Economics 370 Microeconomic Theory Problem Set 1 Due 9 June 2004. Please hand it in at the end of the 9 June 2004 lecture. 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? b) What is the cost of skiing a third day? c) Suppose Bob figures it is worth about $30 a day for him to ski. What should he do? 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. 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. b) Eve likes apples but doesn’t care about pears. c) Tom can’t decide whether he would rather take his vacation in California or buy a pair of skis. d) Ray likes to play billiards and drink beer. But after playing five games of billiards, he doesn’t want to play any more. 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. 4) WinZip used to have the following price schedule for site licenses: Size of Order Price / License 1 $29.00 2 – 9 $22.00 10 – 24 $17.00 25 – 49 $14.00 50 – 99 $10.00 100 – 199 $7.00(that is, for example, if you order 15 site-licenses, you are charged $17 * 15 = $255) If the total amount your organization has to spend is $500, graph your budget constraint for WinZip site licenses and the composite good. 5) 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. 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? c) Of the two programs, which is the more expensive for the government? Which does Carmen prefer? Explain. 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. b) Suppose that Bob’s preferences are given by uB(x1, x2) = x1x2. Draw indifference curves for Bob. c) Suppose that p1 = 5. Draw a budget constraint for Anne and Bob. What would be their optimal choices of rice and