Mary consumes two goods diet coke x and cheeseburgers y

Question

Mary consumes two goods, Diet Coke (X) and Cheeseburgers (Y). Mary’s Utility function is represented by U(X,Y) = 3XY² . Her marginal utility function for X is MU_x = 3Y² . Her marginal utility function for MU_y = 6XY. The current price of Diet Coke is $4. The current price for cheeseburgers is $5. Mary’s income is $120.

a. Write an expression for Mary’s budget line and graph it with Diet Coke on the horizontal axis. Please label all intercepts, slopes, axes, etc.

b. What is the marginal rate of substitution if X=10 and Y=16? Does this number look familiar? If so, why?

c. Calculate a new budget line if the price of diet coke increases to $6. Please graph this and label all intercepts, slopes, etc.

d. If the price of diet coke is $6, what is the marginal rate of substitution if X=20/3 and Y= 16. Does this number look familiar? If so, why?