Take Home Exam #2.ECON 500 – Summer 2004.1) While standing in line at your favourite movie theatre, you hear someone behind you say: “I like popcorn, but I’m not buying any because it isn’t worth the high price.” Letting 1x(buckets of popcorn) and 2x(dollars spent on everything else), graphically illustrate the solution to this individual’s utility maximization problem. (8 points)2) Consider a consumer with 21)( xxXU . Suppose the price of commodity one is 41p, the price of commodity two is 12p, and the income of the consumer is 80I. a. Rank the following bundles in “order of preference,” from “least preferred” to “most preferred”: )10,4(A, )3,25(B, and)6,16(C. (6 points)b. Which of the bundles from part (a) are affordable? Explain. (6 points)3) Consider a utility maximizing individual with monotonic preferences who allocates income between two commodities. Her optimal consumption of commodity one is given by the function 121143),,(pIIppx .a. Is commodity one a normal good or an inferior good? Explain. (6 points)b. Is commodity two an ordinary good or a Giffen good? Explain. (6 points)4) Noel and his brother Liam enjoy going to the pub and consuming 1x=(cigarettes)and 2x=(alcohol). Liam’s utility is given by 214)( xxXUL, while Noel’s utility is given by 22211220544)( xxXUN. As a result, Liam’s marginal utility for cigarettes is 214)( xXMUL and for alcohol is124)( xXMUL. Finally, Noel’s marginal utility for cigarettes is 11202)( xXMUN and for alcohol is 22122)( xXMUN.a. Determine Liam’s Marginal Rate of Substitution (of cigarettes for alcohol), denoting this function by 2,1MRS. (4 points)b. Does Liam have “convex preferences”? Clearly explain. (4 points)c. Derive Liam’s Demand function for cigarettes and Demand function for alcohol, clearly showing all work. (8 points)d. Are Noel’s preferences complete? Clearly explain. (4 points)e. Are Noel’s preferences monotonic? Clearly explain. (4 points)f. Suppose a pack of twenty cigarettes costs $5 (so that the per unit price of cigarettes is 25.1p) and that each drink costs $4 (that is, each unit of alcohol costs 42p). If Noel goes to the pub with $75, how many units of 1x and how many units of 2x will he consume? Clearly explain. (6 points)5) Richard has utility of 21,2min)( xxXU , and as a result optimally consumes21*12 ppIx and 21*222ppIx. Suppose that initially Richard has income of100I, and faces prices of 31p and 12p, but then the price of commodity one decreases to 21p.a. Explain how Richard’s consumption of commodity one changes as a resultof this decrease in price. (6 points)b. Decompose the change in consumption of commodity one into that resulting from the substitution effect and that resulting from the income effect. Clearly explain. (6 points)6) Suppose that at "initial prices and income" of ),,(21Ipp, a consumer maximizesutility by choosing the bundle *X illustrated below. For each of the followingscenarios, identify the area in ),(21xx-space where the "new optimal bundle"could be. Clearly explain your answer.a. good one is “normal” and good two is a “complement to” good one; theprice of commodity one increases, with income and the price ofcommodity two held fixed. (8 points)1x2x*Xb. good one is "normal"; the price of each commodity increases by 10%,with income held fixed. (8 points)1x2x*X7) Suppose demand is given by ppD1120)(.a. Graphically identify the change in Consumers' Surplus as a result of anincrease in price from 7p to 11p. (4 points)b. Noting that the “demand curve becomes flatter as we move to lower price,higher quantity pairs,” place a numerical bound on the change inConsumers' Surplus as a result of an increase in price from 7p to11p. (6
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