EC 203.01 PS: CH 14 FALL 2005
1. Inspector Clouseau likes video games and hamburgers. In fact, his preferences can be represented by U(x,y)=ln(x+1)+y, where x is the number of video games he plays and y is the number of YTL he spends on hamburgers. Let px be the price of a video game and m be his income.
a) Write an expression that says that Clouseau’s marginal rate of substitution equals the price ratio. 1/(x+1)=Px
b) Since Clouseau has __quasilinear_ preferences, you can solve this equation alone to get his demand function for video games, which is _x=(1/Px)-1__. His demand function for the money to spend on hamburgers is __y=m-1+Px______.
c) Video games cost 0.25 YTL and Clouseau’s income is 10 YTL. Then Clouseau demands _3_ video games and _9.25__ YTL’s worth of hamburgers. His utility from this bundle is __10.64___.
d) If we took away all of Clouseau’s video games, how much money would he need to have spend on hamburgers to be just as well off as before? 10.64
e) Now an amusement tax of 0.25 YTL is put on video games and is passed on in full to consumers. With the tax in place, Clouseau demands _1_ video game(s) and ___9.5_ YTL’s worth of hamburgers. His utility from this bundle is __10.19__.
f) Now if we took away all of Clouseau’s video games, how much money would he have to spend on hamburgers to be just as well off as with the bundle he purchased after the tax was in place? 10.19
g) What is the change in Clouseau’s consumer surplus due to the tax? How much money did the government collect from Clouseau by means of the tax? -0.45, 0.25
2. The indirect utility function for a consumer with a utility function U(x1, x2) is defined to be a function V (p1, p2, m) such that V (p1, p2,m) is the maximum of U(x1, x2) subject to the constraint that the consumer can afford (x1, x2) at the prices (p1, p2) with income m.
a. Find the indirect utility function for someone with the utility function U(x, y) = 2x + y.
b. Find the indirect utility function for someone with the utility function U(x, y) = min {2x, y}. Explain how you got your answers.
a. m/(min {p1/2, p2}). Consumer spends entire income on x or y depending upon which gives more utility. b. M/(p1 +2p2). To maximize utility, consumer spends income in increments of one x and 2 y's.
3. Cato's utility function is U(x, y) = x + 10y - y2/2, where x is the number of x's he consumes per week and y is the number of y's he consumes per week. Cato has $200 a week to spend. The price of x is $1. The price of y is currently $5 per unit. Cato has received an invitation to join a club devoted to the consumption of y. If he joins the club, Cato can get a discount on the purchase of y. If he belonged to the club, he could buy y for $1 a unit. How much is the most Cato would be willing to pay to join this club?
a. $8, b. $28, c. $36, d. $56, e. $None of the above, B
4. If Dreyfuss (whose utility function is min {x, y}, where x is his consumption of earrings and y is money left for other stuff ) had an income of $15 and was paying a price of $8 for a pair of earrings, then if the price of earrings went up to $13, the equivalent variation of the price change would be:
a. $5.36., b. $8.33., c. $16.67., d. $2.68., e. $6.85., A
5. If somebody is buying 10 units of x and the price of x falls by $4, then that person's net consumer's surplus must increase by at least $40. FALSE
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