**Unformatted text preview: **Economics 3010
Fall 2009 Professor Daniel Benjamin
Cornell University Problem Set 1 This problem set is due in section on Friday, September 11. Please collect your answers into a stapled packet, and write your own name and your TA’s name on the front of each packet. 0. (Aplia) Please do the assigned problems on the Aplia website. These problems are due at 11:45pm on Thursday, September 10. 1. (Opportunity cost: Common mistakes) (a) Ezra and Cornell are both students at the same upstate New York Ivy League university. Ezra wins a ticket from a radio station to see a jazz band perform at an outdoor concert. Cornell has paid $18 for a ticket to the same concert. On the evening of the concert, there is a tremendous thunderstorm. Ezra decides that because he won’t enjoy the concert while sitting in the rain, he won’t go. Cornell, however, reasons that he doesn’t want the $18 he’s already paid to go to waste, so he’ll go to the concert, even though he would not go if his ticket had been free. Cornell has committed what economists call the “sunk cost fallacy” because he is allowing his behavior to be influenced by costs he incurred in the past (costs which are already “sunk”). (i) Using the concept of opportunity cost, explain why Cornell’s cost‐benefit analysis is mistaken. (ii) Some Americans who continue to support the war in Iraq argue that we need to keep fighting to justify all the money that has already been spent and the lives that have already been lost. Explain why this argument is an example of the sunk cost fallacy. (b) Jane has just moved to a new city and needs to buy a clock radio and a television set. She is about to buy a clock radio at her local electronics store for $20 when a friend sends her a text message saying that the exact same radio is on sale at Wal‐Mart for $10. Even though Wal‐Mart is a 15‐minute drive away, Jane decides to drive there to buy the clock radio since she can get it half off. A week later, she is at her local electronics store shopping for a TV set. The one she likes costs $1010. Before she purchases it, she checks with her friend (who seems to spend a lot of free time at Wal‐Mart), who tells her it sells for $1000 at Wal‐Mart. This time, Jane decides it’s not worth the trip for a 1% savings. Explain why Jane’s behavior is inconsistent with a proper understanding of opportunity cost. [ Note for interested students: The facts that people often commit the sunk cost fallacy (part a) and think in proportions (part b) themselves are relevant for understanding real‐world decision‐making. For that reason, these are ongoing topics of research within the field of behavioral economics (the intersection of economics with psychology). ] 1 2. (Supply and Demand: Log‐linear supply and demand functions) [ You can find solutions to some parts of this question in chs. 15.5, 15.8, 16.4, and the appendix to ch.15. Feel free to use what you learn from those parts of the textbook in writing up your answer, but try the problems first with the textbook closed, and make sure you write up solutions in your own words. ] (a) First suppose the demand function in a market is “linear”: Qd = D(P, a) = max{a – b P, 0} where a > 0, b > 0, and P > 0. (i) Explain why it makes sense to write the demand function this way (with the max) rather than just as D(P, a) = a – b P. (ii) Calculate the price elasticity of demand when a – b P < 0 (the part of the demand curve where Qd = 0). Calculate the price elasticity of demand when a – b P > 0 (the part of the demand curve where Qd > 0). Show that the price elasticity of demand in this latter case depends on which point of the demand curve we’re interested in (i.e., it depends on the level of P). (b) Now suppose the demand and supply functions in a market are given by: Qd = D(P, a) = exp{a} × P^{‐b} (1) (2) Qs = S(P, c) = exp{c} × P^{d} where a, b, c, d, P > 0, and exp is the exponential function. (i) Draw a graph of the supply and demand curves (with P on the y‐axis and Qd, Qs on the x‐axis). (ii) Explain why it is not necessary to use the max formulation (that we used in part (a) of this question) with this specification of the demand and supply functions. (iii) Calculate the price elasticity of demand and the price elasticity of supply. Do these depend on the levels of price and quantity? (iv) Parts (ii) and (iii) explain why economists often find it convenient to use equations (1) and (2) as approximations to the demand and supply functions, rather than linear functions (which are the approximations usually used in math classes). Now, define new variables qd = ln(Qd), qs = ln(Qs), and p = ln(P), where ln is the natural logarithm. Show that equations (1) and (2) can be rewritten as linear in the logarithms of the original variables: (3) qd = a – b p qs = c + d p (4) It is for this reason that equations (1) and (2) are called a log‐linear specification of the demand and supply functions. 2 (v) Use equations (3) and (4) to solve for the equilibrium q* and p*. (vi) Notice that the equilibrium (log) quantity, q*(a, c), and (log) price, p*(a, c), can be considered as functions of a and c (both of which are exogenous variables). Calculate each of the following comparative statics: ∂q*/∂a, ∂p*/∂a, ∂q*/∂c, and ∂p*/∂c. Illustrate these comparative statics on two supply and demand diagrams, one showing the effects of a change in a and one showing the effects of a change in c. (The axes can be either P and Q, or their logarithms, p and q; it’s up to you.) (vii) Total revenue for sellers in this market is R = P Q. Hence in equilibrium, ln(R) = p*+ q*. Prove that ∂(p*+ q*)/∂a > 0. Prove that ∂(p*+ q*)/∂c > 0 if and only if demand is elastic. What do these results imply about how total revenue changes when supply or demand shifts? Use these results to predict how government policies that reduce the supply of heroin will affect the revenues of heroin producers. Also use these results to predict how government policies that reduce the demand for heroin will affect the revenues of heroin producers. 3. (Supply and Demand: Creating a market for live kidneys) [ The figures and numbers for this question are drawn directly from a recent research paper: Becker, Gary S., and Julio Jorge Elias (2006), “Introducing Incentives in the Market for Live and Cadaveric Organ Donations,” University of Chicago mimeo. If you are interested, feel free to read more details: http://home.uchicago.edu/~gbecker/MarketforLiveandCadavericOrganDonations_Becker_Elias.pdf ] Ill individuals often die while waiting years for a kidney transplant because fewer kidneys are donated than are needed. Of the kidneys that are donated, most are from cadavers, and relatively few are from live donors, even though donating a kidney has become much safer in recent years. For the U.S. in the years 1990‐2005, Figure 1 shows the total number of patients on the waiting list, the number of transplants performed, and the number donated from live donors. The gap between the size of the waiting list and the number of transplants performed is increasing every year. Figure 4 shows the annual excess demand for kidneys, the gap between the quantity demanded for kidneys and the quantity supplied of kidneys. (The “annual excess demand” equals the annual number who join the waiting list, as opposed to the number who are on the waiting list. That is the appropriate notion of annual excess demand if we imagined that the market was in equilibrium last year, and this year is the first year where there is excess demand. This is the thought experiment we are interested in because we want to use data from when the market is in disequilibrium to predict what would happen if the market were in equilibrium.) 3 4 (a) It is currently illegal in the U.S. for a person to receive payment for donating a kidney. The vast majority of live donors are family members of individuals on the waiting list. Some people would say that there is no market for kidneys in the U.S. An economist would say that there is a market, but the market has excess demand because there is a price ceiling of $0. Explain the economist’s point of view. (b) Explain why the total quantity of kidneys demanded in 2005 is the number of kidney transplants in 2005 plus the excess demand in 2005. What is the total quantity demanded in 2005? (c) Figure 5 shows a supply and demand diagram for the live kidney market. The current situation is illustrated by the demand curve DD (the curve that starts at “D” and ends at “D”) and the supply curve SS (the curve that starts at “S,” takes a 90‐degree turn, and ends at “S”). The average cost of performing a kidney transplant operation is about $160,000. As long as someone (the patient or insurance company) pays this cost, and as long as a family member is able to donate a live kidney, the operation will be done. Imagine that all family members who can make a donation do so (even without being paid for it). How does that explain why the supply curve is perfectly elastic up to a point and then becomes perfectly inelastic? 5 (d) We want to predict what would happen if it became legal to receive payment in exchange for a kidney donation. The main costs faced by a potential live kidney donor are: • Risk of death. The risk of dying as a result of a kidney transplant is less than 0.1%. A variety of other research studies suggest that individuals who earn $35,000 per year often make decisions about what kind of job to take (in terms of a tradeoff between higher salary and higher risk of death) consistent with valuing their own life at around $5 million. This suggests that many people would be willing to accept an increase of 0.1% in their own chance of death if they were paid at least $5,000. • Recovery from surgery takes about 4 weeks. For an individual who earns $35,000 per year, the opportunity cost of income from losing a month of work is about $35,000 * 4 / 52 ≈ $2,700. • Small reduction in quality of life from only having one kidney. Suppose a potential live donor would be willing to accept this reduction in quality of life in exchange for $7,500. Why does this calculation suggest that a large supply of live kidneys would be available if each donor were paid at least $15,200? Why is the new supply curve S*S* drawn as perfectly elastic at a price of $175,200? Explain why the predicted quantity demanded, Q1, is larger than the number of transplants actually performed today, Q0, but smaller than the quantity demanded today, Q0’. (e) What is the predicted price for kidneys? If the price of kidneys is added to the cost of the surgery, what is the predicted price of the transplant operation for ill individuals? What is the percent change in price? If the elasticity of demand is ‐1, what is the predicted percent decline in quantity demanded? (f) Combining your answers from parts (b) and (e), what is the predicted the number of kidneys demanded at the new equilibrium? How many more kidney transplant operations are predicted to occur if it were legal to give monetary compensation to kidney donors? [ Note for interested students: Clearly this analysis is very rough, based on a variety of estimates that could be inaccurate. This should make you wonder whether the results are robust to alternative assumptions! When results are based on estimates that may be inaccurate, economists often perform a sensitivity analysis. That is, they re‐do the analysis with different assumptions to see how much the results change. I will not ask you to do this, but the authors of the original research paper do. This entire analysis is an example of positive economics. When the authors take the next step of recommending that the government allow a free market in live kidneys, they are now doing normative economics. ] 6 ...

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