Problem 3 (1 point) Suppose that the utility function for the consumer is u(x, y

Question

Problem 3 (1 point) Suppose that the utility function for the consumer is u(x, y) = x + y. Suppose his budget constraint is x + y = 100. Prove either graphically or analytically why only one good will be consumed. Show all your work!

Problem 4 (3 points) Consider the following information about Bruce Wayne. His current wealth is 100. He will meet with Miss Kyle tomorrow. If she is in the good mood, she will help him to fight crime, increasing his wealth to 121. However, she can also decrease his wealth to 64 if she decides to join Bane. You can consider both events equally likely. You can assume that Mr. Wayne’s utility function is u(w) = w. (

a) What is Mr. Wayne’s attitude towards the risk? Explain and show your work! 1

(b) Suppose that in order to hedge himself from Miss Kyle, Mr. Wayne can purchase the insurance: hire Robin. What is the maximum amount Bruce is willing to pay Robin to eliminate potential losses?

(c) How will your answer to the previous question change, if Mr. Wayne has the utility function: u(w) = w? u(w) = w 2 ?

Explanation / Answer

Problem 3.

as budget constraint x+y=100

so we can assume that Px=Py=1

MUx = dU/dx = 1

MUy = dU/dy = 1/2sqrt(y)

MUx/MUy = MRS = 2sqrt(y)

MRS for optimality is equal to Px/Py

2sqrt(y) = 1/1

y = 1/4

So we see that only one good is consumed

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