1. Optimal Bundles Consider a market with two goods, x and z that has the following utility function

U = x^2/5 z^3/5

The price of good x is px = 6 and the price of good z is pz = 2 and the consumer has an income of Y = 120.

a) What is the marginal rate of substitution?

b) What is the marginal rate of transformation?

c) What are the optimal quantities of x and z consumed by the consumer?

2, Deriving Demand Functions

Consider a market with two goods, x and z that has the following utility function U= x^0.5z^0.5

a) What is the marginal rate of substitution?

b) As a function of the price of good x (px), the price of good z (pz) and the income level (Y ), derive the demand functions for goods x and z.

3, Income and Substitution Effects

Using the results from question 2, answer the following questions:

a) Suppose px = 5, pz = 10 and Y = 40. What is the optimal bundle consumed? (Label this as the initial bundle)

b) Now suppose that the price of good x increases to px = 8. Now what is the optimal bundle consumed? (Label this as the final bundle)

c) Calculate the decomposition bundle associated with this price change. (The answers won't be integers)

d) Calculate the Income Effect, Substitution Effect, and Total Effect for good g