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Prelim%201 - Economics 3010 Fall 2008 Professor Daniel...

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Unformatted text preview: Economics 3010 Fall 2008 Professor Daniel Benjamin Cornell University EXAM #1 You have 75 minutes for this exam. No calculators are allowed. There are 65 points on the exam, and you should plan to spend approximately as many minutes per question as they are worth in points. This should leave you five minutes at the beginning to read over the test and five minutes at the end to check your answers. Please do all of the questions on this exam. Use a separate blue book for each part of the exam (I, II, and III), three in total. On the cover of each blue book, please write your name, your TA’s name, your section time, and the part of the exam answered in that book. Read over the whole test before starting. To keep the test as fair as possible, we will not answer any questions during the test. Some advice: Complete answers will include definitions of relevant terms and verbal intuition (in addition to graphs or formulas, if those are appropriate). Do not get hung up on calculations when answering a question. If you get the formulas and explanation correct, little credit will be deducted for mistakes in calculation. The questions vary in difficulty, so try to keep moving through the exam; if you are having trouble with something, it is probably a good idea to skip it and come back later. Good luck! I. True / False / Uncertain Your grade on these questions will depend on the generality, completeness, and persuasiveness of your explanation, not simply on whether the “true” or “false” is correct. The objective here is to provide an answer that convinces; not merely an answer that is “not wrong.” At the very least, make sure that you give clear definitions for the relevant economic terms used in the question. Please use a separate blue book for this section. (5 points) 1) The opportunity cost of going to college includes not only the foregone income from working full‐time, but also all the time and effort spent going to high school. (5 points) 2) The demand for narrow categories of goods (like milk) tends to be more elastic than the demand for broader categories (like food). (5 points) 3) The fact that the marginal rate of substitution between two goods equals the price ratio at a consumer’s optimum means that every consumer gets exactly the same level of utility from those two goods. 4) If Madeleine’s demand function for croissants is x*(p,m) = (m / p)2 , then croissants (5 points) are a luxury good for Madeleine. (5 points) 5) If the price of bread falls, then the quantity of bread demanded will increase. II. Brief Problem (5 points) Bob, Ted, and Alice are trying to decide where to go for dinner. The three possibilities are McDonald’s (MD), Kentucky Fried Chicken (KFC), and Pizza Hut (PH). The preferences of each person are given below: Ted Alice Bob st MD PH KFC 1 Choice nd 2 Choice KFC MD PH rd PH KFC MD 3 Choice They have decided to use majority voting to select a restaurant. For each pair of restaurants, they vote and say that the group prefers the restaurant that gets the most votes. Explain why it is impossible to write down a utility function that describes the group’s preferences. III. Multi‐Part Problem Note: This question is designed so that if you skip part of the question, you still have enough information (stated explicitly earlier in the question) to answer later parts of the question. Please answer as many parts as you can. Suppose Mom’s utility function for gasoline (x) and money (y) is U(x, y) = [x(‐1/σ)+1 / ((‐1/σ)+1)] + y, where σ > 0 is a constant, and her budget constraint is Px + y ≤ m. (4 points) (a) Are her preferences well‐behaved? Explain. Draw a diagram of Mom’s indifference curves. (4 points) (b) Show that Mom’s demand function for gasoline is x*(P, m) = P‐σ if m ≥ P1‐σ, and x*(P, m) = (m / P) otherwise. (From now on, we will assume that m ≥ P1‐σ.) (5 points) (c) Suppose the demand side of the market for gasoline is composed of 100 Moms, each of whom has the preferences given above. Let the (base 10) log of price be denoted by p = log10(P), and let the (base 10) log of market demand for gasoline be denoted by xd = log10(Xd). Explain why the (base 10 log of) market demand for gasoline is xd(p) = 2 – σ p. Show that the price elasticity of demand for gasoline in this market equals ‐σ. (5 points) (d) Suppose the (base 10 log of) market supply for gasoline is xs(p) = 1 + p. Show that the equilibrium (log) price, p, is equal to 1/(1+σ), and the equilibrium (log) quantity, x, is equal to (2+σ)/(1+σ). (5 points) (e) In 1973, the Organization of Petroleum Exporting Countries (OPEC), a major international cartel, successfully colluded in restricting the supply of gasoline. As a result, suppose the (log of) market supply for gasoline is now xs(p) = p. Show that the new equilibrium (log) price, p, is equal to 2/(1+σ), and the equilibrium (log) quantity, x, is equal to 2/(1+σ). How do the new equilibrium price and quantity compare to the old equilibrium? (5 points) (f) Show that revenues of gasoline exporters increase as a result of the supply restriction if and only if σ < 1. Explain intuitively. (7 points) (g) The U.S. government responded to the upward pressure on prices by imposing “price controls,” making it illegal to charge more than a certain price for gasoline (in an effort to prevent inflation). Suppose that σ = 2, and suppose the price ceiling mandated that p ≤ ½. Draw a supply/demand diagram illustrating the price ceiling. Calculate the new equilibrium (log) quantity of gasoline supplied and demanded. Show that the quantity traded is x = ½. Explain why there were long lines at gas stations in 1973. ...
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