Final Exam cheat sheet The space provided below each question should be sufficient for your answer. If you need additional space, use additional paper. You are allowed to use a calculator, but only the basic functions. Use of advanced formulas (e.g., if your calculator does present value) or of material that you have programmed into your calculator is not allowed. Show your work for partial credit. It is very difficult to give partial credit if the only thing on your page is x = 3. Expected value is given by summing likelihood times value over all possible outcomes: Expected Value = Probability(i) Value(i). Outcomes i A fair bet is a bet with an expected value of zero. The future value of a lump sum payment of $x invested for n years at interest rate r is FV = x(1+r) n. The present value of a lump sum x payment of $x after n years at interest rate r is PV = (1 + r) n. (Note that this formula also works for values of n that are negative or zero.) The present value of an annuity paying $x at the end of each year for n year at interest rate r is 1 1 PV = x (1 + r) n r. The present value of the related perpetuity (with annual payments forever) is PV = x r. The inflation rate, i, is the rate at which prices rise. The nominal interest rate, r N, is the interest rate in terms of dollars. The real interest rate, r R, is the interest rate in terms of purchasing power. These are related by 1 + r R = 1 + r N 1 + i. When the inflation rate is small, we can approximate this as r R r N i.
A Pareto efficient (or Pareto optimal) allocation or outcome is one in which it is not possible find a different allocation or outcome in which nobody is worse off and at least one person is better off. An allocation or outcome B is a Pareto improvement over A if nobody is worse off with B than with A and at least one person is better off. A (strictly) dominant strategy is a strategy which yields higher payoffs than any other strategy regardless of the other players strategies. In an ascending price auction, the price starts out at a low value and the bidders raise each other s bids until nobody else wants to bid. In a descending price auction, the price starts out at a high value and the auctioneer lowers it until somebody calls out, Mine. In a first-price sealed-bid auction, the bidders submit bids in sealed envelopes; the bidder with the highest bid wins, and pays an amount equal to his or her bid (i.e., the highest bid). In a second-price sealed-bid auction, the bidders submit bids in sealed envelopes; the bidder with the highest bid wins, but pays an amount equal to the second-highest bid. Total revenue is price times quantity: T R = pq. The price elasticity of demand at point A measures the percentage change in quantity demanded (relative to the quantity demanded at point A) resulting from a 1% increase in the price (relative to the price at point A). The formula is ε(a) = % change in q % change in p = q q A q = p p pa = q B q A pa. q A p B p A q A p A In English If, at point A, a small change in price causes the quantity demanded to increase by a lot, demand at point A is elastic; if quantity demanded only changes by a little then demand at point A is inelastic; and if quantity demanded changes by a proportional amount then demand at point A has unit elasticity. In math If, at point A, the price elasticity of demand is less than 1 (e.g., 2), then demand at point A is elastic; if the elasticity is greater than 1 (e.g., 1 2 ), then demand at point A is inelastic; if the elasticity is equal to 1 then demand at point A has unit elasticity.
Name: 1. Consider the market for coal, which is used in power plants, Christmas stockings, etc. (a) (5 points) Explain what makes this (or any) market a competitive market. (b) (5 points) Give an example of a news story or other development that would increase demand for coal (without affecting supply). Draw a graph to show how the relevant curve shifts and what the impact is on the equilibrium price in the market. (c) (5 points) Give an example of a news story or other development that would increase supply of coal (without affecting demand). Draw a graph to show how the relevant curve shifts and what the impact is on the equilibrium price in the market. 2. (10 points) Explain, as if to a non-economist, why the intersection of the market supply curve and the market demand curve identifies the market equilibrium.
3. These questions are about carbon emissions. (a) (5 points) Carbon emissions fit into the pessimistic answer to the Big Question in microeconomics, i.e., when considering the market for carbon it is likely that individual optimization will not lead to good outcomes for the group as a whole. Explain why. Your answer should feature either a supply-and-demand analysis or a game theory analysis (or both). (b) (5 points) A cap-and-trade system (with a cap of, say, Q ) can be modeled as a perfectly inelastic supply curve for carbon. Draw a graph of the carbon market showing this; your graph should have labels on the axes (price and quantity) as well as the supply and demand curves. (Just make up a downward-sloping demand curve for carbon.) (c) (5 points) Under a cap-and-trade system, what would be the effect on the market equilibrium (both p and q) of a cash for caulkers program that promoted energy efficiency? Draw a supply-and-demand graph to explain your answer.
4. Below is a hypothetical market for oranges. P ($/pound) $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Q (millions of pounds per day) Suppose that the government decides to impose a sales tax of 50% on the sellers of oranges. (With a sales tax, if sellers sell a pound of oranges for $1, they get to keep $.50 and have to pay the government $.50; if they sell a pound of oranges for $2, they get to keep $1 and have to pay the government $1.) (a) (5 points) Show the impact of this tax on the supply and demand curves above. (b) (5 points) Explain (as if to a non-economist) why the tax shifts the curves the way it does. Your answer here must be quantitative, i.e., must explain not only the direction of the curve shift(s) but also the amount of the curve shift(s). (c) (5 points) Calculate the economic incidence of the tax, i.e., the amount of the tax burden borne by the buyers (T B = p 2 p 1 ) and the amount borne by the sellers (T S = p 2 t p 1 ). Then calculate T B their ratio. T S
(d) (5 points) Calculate the price elasticity of supply, ε S, at the original (pre-tax) equilibrium. Then calculate the price elasticity of demand, ε D, at the original (pre-tax) equilibrium. Circle your answers. (e) (5 points) Calculate the ratio ε S ε D. How does this ratio compare to the ratio of the tax burdens? P ($/pound) $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Q (millions of pounds per day) Figure 1: An extra graph in case you need it for anything...
5. Below is a hypothetical market for oranges. P ($/pound) $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Q (millions of pounds per day) Suppose that the government decides to impose a per-unit tax of $.40 per pound on the buyers of oranges. (a) (5 points) Show the impact of this tax on the supply and demand curves above. (b) (5 points) Explain (as if to a non-economist) why the tax shifts the curves the way it does. Your answer here must be quantitative, i.e., must explain not only the direction of the curve shift(s) but also the amount of the curve shift(s). (c) (5 points) Use either the marginal cost perspective or the supply curve perspective (your choice) to explain the perfectly elastic supply curve that we have in this example.
(d) (5 points) Calculate the economic incidence of the tax, i.e., the amount of the tax burden borne by the buyers (T B = p 2 + t p 1 ) and the amount borne by the sellers (T S = p 2 p 1 ). (e) (5 points) In some cases (including, hopefully, this one!) buyers end up bearing the entire economic burden of taxes. This makes it sound like it would be awesome to be a seller, but the book says that the reason buyers have to bear the entire tax burden is that competition is squeezing sellers so hard that sellers can t be squeezed any more. Explain this idea. Hint: it will almost certainly help to use the phrase market rate of return.
(f) (10 points) How would the economic incidence of the tax change if the $.40 per-unit tax was placed on the sellers instead of on the buyers? Use the graph below to analyze this situation (5 points), and briefly explain your answer (5 points). Your answer should indicate whether or not your analysis supports the idea of the Tax Equivalence Theorem. P ($/pound) $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Q (millions of pounds per day)
6. (Overinvestment as a barrier to entry) Consider the following sequential move games of complete information. The games are between an incumbent monopolist (M) and a potential entrant (PE). You can answer these questions without looking at the stories, but the stories do provide some context and motivation. Story #1 (See figure 2): Firm M is an incumbent monopolist. Firm PE is considering spending $30 to build a factory and enter the market. If firm PE stays out, firm M gets the whole market. If firm PE enters the market, firm M can either build another factory and engage in a price war or peacefully share the market with firm PE. PE Enter M War Peace (M: 10; PE: 10) (M: 35; PE: 5) Stay Out (M: 100; PE: 0) Figure 2: Story #1 (a) (5 points) Identify (e.g., by circling) the likely outcome of this game. (b) (5 points) Is this outcome Pareto efficient? Yes No (Circle one. If it is not Pareto efficient, identify, e.g., with a star, a Pareto improvement.) Story #2 (See figure 3 on next page): The monopolist (firm M) chooses whether or not to overinvest by building a second factory for $30 even though one factory is more than enough. Firm PE (the potential entrant) sees what firm M has done and decides whether to enter or stay out, and if PE enters then M decides whether or not to engage in a price war. (a) (5 points) Identify (e.g., by circling) the likely outcome of this game. (b) (5 points) Is this outcome Pareto efficient? Yes No (Circle one. If it is not Pareto efficient, identify, e.g., with a star, a Pareto improvement.)
Overinvest PE Enter M War Peace (M: 10; PE: 10) (M: 5; PE: 5) M Stay Out (M: 70; PE: 0) Don t Invest PE Enter M War Peace (M: 10; PE: 10) (M: 35; PE: 5) Stay Out (M: 100; PE: 0) Figure 3: Story #2 7. A Pareto efficient outcome may not be good, but a Pareto inefficient outcome is in some meaningful sense bad. (a) (5 points) Give an example or otherwise explain, as if to a noneconomist, the first part of this sentence, A Pareto efficient outcome may not be good. (b) (5 points) Give an example or otherwise explain, as if to a noneconomist, the second part of this sentence, A Pareto inefficient outcome is in some meaningful sense bad.
8. The Intergovernmental Panel on Climate Change reports that human activity (especially the burning of fossil fuels such as coal, oil, and natural gas) is warming the earth. (Note: With the exception of this fact, all of the numbers &etc in this question are completely made up.) (a) (5 points) Assume that global warming will raise sea levels and increase the frequency of hurricanes, leading to damages of $1 trillion (= 10 12 = 1, 000, 000, 000, 000) at the end of each year for the next seven years. What is the present value of that damage if the relevant interest rate is 4%? [Note: If all the zeroes confuse you or your calculator, use $1,000,000 or $1,000 instead.] Also: is the relevant interest rate nominal or real? (Circle one.) (b) (5 points) Next, assume that the full damages you ve calculated above will only occur with probability 1/3. With probability 1/3 the damages will be only half as big, and with probability 1/3 the damages will be zero. What is the expected value of the damage caused by global warming? [Note: If you didn t answer part 8a above, just assume for this part that the total damage is $1,000,000.] (c) (5 points) Next, assume that the hurricanes &etc won t happen for 100 years. So: take the expected damages you calculated in part 8b and compute the present value of having that amount of damage occur 100 years in the future if the relevant interest rate is 4%. [Note: If you didn t answer part 8b, assume for this part that the total damage is $1,000,000.]
9. Assume that you ve just bought a new carpet. The good news is that the carpet will last forever. The bad news is that you need to steam-clean it at the end of every year (i.e., one year from today, two years from today, etc.). What you need to decide is whether to buy a steam-cleaner or just rent one every year. You can use the bank to save or borrow money at a 5% interest rate. (a) (5 points) Will the amount you paid for the carpet affect your decision regarding renting versus buying? Why or why not? (b) (5 points) One year from today (i.e., when you first need to clean the carpet), you ll be able to buy a steam-cleaner for $500; like the carpet, the steam-cleaner will last forever. Calculate the present value of this cost. (c) (5 points) The alternative to buying is renting a steam-cleaner, which will cost you $20 at the end of every year forever. Calculate the present value of this cost. Is it better to rent or buy? (Circle one.) (d) (5 points) Imagine that your friend Jack calls to tell you that steamcleaners are on sale (today only!) for $450: You d have to be a moron to pay $20 every year forever when you can just pay $450 today and be done with it! Write a brief response explaining (as if to a non-economist) why you do or do not agree.
10. Catalytic converters are devices that reduce the amount of pollution produced by motor vehicles. Imagine that each of the 500,000 residents of X-ville (including you) owns a car without a catalytic converter, and that each of you has to decide whether or not to purchase one. Imagine further that (1) it will cost you $100 to purchase and install a catalytic converter; (2) each car that does not have a catalytic converter results in extra pollution that imposes health costs of one-tenth of one penny ($0.001) on you and every other resident of the city; and (3) like your fellow X-villians, you just want to do whatever has the lowest cost for you personally. (a) (5 points) If you and other X-ville residents are each allowed to choose whether or not to purchase a catalytic converter, what outcome does game theory predict? (b) (5 points) Is this outcome Pareto efficient? Explain briefly, e.g., by identifying a Pareto improvement if the outcome is Pareto inefficient. (c) (5 points) The central difficulty here is that each resident must decide what to do without knowing what the other residents are doing. If you knew what the others decided, you would behave differently. Do you agree with this argument? Circle one ( Yes No ) and briefly explain. (d) What sort of mechanism might you suggest for reaching the optimal outcome in this game? Hint: Make sure to think about enforcement!
11. These questions are about the Prisoners Dilemma and the Tragedy of the Commons. (a) (5 points) What do the Tragedy of the Commons and the Prisoners Dilemma have in common? (b) (5 points) What differentiates the Tragedy of the Commons and the Prisoners Dilemma? (c) (5 points) How can the Tragedy of the Commons be avoided? Briefly explain and give an example.