广东财经大学-广东商学院-中级微观经济学-试题-Problem Set 1

Intermediate Microeconomics

Fall 2010

Problem set 1

Handing Form: Only Hand Writing

Assigned Time: 9/18

Due Time: by 9/25, 5:40 pm

1. Given the following utility functions, a) what type of utility is represented? b) Derive these utility functions’ MRS. Do their results have something in common? c) Compute MRS values for each utility function at the point of (x=1,y=4) and (x=4,y=1), can you interpret the result? (Hint: it may be related to some properties of utility function)

Utility Function1: U(x,y) x y

Utility Function2: U(x,y) xy0.50.5

Utility Function3: U(x,y) 0.5lnx 0.5lny

Utility Function4: U(x,y) 2x0.5 2y0.5

2. Assume there are two restaurants to choose in Peking University, namely Campus (C) and Subway (S). Your utility function is U(C,S) CS0.40.6 .To make a simplification, we also assume that each meal costs 5 Yuan in Campus and 15 Yuan in Subway, denoted asPC 5and PS 15. You have 100 Yuan (I) to consume on these two restaurants. Then, a) how many times will you visit each restaurant? b) Howt your decision will be changed if Campus’s pricePC rises to 8 Yuan? c) Now, get back to the original prices. However, you lose 25 Yuan with a bad luck. What is your new decision?

3. After having the dinner at home, Junpeng getsIYuan. Then he has decided to use this money either buying books (B) or going swimming(S). Prices arePBYuan for one book andPSYuan for swimming once. His utility function isU(B,S) BS0.50.5.

a) Derive his individual demand curve in terms ofI,PB,PS. Assume I 800, PB 25, PS 16, what are his optimal decision and his maximum of utility?

b) Derive his Compensated Demand Curve in terms ofU,PB,PS. AssumeU 20,PB 25,and PS 16, what are his optimal decision and his minimum of expenditure?

c) Comparing the result in a) with the result in b), what’s their relationship? Can you explain it by words?

d) Compute the income effect and the substitution effect at the optimal point in a) or b). Using the results to show that Slutsky equation holds at the optimal point.