# Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 1

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2 2 b. If there is no change in the productivity of capital and labor in producing civilian goods and services, then the maximum amount of civilian output we can produce doesn t change. Thus the point where the C intersects the horizontal axis doesn t change. But since capital and labor are more productive in producing military goods and services than before, if we devote some of our capital and labor to the military sector, we get more military output than before. Thus at any point except where the C intersects the horizontal axis, the new C is above the old C. That is, the C shifts outward asymmetrically from something like C 1 to something like C 2. Military C 1 C 2 Civilian c. The problem focuses on a change in the composition of production, not on the level of production. This means that it describes a movement along the C. Since a decision to spend more on military goods and services doesn t change the economy s productive possibilities, it can t move us to a point outside the old C. Given our productive capacities, with the economy starting at full employment (so that we re already on the C), the only way we can have more military goods and services is by having fewer civilian goods and services. Thus the change would move us from one point on the C (such as point A) to another point (such as point B) with more military output and less civilian output. Military B A C Civilian 3.a. The opportunity cost of a croissant for a worker is the number of baguettes he or she could produce in the time it takes to produce 1 croissant. Since Juliette could produce 3 croissants in an hour or 3 baguettes, her opportunity cost of 1 croissant is 1 baguette. Likewise, her opportunity cost of 1 baguette is 1 croissant. The opportunity costs for each of the workers are given in the table below. Opportunity Cost of 1 Croissant (in Baguettes) Opportunity Cost of 1 Baguette (in Croissants) Juliette 1 1 Marie 4 ¼ ierre ⅓ 3 b. When there is no specialization, we think of each worker splitting his or her time in the same way as the others. That is, if one worker produces croissants for 1 hour and baguettes for 5 hours, the other two workers also produce croissants for 1 hour and baguettes for 5 hours. We don t allow one worker to spend more time on some activity than another worker. Since the workers always do the same thing, there s a constant opportunity cost for the collective. Every time the three workers work an hour producing baguettes, they produce 8 baguettes. Every time the three workers work an hour producing croissants, they produce 7 croissants. Therefore, for the collective as a whole, when there is no specialization, the opportunity cost of 1 croissant is ⁸ ⁷ baguettes.

3 The vertical intercept of the C shows the number of baguettes the three workers could produce in a day if they produced no croissants. Since they work for 6 hours per day and produce 8 baguettes per hour, they could produce 48 baguettes. The slope of the C is minus the opportunity cost of the good on the horizontal axis. Therefore, if we put croissants on the horizontal axis, the slope of the C for the collective, assuming no specialization, is ⁸ ⁷. Therefore, the C for the collective with no specialization is a line starting at 48 baguettes and 0 croissants, with a slope of ⁸ ⁷. The horizontal intercept shows the number of croissants the three workers could produce if they produced no baguettes. If the collective produced no baguettes, it could Baguettes 48 C without specialization Croissants produce 42 croissants (7 croissants per hour times 6 hours). Notice that this is the point we get to if we start at no croissants and 48 baguettes and draw a line with a slope of ⁸ ⁷ until we get to the horizontal axis. The C for the collective without specialization is a straight line because the opportunity cost of a croissant doesn t rise as more are produced. This is true because each worker s abilities are constant and we are forcing the three workers to always split their time in the same way. Therefore, every time they produce one more croissant, they give up ⁸ ⁷ baguettes. c. When we allow the workers in the collective to specialize, they will no longer split their time in exactly the same way. Instead, they will divide the activities according to comparative advantage. This means that as we think about producing progressively more of one of the goods, the worker with the lowest opportunity cost produces first, the second lowest next, and the highest last. If the collective decides to have the workers specialize according to who has the lower opportunity cost, it will use ierre to produce croissants first, then Juliette, and then Marie. The specialization will cause the slope of the C to change as we move along it. Between 0 croissants and the maximum amount that ierre can produce in a day (which is 18 croissants), the relevant opportunity cost is ierre s he is the one switching between baguette production and croissant production; Juliette and Marie are just making baguettes. Therefore, the slope of the C is ⅓ in this range. Between 18 croissants and 36 croissants, which is the maximum amount ierre and Juliette can produce together, the relevant opportunity cost is Juliette s she is the one who is switching between the two activities; Marie is just producing baguettes and ierre is just producing croissants. Therefore, the slope of the C is 1 in this range. Finally, between 36 croissants and 42 croissants, which is the maximum number of croissants the three can produce if they all just produce croissants, the relevant opportunity cost is Marie s she is the one switching between the two activities. Therefore, the slope of the C is 4 in this range. The vertical intercept of the C is 48 baguettes the total number of baguettes the three workers can produce if they each spend all 6 hours making baguettes. The horizontal intercept is 42 croissants the total number of croissants the three workers can produce if they each spend all 6 hours making croissants. 42 3

4 4 With specialization, the C of the collective has two kinks in it. This reflects the fact that with specialization, the opportunity cost rises as the collective produces more of a good. The slope of the C changes from ⅓ (ierre s opportunity cost) for the first segment, to 1 (Juliette s opportunity cost) for the second, and finally to 4 (Marie s opportunity cost) for the third. This happens simply because the collective uses the worker with the lowest opportunity cost first, the next lowest opportunity cost second, and so on. As we add more and more workers, the C would start to take on its characteristic curved shape. Baguettes C with specialization Croissants The quantities of croissants and baguettes at each kink point are calculated by thinking about how much the workers can produce. The first kink occurs at the point where ierre is producing croissants full time and Juliette and Marie are producing baguettes full time. When ierre is spending 6 hours producing croissants, he will make 18 croissants; when Juliette and Marie are producing baguettes full time, they will make 42 baguettes (18 from Juliette and 24 from Marie). The second kink point occurs at the point where ierre and Juliette are both producing croissants full time and Marie is making baguettes full time. If ierre and Juliette work 6 hours producing croissants, they will make 36 croissants (18 from ierre and 18 from Juliette); when Marie is producing baguettes for 6 hours, she will make 24 baguettes. 4.a. As in lecture, for Robinson the opportunity cost of 1 coconut is 1 fish, and for Friday the opportunity cost of 1 coconut is 4 fish. And as in lecture, if Robinson and Friday both spend all their time fishing, they will catch 54 fish (6 from Robinson and 48 from Friday), and if they spend all their time gathering coconuts they will get 18 coconuts (6 from Robinson and 12 from Friday). However, what happens between the two extremes is different than in lecture. Starting from the point where they are both spending all day catching fish, suppose they decide to gather some coconuts. The rule is that Friday must be the first one to do this. For each coconut he gathers, he catches 4 fewer fish. Thus the slope of their production possibilities over this range is 4. Robinson isn t allowed to gather any coconuts until Friday is spending all his time doing so. Thus the slope is 4 up to the point where Robinson is still spending all his time fishing, but Friday is spending all his time gathering coconuts. At this point, they re getting 6 fish and 12 coconuts. Beyond that point, if they want more coconuts, it s Robinson who switches from fishing to coconut-gathering. Thus over that range, the slope is determined by Robinson s opportunity cost, and so is 1. Fish Coconuts

6 also buy fewer limes (and buy more of goods whose enjoyment isn t linked to their consumption of avocados salsa, for example). As a result, at a given price of limes, fewer will be demanded than before. This corresponds to a shift back in the demand curve (from to D 2). The equilibrium price and quantity of limes will both fall (from to 2 and from 1 to 2, respectively). c. Before the imposition of the price ceiling, the equilibrium price of limes was and the equilibrium quantity was 1. The statement that the price ceiling is binding means that it s less than the price where supply and demand intersect that is, that it s below. At the price ceiling of, the quantity supplied ( S) is less than the quantity demanded ( D). The price of limes will fall (from to ), and the quantity bought and sold will fall (from 1 to S). Because the quantity demanded will exceed the quantity supplied at the new price, there will be a shortage of limes. d. A tax that is paid by consumers shifts the demand curve down by the amount of the tax: consumers are willing to pay less at a given quantity because they know they will also have to pay the tax. Because the tax is paid by consumers, the supply curve isn t affected. The downward shift of the demand curve lowers the equilibrium quantity (from 1 to 2). In addition, the equilibrium price, which is what firms receive, also falls (from to 2). The price paid by consumers was, but after the tax is imposed the total amount they pay for each lime is 2 plus the tax. Since the distance between and D 2 is the amount 2 + tax 2 Shortage 2 1 Tax (25 ) of the tax, we find this amount paid by consumers by looking at the point on corresponding to the new equilibrium quantity ( 2). With a normal, downward-sloping demand curve and a normal, upward-sloping supply curve, the tax decreases the amount suppliers receive for the good and increases the amount that consumers pay. 6.a. For most consumers, there are many close substitutes for pepperoni pizza. Most obviously, there are other types of pizza; but there are also meatball subs, burgers, calzones, and so on. With the presence of many close substitutes, one would expect a small price increase to lead to a large reduction in the quantity of pepperoni pizza demanded, and a small price decrease to lead to a large increase in the quantity demanded. If so, the price elasticity of demand is fairly high. (Of course, one could try to make an argument for a low elasticity. There are some consumers who strongly prefer pepperoni pizza to any of the usual alternatives. The quantity of pepperoni pizza that these consumers demand may be relatively unresponsive to the price. If these consumers are the source of most of the demand for pepperoni pizza, the elasticity of demand is fairly low.) b. The shift up of the supply curve will lead to a fall in quantity and a rise in price as we move along the demand curve. In part (a), we argued that the price elasticity of demand for pepperoni pizza is probably fairly high. If the elasticity of demand is greater than 1, the percentage fall in the quantity of pepperoni pizza will be larger than the percentage rise in the price. As a result, total spending on pepperoni pizza (which is price times quantity) will fall. S 1 D D 2 6

7 7 All of this is shown is the diagram. When the price elasticity of demand is high then, over the relevant range, the demand curve is fairly flat. In this case, when the supply curve shifts up, the percentage S 2 fall in quantity (the percentage change from 1 to 2) is larger than the percentage rise in price (the 2 percentage change from to 2). Total spending is the product of price and quantity. Thus it is shown by the shaded rectangles in the diagram. For example, total spending before the shift in supply is given by the rectangle with corners at the origin, 1 on the horizontal axis, on the vertical axis, and the 2 1 intersection of and. This rectangle has width 1 and height, and so its area is 1 times, which is total spending on pepperoni pizza. Total spending after the shift in supply is shown by the rectangle with width 2 and height 2. As the diagram shows, with a high price elasticity of demand, total spending falls when supply shifts up.

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