7. Fred's preferences between pairs of shoes, S, and dollars available to spend on all other goods, D, can be represented by the utility function u(S, D) = SD. Because of government regulations, pairs of shoes are not sold together. Left and right shoes must be purchased separately at prices pr, and pR, respectively. Fred's endowment consists of m dollars and the price of D is 1. (a) Solve Fred's optimization problem and derive expressions for his optimal purchases and his optimized level of utility as functions of the exogenous variables (prices). (b) Fred's one-legged uncle has died and left him all his shoes (and they wear the same size.) Thus, Fred now enters the market with m dollars and Lo left shoes. Answer part (a) for this case. (Hint: Assume that Fred can sell shoes on the market for the same price that he purchases them.)
7. Fred's preferences between pairs of shoes, S, and dollars available to spend on all other goods, D, can be represented by the utility function u(S, D) = SD. Because of government regulations, pairs of shoes are not sold together. Left and right shoes must be purchased separately at prices pr, and pR, respectively. Fred's endowment consists of m dollars and the price of D is 1. (a) Solve Fred's optimization problem and derive expressions for his optimal purchases and his optimized level of utility as functions of the exogenous variables (prices). (b) Fred's one-legged uncle has died and left him all his shoes (and they wear the same size.) Thus, Fred now enters the market with m dollars and Lo left shoes. Answer part (a) for this case. (Hint: Assume that Fred can sell shoes on the market for the same price that he purchases them.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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6.
Transcribed Image Text:7. Fred's preferences between pairs of shoes, S, and dollars available to spend on
all other goods, D, can be represented by the utility function u(S, D) = SD.
Because of government regulations, pairs of shoes are not sold together. Left
and right shoes must be purchased separately at prices pL and pR, respectively.
Fred's endowment consists of m dollars and the price of D is 1.
(a) Solve Fred's optimization problem and derive expressions for his optimal
purchases and his optimized level of utility as functions of the exogenous
variables (prices).
(b) Fred's one-legged uncle has died and left him all his shoes (and they wear
the same size.) Thus, Fred now enters the market with m dollars and Lo
left shoes. Answer part (a) for this case. (Hint: Assume that Fred can
sell shoes on the market for the same price that he purchases them.)
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