Question

Answer following questions. It includes hints to follow and results in a better understanding of utility maximization.

          Homer buys donuts (x1) and beer (x2 )

          The price of donuts (1 doz.) is P1=5 and the price of beer (6 pack) is P2=10.

          Homer’s income (m) for spending on two goods is $100, m=100.

1. What is Homer’s budget constraint? What does this look like graphically?

2. What is Homer’s optimal bundle if his utility function is U homer=(X¹^3/4)(X²^1/4)

   Find an answer the following steps:

1. Take the natural log of both sides of the equation in order to simplify the utility functions. (This is the process for monotonic transformation. See handout for rule. When you take log transformation of lnXY = lnX+lnY )        

2. In order to maximize this utility function ( answer for 1), set the slope of budget line is equal to the slope of the indifference curve.

                   Thus, we are using MRS=MU1/MU2=P1/P2

1. Find out (x1* ) and (x2* ). thus, the optimal amount of beer and donut, Homer

consumes by solving the system equations

               Hint: Now, we have two equations and two unknowns.

Two equations: (answer for b) and budget constraint (answer for a)

Two unknowns: x1,y1

                        you can solve this system equation by substitution.

Answer 1