Bianca spends her income on entertainment (E) and clothes (C). Her preferences can be

represented by the utility function U(E, C)=EC

a. [5 points] Compute the marginal rate of substitution of entertainment for clothes. Is the

MRS increasing or decreasing in entertainment? What does it mean?

b. [8 points] Suppose that the price for entertainment is pE=2, the price of clothes if pC=3,

and Bianca's income I is 10. What is the amount of entertainment and clothes Bianca

consumes if she maximizes utility subject to her budget?5

c. [5 points] Suppose that the price of entertainment increases to pE'=4. What is Bianca's

new optimal bundle?

d. [12 points] In a diagram with entertainment on the x-axis and clothes on the y-axis, draw

the budget constraints from part b and c. Indicate the optimal bundles. Show the

substitution effect and the income effect of the increase in the price of entertainment.

Explain.

The graph for d should look something like this