1- Suzie purchases two goods, food and clothing. She has the utility function U(x, y) = xy, where x denotes the amount of food consumed and y the amount of clothing. The marginal utilities for this utility function are MUx = y and MUy = x.

a) Show that the equation for her demand curve for clothing is y = I/(2Py).

b) Is clothing a normal good? Draw her demand curve for clothing when the level of income is I = 200. Label this demand curve D1. Draw the demand curve when I = 300 and label this demand curve D2.

c) What can be said about the cross-price elasticity of demand of food with respect to the price of clothing?

2- Lous preferences over pizza (x) and other goods (y) are given by U(x, y) = xy. His income is $120.

a) Calculate his optimal basket when Px = 4 and Py = 1.

b) Calculate his income and substitution effects of a decrease in the price of food to $3.

c) Calculate the compensating variation of the price change.

d) Calculate the equivalent variation of the price change.

3- A firm's production function is Q = 5L^2/3 K^1/3 .

a) Does this production function exhibit constant, increasing, or decreasing returns to scale?

b) What is the marginal rate of technical substitution of L for K for this production function?

c) What is the elasticity of substitution for this production function?

4- Suppose a firm's production function initially took the form Q = 500(L+3K). However, as a result of a manufacturing innovation, its production function is now Q = 1000(0.5L + 10K).

a) Show that the innovation has resulted in technological progress in the sense defined in the text.

b) Is the technological progress neutral, labor saving, or capital saving?

5- Consider the production function Q = LK. Suppose that the price of labor equals w and the price of capital equals r. Derive expressions for the input demand curves