Miami ECO315 Assignment 4 – Anita’s utility function
Miami University
Economics 315 Fall 2022
Assignment #4
1. Anita’s utility function is U(x,y) = x4y6 where x=basketball games and y=punching bags. Which bundle does Anita prefer: 1 basketball game and 5 punching bags, or 2 basketball games and 2 punching bags?
2. (not true, obviously!) President Crawford is deciding whether to invest more funds in the football program or the economics department, and he commissioned a study to estimate what the average Miami student wants. Controlling for many other things, the study’s estimate of the average student’s utility function is: U(W, E, T) = 2450W + 3670E – 1.26T where W=number of wins in Miami’s football season, E=number of economics classes offered at Miami, and T=tuition costs (in $).
a. How much extra tuition is the average student willing to pay for an additional win?
b. How much extra tuition is the average student willing to pay for an additional economics class?
3. Lillibet consumes only tea and shepherd pies. Assume that her monthly income is $180, the price of tea is $2/cup, and the price of a shepherd pie is $9.
a. Draw Lillibet’s budget constraint (with pies on the y?axis) and label it BC1.
b. In August, she maximizes utility by consuming 45 cups of tea and 10 pies. Add this point to BC1 (label it A) and draw the relevant indifference curve.
c. In September, the price of tea increases to $3/cup and the price of pie falls to $4.50. Her income is still $180. Draw the new budget constraint and label it BC2. Can Lillibet still afford her August consumption bundle of 45 cups of tea and 10 pies at the new prices?
d. Will 45 cups of tea and 10 pies still be optimal at the new prices? Explain what you know about the new optimal bundle.
4. Charles maximizes utility and consumes X and Y. The price of X is $12 and the price of Y is $20, and Charles’ total income is $300. Charles’ utility is given by U(x,y) = 4X0.5Y0.5.
a. How much of each good will Charles consume? Show your work (there are multiple ways to do this – any are fine, just show how you do it).
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