c+d+e+f+h+i Government Expenditure (e+f+g+h+i) Total Surplus a+b+c+d a+b+c+d g Deadeight Loss g 4. The demand curve for textile orkers is derived from profit maximization on the part of textile firms. It is the donard-sloping marginal revenue product of labor (MRP L) curve because profit-maximizing firms ant to hire labor up to the point here the MRP L of another orker is just equal to the going age. The supply curve of textile orkers is derived from utility maximization on the part of households. As discussed in class, the income and substitution effects of a age change on labor supply go in opposite directions. Hoever, as an empirical matter, the substitution effect is typically stronger than the income effect, so the labor supply curve is upard sloping. The equilibrium age and level of employment of textile orkers are determined by the intersection of the labor demand and labor supply curves in this market. a. The MRP L is the extra revenue generated by another orker. It is equal to the marginal (physical) product of another orker times the marginal revenue associated ith selling one more unit of the good. Assuming that the market for cotton textiles is competitive (as it surely is), the marginal revenue associated ith selling one more unit is just the going market price for cotton textiles. The increased supply of textiles coming from foreign producers reduces the price of textiles in the United States. Because the price of the output has fallen, the MRP L of U.S. textile orkers has fallen. Thus, this development ill shift back the labor demand curve for U.S. textile orkers (from 1 2 L 2 L 1 D 2 L
8 to D 2). As a result, the age and employment of U.S. textile orkers ill decrease (from 1 to 2 and from L 1 to L 2, respectively). (Note: We have dran D 2 as being asymmetrically belo. This is technically correct because the MRP L is marginal product times price. Therefore, if e reduce the price, the ne MRP L is loer by a fixed proportion, not by a constant vertical distance.) This problem shos that increased foreign supplies of a good can indeed reduce employment in the industry producing that good in the U.S. But, it also makes clear that American consumers gain from this development because the price of something that e buy falls. b. Widespread immigration ill increase the number of people illing to ork in the textile industry at a given age. Thus, it ill shift out the supply curve of textile orkers (from to S 2). This shift out in the labor supply curve ill decrease the equilibrium age of textile orkers (from 1 to 2) and increase the equilibrium level of employment (from L 1 to L 2). Ho much the immigration is likely to affect the age in this industry depends on many factors. For example, the more elastic labor demand is, the less the age falls and the more employment rises. 1 2 L 1 L 2 S 2 L c. The adoption of neer, more efficient looms ill make textile orkers able to produce more in a given amount of time. This ill increase the marginal (physical) product of textile orkers the amount of cloth produced by another orker ill no be greater than before at every level of employment. This increase in the marginal (physical) product of labor ill tend to increase the marginal revenue product of labor (hich is marginal product times marginal revenue). The only complication is that the increase in productivity ill tend to shift out the supply curve of textiles and hence loer the price. For a competitive industry, marginal revenue is just equal to the prevailing price of the good. Therefore, this reduction in the price ill tend to loer the MRP L. Theoretically, this negative effect on marginal revenue product could counteract the positive effect of the increase in the marginal product. Hoever, the demand for textiles ould 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 textile orkers ill increase because of the more efficient looms. Since the demand curve for labor is the marginal revenue 2 product of labor, the demand curve for textile 1 orkers ill shift out (from to D 2). The shift out in the demand curve ill result in a rise in both the age of textile orkers (from 1 to 2) and the level D 2 of employment (from L 1 to L 2). This problem illustrates the important point that technological L 1 L 2 L progress is typically beneficial to orkers.
9 d. The tax means that it is more expensive for textile firms to hire orkers at a given age: in addition to paying the age, firms have to pay the tax. The profit maximizing condition for hiring orkers is thus no MRP L = age + tax, or age = MRP L tax. The labor demand curve therefore shifts don by the amount of the tax. The shift don of the demand curve ill result in a fall in both the age of textile orkers (from 1 to 2) and the level of employment (from L 1 to L 2). 1 2 D 2 L 2 L 1 L