Economics 2 Spring 2019 rofessor Christina Romer rofessor David Romer SUGGESTED ANSWERS TO ROBLEM SET 1 1.a. Opportunity cost is defined as the value of what is forgone to undertake an activity. What you are forgoing by reading a comic book is spending 30 minutes studying for your statistics exam, and what you would gain from the studying is a higher score on the exam. Since each hour of studying raises your score by 2 points, 30 minutes of studying would raise your score by 1 point. Thus, the opportunity cost of reading the comic book is 1 point on your statistics exam. (One can imagine possible complications. For example, if the studying would not just raise your score but also improve your knowledge of statistics in the long run, then the opportunity cost would be 1 point on the exam plus some greater long-run knowledge of statistics. But based on the information given in the problem, the main opportunity cost of reading the comic book is a point on the exam.) b. Here, the opportunity cost is simple: what you are forgoing or giving up to get the jewelry is $200, so the opportunity cost is $200. (You might be tempted to make this more complicated by bringing in the small amount of time it would take you to order the jewelry and open the package, or by discussing what you would do with the $200 if you did not spend it on the jewelry. But the main thing you are giving up to get the jewelry is the $200, and the value of $200 is $200. Just as with the Hamilton example from Lecture 1, where we did not need to talk about what the Romer family would have done with the money if we had resold our tickets to figure out the opportunity cost of going to the show, here we do not need to discuss what you would do with the $200 if you did not spend it on the jewelry to figure out the opportunity cost. Recall from Lecture 1: Opportunity cost is often obvious. ) c. To an economist, the cost of something is the value of what must be forgone to do it that is, it is the opportunity cost. What you forgo to order the meal is $30 and 2 minutes of your time; what you forgo if you make the meal from scratch is $10 and 2 hours of your time. So if the amount you value the hour and 58 minutes you would save by ordering the meal is more than $20, the opportunity cost of ordering the meal is less than the opportunity cost of making the meal from scratch. The analysis does not change if the way you would use the 1 and 58 minutes is on a pure leisure activity. Economics does not assume that only things that have monetary value matter. If you would value an hour and 58 minutes playing video games more than $20, then the cost of the meal if you order it is less than the cost if you make it from scratch. 2.a. The C for civilian goods and services and military goods and services shows the various combinations of these two types of output that the economy can produce using exactly all of the available resources. The point where the C intersects the vertical axis is the point on the C where military output is zero. Thus, it shows the amount of civilian goods and services we could get
2 if we devoted all of our resources to producing civilian output and none to military output. Similarly, the point where the C intersects the horizontal axis shows the amount of military goods and services the economy can produce if we devoted all of our resources to producing military output. The slope of the C at a given point shows the amount that civilian output would fall if we increased military output by 1 unit. Thus, the slope is (minus) the opportunity cost of military output. Civilian Output C Military Output This C probably has the conventional bowed-out shape. Some labor and capital are well suited to the production of civilian goods and services, while other labor and capital are well suited to the production of military goods and services. Therefore, the opportunity cost of producing either of these types of output rises as we produce more of it. b. A reduction in the number of people who are available to work implies that the resources available to produce both types of output are lower than before. Therefore, the production possibilities using all available resources will be less than they were before the fall in the population of working age. This corresponds to a shift back in the C (from C 1 to C 2). All of the combinations of military output and civilian output that can be produced are less good than before. Civilian Output C 1 C 2 Military Output Without more information, it is not possible to know if the C shifts back evenly or unevenly. If the workers who are no longer available to work were mainly ones with a comparative advantage in one of the two sectors, that sector would see a larger drop in its production possibilities. c. Technological progress that only improves our Civilian Output ability to produce civilian output would cause the C to shift out, but not symmetrically. Since there has been no change in our ability to produce military C output, the amount of output we would get if we 2 devoted all of our resources to the military sector the point where the C intersects the horizontal C 1 axis does not change. But the fact that there has been technological progress in our ability to produce civilian output means the amount of output we would get if we devoted all of our resources to the civilian Military Output sector the point where the C intersects the vertical axis increases. More generally, the technological progress would increase the amount of output we would get from a given amount of resources devoted to the civilian sector. Thus the C would shift up at any point where some resources were being devoted to the civilian sector, and the shift up would be larger when more resources were devoted to that sector. The end result is an asymmetric outward shift of the C, as shown in the figure.
3 d. These developments would cause both a shift of the C and a change in the point on the C where we are producing. The destruction of many factories making both military and civilian goods means that the resources available to produce both types of output are lower than before. Therefore, the production possibilities using all available resources are less good than before. Although the shift need not be exactly symmetric, in general terms it would be like a shift from C 1 to C 2. Civilian Output C 1 A C 2 B In addition, we know that the total amount of Military Output military goods and services we are producing rises. Thus, the point showing the combination of military and civilian output we are producing must be to the right of where we were before that is, the economy moves from a point like A on the old C to a point like B on the new C. Note that because the C has shifted in, this can only happen if there is a substantial reduction in civilian output. That is, point B must be well below point A. 3.a. The opportunity cost of a biscotto for a worker is the number of cannoli they could produce in the time it takes to produce 1 biscotto. Since Giovanni could produce 80 biscotti in an hour or 20 cannoli, his opportunity cost of 1 biscotto is ¼ cannolo (yes, the singular of cannoli really is cannolo). Likewise, his opportunity cost of 1 cannolo is 4 biscotti. The opportunity costs for each of the workers are given in the table below. Opportunity Cost of 1 Biscotti (in Cannoli) Opportunity Cost of 1 Cannolo (in Biscotti) Giovanni ¼ 4 Luisa 1⅔ ⅗ Maria ¾ 1⅓ b. When there is no specialization, we think of each worker splitting their time in the same way as the others. That is, if one worker produces biscotti for 1 hour and cannoli for 5 hours, the other two workers also produce biscotti for 1 hour and cannoli for 5 hours. We do not allow one worker to spend more time on some activity than another worker. Since the workers always do the same thing, there is a constant opportunity cost for the bakery. Every time the three workers work an hour producing biscotti, they produce 150 biscotti. Every time the three workers work an hour producing cannoli, they produce 100 cannoli. Therefore, for the bakery as a whole, when there is no specialization, the opportunity cost of 1 biscotto is ⅔ cannolo, and the opportunity cost of 1 cannolo is 1½ biscotti.
4 The vertical intercept of the C shows the number of biscotti the three workers could produce in a day if they produced no cannoli. Since they work for 6 hours per day and produce 150 biscotti per hour, they could produce 900 biscotti. The slope of the C is minus the opportunity cost of the good on the horizontal axis. Therefore, if we put cannoli on the horizontal axis, the slope of the C for the bakery, assuming no specialization, is 1½. Thus, the C for the bakery with no specialization is a line starting at 900 biscotti and 0 cannoli, with a slope of 1½. The horizontal intercept shows the number of cannoli the three workers could produce if they produced no biscotti. If the bakery produced no Biscotti 900 C without specialization Cannoli biscotti, it could produce 600 cannoli (100 cannoli per hour times 6 hours). Notice that this is the point we get to if we start at no cannoli and 900 biscotti and draw a line with a slope of 1½ until we get to the horizontal axis. The C for the bakery without specialization is a straight line because the opportunity cost of a cannolo does not 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 cannolo, they give up 1½ biscotti. c. When we allow the workers in the bakery 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 bakery decides to have the workers specialize according to who has the lower opportunity cost, it will use Luisa to produce cannoli first, then Maria, and then Giovanni. The specialization will cause the slope of the C to change as we move along it. Between 0 cannoli and the maximum amount that Luisa can make in a day (which is 300), the relevant opportunity cost is Luisa s they are the one switching between biscotti production and cannoli production; Giovanni and Maria are just making biscotti. Therefore, the slope of the C is ⅗ in this range. Between 300 and 480 cannoli, which is the maximum amount Luisa and Maria can make together, the relevant opportunity cost is Maria s they are the one who is switching between the two activities; Giovanni is just making biscotti and Luisa is just making cannoli. Therefore, the slope of the C is 1⅓ in this range. Finally, between 480 and 600 biscotti, which is the maximum amount the three can produce if they all just make biscotti, the relevant opportunity cost is Giovanni s they are 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 900 biscotti the total number the three workers can produce if they each spend all 6 hours making biscotti. The horizontal intercept is 600 cannoli the total number the three workers can produce if they each spend all 6 hours making cannoli. 600
5 With specialization, the C of the bakery has two kinks in it. This reflects the fact that with specialization, the opportunity cost rises as the bakery produces more of a good. The slope of the C changes from ⅗ (Luisa s opportunity cost) for the first segment, to 1⅓ (Maria s opportunity cost) for the second, and finally to 4 (Giovanni s opportunity cost) for the third. This happens simply because the bakery 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. Biscotti 900 720 480 C with specialization 300 480 600 Cannoli The quantities of cannoli and biscotti at each kink point are calculated by thinking about how much the workers can produce. The first kink occurs at the point where Luisa is producing cannoli full time and Maria and Giovanni are producing biscotti full time. When Luisa is spending 6 hours making cannoli, they will make 300 cannoli; when Maria and Giovanni are making biscotti full time, they will make 720 biscotti (240 from Maria and 480 from Giovanni). The second kink point occurs at the point where Luisa and Maria are both making cannoli full time and Giovanni is making biscotti full time. If Luisa and Maria work 6 hours making cannoli, they will make 480 cannoli (300 from Luisa and 180 from Maria); when Giovanni is making biscotti for 6 hours, they will make 480 biscotti. 4.a. The supply curve for chocolate chip cookies shows the quantity of cookies supplied by producers at each price; the demand curve shows the quantity of cookies demanded by consumers at each price. The initial curves ( and ) show the state of supply and demand before any of the developments discussed in the problem. The initial equilibrium price is 1 and the initial equilibrium quantity is 1. A fall in the price of cocoa means that the price of an input to the production process has fallen. rofit-maximizing firms will now be willing supply a given quantity of cookies at a lower price than before. Equivalently, firms will want to supply more cookies at a given price. This corresponds to a shift down or to the right of the supply curve (from to S 2). The equilibrium price of cookies will fall (from 1 to 2) and the equilibrium quantity will rise (from 1 to 2). 1 2 S 2 1 2 b. Milk and chocolate chip cookies are complements: they are often consumed together. To put it another way, consuming more milk makes consuming chocolate chip cookies more attractive (and consuming more chocolate chip cookies makes consuming milk more attractive). When the price of milk falls because of a shift in supply, consumers buy more milk. As a result, consumers seeking to make themselves as well off as possible find that they can have more total happiness if they also buy more 2 1 1 2 D 2
6 chocolate chip cookies (and buy less of goods whose enjoyment is not linked to their consumption of milk for example, bagels or candy). As a result, at a given price of chocolate chip cookies, more will be demanded than before. This corresponds to a shift out in the demand curve (from to D 2). The equilibrium price and quantity of cookies will both rise (from 1 to 2 and from 1 to 2, respectively). c. The problem states that the government imposes a tax of $0.25 per cookie. Let us focus on the (realistic) case where the tax is physically collected from sellers. A tax paid by sellers will show up in the supply curve. At any quantity, the price it takes to get sellers to supply the good is higher than before by the amount of the tax, because sellers know that in addition to whatever costs they had before, they have to pay the tax to the government on each unit they sell. Thus, S 2 is above by $0.25 at each quantity. Because the seller pays the tax, the demand curve is unaffected: at a given price, the attractiveness of cookies to consumers is the same as before, and so they demand the same quantity as before. The equilibrium quantity therefore falls (from 1 to 2) and the equilibrium price rises (from 1 to 2). The after-tax amount that sellers receive on each unit is 2 tax, which is lower than 1. Notice that the tax decreases the amount bought and sold in the market. Also, even though the tax is physically paid by sellers, both buyers and sellers feel the impact: relative to the initial price, 1, the price buyers pay rises, and the after-tax amount sellers receive falls. (We can also consider what would happen if it was consumers who were responsible for sending $0.25 to the government each time they bought a cookie. In this case, the amount that consumers would be willing to pay for another cookie is lower by the amount of the tax because they know that in addition to the price, they have to send $0.25 to the government. Therefore, the demand curve would shift down by the amount of the tax (from to D 2) and the supply curve would be unaffected. The quantity of cookies would fall (from 1 to 2), and the price would also fall (from 1 to 2). However, Tax ($0.25) S 2 the price of the cookie including the tax would rise. In fact, the impact on the quantity, the aftertax price received by sellers, and the after-tax price paid by consumers would be exactly the same as when the price is physically collected from sellers.) 2 1 2 tax 2 + tax 1 2 2 1 2 1 Tax ($0.25) D 2 d. These developments will shift both the demand curve and the supply curve. The news that chocolate has health benefits causes consumers, trying to obtain as much happiness as possible, to buy more cookies than before at a given price (and to buy less of other goods and services). Thus, the demand curve shifts to the right. The rise in the price of flour causes the price it takes to get firms to supply a given quantity to be higher than before. Thus the supply curve shifts up or back. 2 1 1, 2 S 2 D 2
7 The price of cookies unambiguously increases ( 2 is larger than 1). This is true because each of the individual shifts will increase the equilibrium price so the two together will definitely increase it. What happens to the equilibrium quantity, however, is ambiguous. A shift out in the demand curve will raise the equilibrium quantity, while a shift up in the supply demand curve will lower it. Therefore, what actually happens to the equilibrium quantity when both curves shift up will depend on which of the curves shifts more. As we have drawn it in the figure, the equilibrium quantity is essentially unchanged ( 2 looks to be the same as 1). However, there is no reason that this need be the case. 5.a. Although one could argue this question either way, it seems easier to make a case for a low price elasticity of demand than for a high one. Babies and young children are legally required to be in a safety seat when they are in a car, and most parents care enormously about the safety of their children. Thus, most parents who own a car will buy a safety seat regardless of whether the price is fairly high or fairly low. As a result, the number of safety seats demanded is likely to be pretty insensitive to their price. rice elasticity of demand is defined as the percentage change in the quantity demanded divided by the percentage change in price. This discussion implies that the percentage change in the quantity of safety seats demanded is likely to be smaller than the percentage change in the price. That is, the demand for safety seats is likely inelastic. (At the same time, demand is almost certainly not perfectly inelastic. For example, a fall in the price of safety seats would probably cause some parents who owned two cars to buy a second safety seat rather than only having one seat and moving it between their two cars.) b. Total expenditure on a good at the market equilibrium is the equilibrium price times the equilibrium quantity. If demand for a good is inelastic that means that the percentage change in the quantity will be less than the percentage change in price as we move along the demand curve. As a result, when the price falls because of a shift in supply, price times quantity will be smaller. The diagram shows the market for safety seats. In part (a), we suggested that the demand for safety seats is relatively inelastic. We can represent this (imperfectly) in the diagram as a demand curve that is relatively steep in the relevant range. The new discoveries will change the supply of safety seats. At a given price, firms are willing to supply more safety seats than before because the discoveries have reduced the costs of producing safety seats. Thus, the supply curve shifts down or to the right (from to S 2). When the supply curve shifts down, the percentage rise in quantity (the percentage change from 1 to 2) is smaller than the percentage fall in price (the percentage change from 1 to 2). Total spending is the product of price and quantity. Thus it is shown by the shaded rectangles in the diagram. Total spending before the shift in supply is given by the rectangle with corners at the origin, 1 on the horizontal axis, 1 on the vertical axis, and the intersection of and. This rectangle has width 1 and height 1, and so its area is 1 times 1, which is total spending on safety seats. Total spending after the shift in supply is shown by the rectangle with width 2 and height 2. As the diagram shows, with a low price elasticity of demand, total spending falls when supply shifts down. 1 2 1 2 S 2
8 c. The change will shift the demand curve for safety seats to the right. One way to say it is that the change means that more people are legally required to have car seats, and so at a given price, more people will buy car seats. Another way to say it is that the change will increase the additional utility people get from a safety seat, because of the reduced worries about penalties from breaking the law and because of the satisfaction of knowing that they are complying with laws about how to keep their children safe. So, at a given quantity, people would be willing to pay more. The outward shift of the demand curve from to D 2 will increase both the price and quantity of car seats (from 1 to 2 and from 1 to 2, respectively). 2 1 1 2 D 2 As always, total expenditure at the market equilibrium is the equilibrium price times the equilibrium quantity. Total spending before the shift in demand is shown by the rectangle with width 1 and height 1. Total spending after the shift in supply is shown by the rectangle with width 2 and height 2. Since price and quantity both rise, total spending in the market rises. Notice that this is true regardless of the elasticity of demand here, price and quantity are changing not because we are moving along the demand curve, but because the demand curve shifts. Because the demand curve shifts out, we are moving up along the supply curve, and so both price and quantity (and hence total spending) necessarily rise. d. Before the imposition of the price ceiling, the equilibrium price of safety seats was 1 and the equilibrium quantity was 1. The statement that the price ceiling is binding means that it is less than the price where supply and demand intersect that is, that it is below 1. At the price ceiling of, the quantity supplied ( S) is less than the quantity demanded ( D). The price of car seats will fall (from 1 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 safety seats. 1 S 1 D Shortage Once again, total spending is price times quantity. Total spending before the imposition of the price ceiling is therefore shown by the rectangle with width 1 and height 1; total spending after the imposition of the ceiling is shown by the rectangle with width S and height. Since price and quantity both fall, total spending in the market necessarily falls. As in part (c), this is true regardless of the elasticity of demand. As in that example, we are moving along the supply curve, and price and quantity both change in the same direction as we move along the curve.