Economics 2 Spring 2018 rofessor Christina Romer rofessor David Romer SUGGESTED ANSWERS TO ROBLEM SET 1 1.a. Opportunity cost is defined as the value of what must be forgone to undertake an activity, where what is foregone is the next-best alternative use of the same resources. The software entrepreneur does two activities at work coding and long-term planning. If the entrepreneur devotes two of their working hours to long-term planning, that is 120 minutes of coding they are not doing. In 120 minutes, they could have written 360 lines of code, so that is the opportunity cost of undertaking two hours of long-term planning. b. The family decided to leave the house unoccupied while they were away. The next-best alternative activity would almost surely have been to rent the house out for the year. Therefore, the opportunity cost of the decision is the rent that could have been earned (minus any costs associated with the rental, such as taxes and wear and tear). (There are plenty of other possibilities or complications that one could imagine. For example, suppose that the next-best alternative use of the house was to let friends or family stay in it for free. Then the opportunity cost would be the happiness (or savings on rent and hotels) that the friends and family receive. Or, you might want to say that having someone live in the house would reduce the risk that the house would be broken into or be damaged by a broken pipe or fire. In that case, the opportunity cost of leaving the house empty could also include some estimate of the probable loss from having the house unoccupied; for example, you could multiply the probability of a burglary times the average loss for similar houses.) c. Again, opportunity cost is the value of what must be foregone to undertake an activity. When there is an active resale market for theater tickets, what must be foregone to attend the show is the resale value of the tickets on the date of use. In the example, that is 6 times $50, or $300. Notice, the fact that the family paid $1200 is not relevant on the day of use because they do not have the option of going back in time and not purchasing the tickets in the first place. What matters is what they are giving up on the day of use. 2.a. The C for health care and all other 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. This C probably has the conventional bowed-out shape. Some labor and capital are well suited to the production of health care, while other labor and capital are well suited to the production of everything else. Therefore, the opportunity cost of producing either of these types of output rises as we produce more of it. (Note: a nice thing about this problem is that it illustrates how any multidimensional classification can be reduced to a two-dimensional one x and not x.) C
The point where the C intersects the vertical axis is the point on the C where health care output is zero. Thus, it shows the amount of all other goods and services we could get if we devoted all of our resources to producing non-health care output and none to health care output. Similarly, the point where the C intersects the horizontal axis shows the amount of health care the economy can produce if we devoted all of our resources to producing health care. The slope of the C at a given point shows the amount that everything else would fall by if we increased health care output by 1 unit. Thus, the slope is (minus) the opportunity cost of health care output. 2 b. A reduction in H-1B visas that reduces the number of foreigners allowed to work in the U.S. 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 reduction in the labor force. This corresponds to a shift back in the C (from C 1 to C 2). All of the combinations of health care and everything else that can be produced are less good than before. C 1 C 2 Without more information, it is not possible to know if the C shifts back evenly or unevenly. If workers on H-1B visas were more common in one sector than the other, the sector where they were more common would see a larger drop in its production possibilities. c. Fundamentally, this problem focuses on the composition of production, not on the level of production. That is, it describes a movement along the C. The aging of the population suggests that the U.S. is likely to move to a point on the C that involves more production of health care and less production of everything else (say, from point A to point B). (Now, it is certainly possible indeed likely that the aging of the population would also affect the position of the C. Older people tend to retire, so for a constant level of population, aging implies a reduction in the available labor input. This would correspond to a shift back or to the left in the C; all of the combinations of health care and everything else would be worse than before. In reality, because of population growth and immigration, the available labor input is still growing despite the aging of the population. What is actually happening is that the aging of the population means that the C is shifting out less rapidly than it was in the past.) A B C d. There are two ways to think about what is going on in this example both equally valid. One is to think of there as being a true C for the economy (C 1) that shows the combinations of health care and everything else that could be produced in the economy if we used all of the available resources and organized them according to comparative advantage. In this specification, discrimination in the health care sector could be captured by there being an implicit C that lies inside the true C (illustrated by the A B C 1
dashed line). Because of discrimination, the economy doesn t reach its true C, and the shortfall is particularly large if we want to have a lot of health care. In this way of visualizing the situation, a reduction in discrimination would be captured by moving from a point inside the true C to one on the true C (say from a point like A to a point like B). An alternative way to think about the situation is to think of the initial C (C 1) as embodying the institutional constraint of discrimination in the health care sector. It shows the combinations of the two types of goods that the economy can produce given the available resources and the prevailing institutions. A reduction in discrimination in this C 2 formulation would show up as an outward shift of the C C (from C 1 to C 2). Notice that the C would 1 not shift out symmetrically. At a point where the economy is not producing much health care, discrimination against women in the health care sector does not reduce the production possibilities much. But, as we consider points where the economy produces more health care, the inefficiency caused by not using female workers who are very productive in health care is much larger. Thus, C 2 is particularly further out along the health care dimension. (Notice that allowing women to work in the health care sector gives us the ability to get more of both health care and everything else. This reflects the benefits of being able to specialize according to comparative advantage. When there is discrimination, women with a strong comparative advantage in health care cannot work in that sector. If discrimination is reduced, we can have these women (who have a low opportunity cost of producing heath care) work in the health care sector, and have some men who were producing health care (but who have a higher opportunity cost) produce other goods and services. As a result, we can have more of both types of output.) 3 3.a. The opportunity cost of a serving of haggis for a worker is the number of scones they could produce in the time it takes to produce 1 haggis. Since Angus could produce 2 scones in an hour or 4 servings of haggis, his opportunity cost of 1 haggis is ½ scone. Likewise, his opportunity cost of 1 scone is 2 haggis. The opportunity costs for each of the workers are given in the table below. Opportunity Cost of 1 Haggis (in Scones) Opportunity Cost of 1 Scone (in Haggis) Angus ½ 2 Fiona 5 1 5 Hamish 1 1 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 haggis for 1 hour and scones for 7 hours, the other two workers also produce haggis for 1 hour and scones for 7 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 restaurant. Every time the three workers work an hour producing haggis, they produce 6 servings. Every time the three workers work an hour producing scones, they produce 8 scones. Therefore, for the restaurant as a whole, when there is no specialization, the opportunity cost of 1 haggis is 4 3 scones.
The vertical intercept of the C shows the number of scones the three workers could produce in a day if they produced no haggis. Since they work for 8 hours per day and produce 8 scones per hour, they could produce 64 scones. The slope of the C is minus the opportunity cost of the good on the horizontal axis. Therefore, if we put haggis on the horizontal axis, the slope of the C for the restaurant, assuming no specialization, is 4 3. Therefore, the C for the restaurant with no specialization is a line starting at 64 scones and 0 haggis, with a slope of 4 3. The horizontal intercept shows the number of haggis the three workers could produce if they produced no scones. If the restaurant Scones 64 C without specialization 48 Haggis produced no scones, it could produce 48 haggis (6 haggis per hour times 8 hours). Notice that this is the point we get to if we start at no haggis and 64 scones and draw a line with a slope of 4 3 until we get to the horizontal axis. The C for the restaurant without specialization is a straight line because the opportunity cost of a serving of haggis 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 haggis, they give up 4 3 scones. c. When we allow the workers in the restaurant 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 restaurant decides to have the workers specialize according to who has the lower opportunity cost, it will use Angus to produce haggis first, then Hamish, and then Fiona. The specialization will cause the slope of the C to change as we move along it. Between 0 servings of haggis and the maximum amount that Angus can produce in a day (which is 32 servings), the relevant opportunity cost is Angus s he is the one switching between scone production and haggis production; Fiona and Hamish are just making scones. Therefore, the slope of the C is ½ in this range. Between 32 servings of haggis and 40 servings, which is the maximum amount Angus and Hamish can produce together, the relevant opportunity cost is Hamish s he is the one who is switching between the two activities; Fiona is just producing scones and Angus is just producing haggis. Therefore, the slope of the C is 1 in this range. Finally, between 40 servings of haggis and 48 servings, which is the maximum number of servings the three can produce if they all just produce haggis, the relevant opportunity cost is Fiona s she is the one switching between the two activities. Therefore, the slope of the C is 5 in this range. The vertical intercept of the C is 64 scones the total number of servings the three workers can produce if they each spend all 8 hours making scones. The horizontal intercept is 48 servings of haggis the total number of servings the three workers can produce if they each spend all 8 hours making haggis. 4
5 With specialization, the C of the restaurant has two kinks in it. This reflects the fact that with specialization, the opportunity cost rises as the restaurant produces more of a good. The slope of the C changes from ½ (Angus s opportunity cost) for the first segment, to 1 (Hamish s opportunity cost) for the second, and finally to 5 (Fiona s opportunity cost) for the third. This happens simply because the restaurant 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. Scones 64 48 40 C with specialization 32 40 48 Haggis The quantities of haggis and scones at each kink point are calculated by thinking about how much the workers can produce. The first kink occurs at the point where Angus is producing haggis full time and Hamish and Fiona are producing scones full time. When Angus is spending 8 hours producing haggis, he will make 32 servings; when Hamish and Fiona are producing scones full time, they will make 48 scones (8 from Hamish and 40 from Fiona). The second kink point occurs at the point where Angus and Hamish are both producing haggis full time and Fiona is making scones full time. If Angus and Hamish work 8 hours producing haggis, they will make 40 servings (32 from Angus and 8 from Hamish); when Fiona is producing scones for 8 hours, she will make 40 scones. 4.a. The supply curve for paper shows the quantity of paper supplied by producers at each price; the demand curve shows the quantity of paper 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 rise in the price of pulpwood means that the price of an input to the production process has risen. rofit-maximizing firms will only be willing supply a given quantity of paper at a higher price. Equivalently, firms will want to supply less at a given price. This corresponds to a shift up or left in the supply curve (from to S 2). The equilibrium price of paper will rise (from 1 to 2) and the equilibrium quantity will fall (from 1 to 2). 2 1 2 1 S 2 S1 b. If greater environmental awareness leads consumers to prefer digital documents to paper ones, there has been a change in tastes away from paper. At every price for paper, the quantity demanded is lower. This suggests that the demand curve for paper has shifted down or to the left (from to D 2). The equilibrium price and quantity of paper will both fall (from 1 to 2 and from 1 to 2, respectively). 1 2 2 1 D 2
6 c. Before the imposition of the price floor, the equilibrium price of paper was 1 and the equilibrium quantity was 1. The government imposes a price floor or a minimum price that is above the initial equilibrium price. Therefore, the price of paper will rise (from 1 to ). At the price floor of, the quantity demanded ( D) is less than the quantity supplied S); there is an excess supply (or surplus) of paper. When there is a price control, the quantity bought and sold will correspond to the smaller of the quantity supplied and the quantity demanded at the controlled price. In this case, the quantity falls from 1 to D. Even though many sellers would like to sell more at, they are unable to because there is insufficient demand. 1 D 1 S Excess Supply d. A subsidy is a negative tax; instead of collecting money from people, the government gives them money. The problem states that the government implements of subsidy of $0.50 per unit of paper, which is paid to sellers. A subsidy paid to sellers will show up in the supply curve. At any quantity, the price that it would take to get sellers to supply the good is lower than before (by the amount of the subsidy). This is true because sellers know they will receive both the price and the payment from the government on each unit they sell. Thus, S 2 is below by $0.50 at each quantity. Because the seller receives the subsidy, the demand curve is unaffected. Subsidy ($0.50) As a result of the subsidy, the equilibrium quantity increases (from 1 to 2) and the equilibrium price falls (from 1 to 2). The amount that sellers receive on each unit is 2+subsidy. Notice that a subsidy increases the amount bought and sold in the market. Also, even though the subsidy is physically paid to sellers, both buyers and sellers get some benefit. Relative to the initial price, 1, the price buyers pay falls and the amount sellers receive rises. 2 + subsidy 1 2 1 2 S 2 5.a. Both the supply curve and demand curve of some good shift out. That is, S 2 is to the right of, and D 2 is to the right of. The equilibrium quantity will unambiguously increase ( 2 is larger than 1). This is true because both of the individual shifts will increase the equilibrium quantity so the two together will definitely increase it. 2, 1 S 2 D 2 1 2 b. What happens to the equilibrium price, however, is ambiguous. A shift out in the supply curve will lower the equilibrium price, while a shift out in the demand curve will raise it. Therefore, what actually happens to the equilibrium price when both curves shift out will depend on which of the curves shifts more. As we have drawn it in the figure, the equilibrium price is essentially unchanged ( 2 is the same as 1). However, there is no reason that this need be the case.
6.a. Residential natural gas is used for things like furnaces, hot water heaters, clothes dryers, and stoves. For most consumers, the amount of natural gas they consume is determined mainly by their choice of appliances. Since that decision is made very infrequently, it is unlikely that households will be very sensitive to the price of natural gas in the short run. If the price of natural gas falls, they might set the temperature on their thermostats a little higher or dry some clothes they used to let air dry (and so use more natural gas), but their options for using more or less natural gas in the short run are likely quite limited. For this reason, we would expect households price elasticity of demand for natural gas to be quite low. rice elasticity of demand is defined as the percentage change in the quantity demanded divided by the percentage change in price. In the short run, the percentage change in the quantity demanded of natural gas is likely to be smaller than the percentage change in the price. Thus, the short run demand for natural gas is likely inelastic. 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 a result, when the price falls, price times quantity will be smaller. The diagram shows the residential market for natural gas. In part (a) we suggested that the demand for natural gas is relatively inelastic in the short run. We can represent this (imperfectly) in the diagram as a demand curve that is relatively steep in the relevant range. The widespread adoption of fracking corresponds to a technological change in the supply of natural gas. At every price, firms are willing to supply more natural gas than before because the new technology has reduced the extra cost associated with producing another unit of natural gas. 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 residential spending on natural gas. 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. c. Over the longer run, households are more likely to be replacing their major appliances either because the appliances break or because households have the time and energy to choose new appliances and line up delivery and installation. For this reason, we would expect households to be more sensitive to the price of natural gas. For example, if the price of natural gas stays low for a while, households may decide that they should replace their oil furnace with a natural gas one. Thus, demand for natural gas is likely to be more elastic in the long run than in the short run. (One complication you may realize is that there is a non-residential market for natural gas. Over the long run, electric power plants too may choose to switch fuel (indeed, in recent years natural gas use in electricity generation has increased substantially). The fall in the price of natural gas in the non-residential market may thus affect the price of electricity. It is still the case that household demand will be more sensitive to the price of natural gas in the longer run for the reasons described above. But, it may also be the case that the prices of both residential natural gas and residential electricity fall in the longer run because of the fall in the price of natural gas.) 2 1 1 2 S 2 7