Economics 370 Microeconomic Theory Problem Set 1 Answer Key 1) Bob has decided to go skiing for the weekend, but (absentminded professor that he is) he has forgotten his skis. He is considering three options: (1) stay indoors and read economics texts; (2) ski for two days and read economics texts one day; (3) ski for three days and forget economics. The costs of skiing are as follows: Transportation, $100; Lodging, $200; Ski pass, $20 per day; and Ski rental, $25 per day. Bob has also found out that the resort has a special three-day pass including rental for $75. Assume that Bob has already reached the ski slopes and that he cannot cancel his room reservations. a) What are the costs of the three options? First, note that the costs of transportation and lodging are sunk and cannot be recovered. Also, when more than one means of doing the same thing is available, Bob will chose the means that costs the least. In particular, in skiing two days, he can choose to buy the three-day pass and ski two days (the pass does not come with an obligation to use it all three days). That leaves costs as: Choice Cost Description Cost Read Economics $ 0 Ski two days min{ 2 × ( 20 + 25 ), 75 } 75 Ski three days min{ 2 × ( 20 + 25 ), 75 } 75 b) What is the cost of skiing a third day? The additional cost of the third day of skiing is $0. c) Suppose Bob figures it is worth about $30 a day for him to ski. What should he do? Choice Benefit Benefit – Cost = Net Benefit Read Economics $0 $0 Ski two days 2 × 30 = $60 60 – 75 = $ -15 Ski three days 3 × 30 = $90 90 – 75 = $15 Bob will choose the option that gives him the greatest net benefit. He will ski all three days. 2) In preparation for the 1996 Olympic Games, the city of Atlanta, Georgia, embarked upon a $500 million construction program. Brick masons who had earned $13 to $14 an hour in 1993 were commanding $17 to $18 in 1995. Use a supply and demand model to represent this situation. The most reasonable assumption is that the supply curve for brick masons did not change between 1993 and 1995. Demand, however, increased. This gives:3) Sketch indifference curves consistent with the following cases and comment on any of the assumptions A1 to A4 which are contradicted by the indifference curves you have drawn. a) John is willing to give away a cold beer in exchange for a dirty pair of old gym socks. The preferences are strange, but perfectly consistent with our assumptions. b) Eve likes apples but doesn’t care about pears. The preferences violate Assumption A3, Non-satiation, since more pears are not better. c) Tom can’t decide whether he would rather take his vacation in California or buy a pair of skis. There are two ways to interpret this question. Either Tom can’t decide because he is indifferent between the two: Or he can’t decide because he violates assumption A1 (completeness): he can’t figure out how to rank the two. The best way to draw that would be like this: P QSupply1993 Demand 13 1995 Demand 17 Cold Beer Gym Socks 1 1 Pears Apples Vacation Skis Vacation Skisd) Ray likes to play billiards and drink beer. But after playing five games of billiards, he doesn’t want to play any more. This violates non-satiation. More billiards is not better. Two possible forms of the indifference curves are shown below. In the second, more is not better, but it is not worse either. e) An individual consumes two goods, coffee and cake. More coffee is always preferred. If the individual has few cakes, more cakes are preferred but after some point additional cakes subtract from utility. This violates non-satiation. More cakes are not better. 4) WinZip used to have the following price schedule for site licenses (further below). If the total amount your organization has to spend is $500, graph your budget constraint for WinZip site licenses and the composite good. Size From Size To Price / License Min Expenditure Max Expenditure 0 1 $29.00 0 29 2 9 $22.00 44 198 10 24 $17.00 170 408 25 49 $14.00 350 686 50 99 $10.00 500 990 Note that two numbers of licenses will give an expenditure of $500. The first is between 35 and 36, and the second is 50. 0501001502002503003504004505000 5 10 15 20 25 30 35 40 45 50 BeerBilliards5 CoffeeCakes5) Carmen has an income of $10 which she spends on potatoes and all other goods. Potatoes cost $0.50 per pound. a) Suppose that the government agrees to pay half of Carmen’s potato bill so that potatoes now only cost her $0.25 per pound. She now chooses to buy 16 pounds of potatoes. Show how the government program affects Carmen’s budget line. Show Carmen’s optimal consumption point, x* and list its coordinates. The entire graph is shown below. The Government-induced budget curve is in dark blue. Carmen’s optimal consumption point is (16, $6) b) Now suppose that the government ends the program in part (a) and instead decides to give Carmen a cash gift of $4. Show Carmen’s new budget line. Does it go above, below or through x*? How do you know? Her new budget line goes through the old x* (in Magenta). To see this, observe that if she were to buy 16# of potatoes she would still be left with $6 exactly as before. 02468101214160 10203040 c) Of the two programs, which is the more expensive for the government? Which does Carmen prefer? Explain. In the first case, the government pays 16# × $0.25 / # = $4, which is exactly what it pays in the second case. Carmen will prefer the second program. To see this, notice first that, since her former bundle is affordable, she cannot be made worse off. Second, if preferences are “smooth”, then, since the new budget line cuts through the old indifference curve, the cash option will put her on a higher indifference curve. 6) Consider an economy consisting of two consumers: Anne and Bob both of whom have income of m = 100. Both consume rice and pasta only. Denote quantities of rice by x1 and quantities of pasta by x2. The price of pasta is p2 = 2. For both consumers rice and pasta are perfect substitutes: a) Anne’s preferences are given by uA(x1, x2) = 2x1 + x2. Draw indifference curves for Anne. Below, in Green. b) Suppose that Bob’s preferences are given by uB(x1, x2) = x1x2. Draw indifference curves for Bob. Below, in blue. In spite of what it said in the question above, these preferences are not consistent with perfect substitutes.c) Suppose that p1 = 5. Draw a budget constraint