5.5. Ann consumes five goods. The prices of all goods are fixed. The price of good x is p,. She spends 25 percent of her income on good x, regardless of the size of her income. a. Show that her income elasticity of demand of good x is the same for any level of income, and determine its value. b. Would the value of the income elasticity of demand for x be different if Ann always spends 60 percent of her income on good x? 5.6. 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 MUy =y and MUy = x. a. Show that the equation for her demand curve for clothing is y = I/(2P,). b. Is clothing a normal good? Draw her demand curve for clothing when the level of income is I = 200. Label this demand curve D;. Draw the demand curve when I = 300 and label this demand curve D,. c. What can be said about the cross-price elasticity of demand of food with respect to the price of clothing? 5.7. Karl's preferences over hamburgers (H) and beer (B) are described by the utility function: U(H, B) = min(2H, 3B). His monthly income is I dollars, and he only buys these two goods out of his income. Denote the price of hamburgers by Py and of beer by Pg. a. Derive Karl's demand curve for beer as a function of the exogenous variables. b. Which affects Karl's consumption of beer more: a one dollar increase in Py or a one dollar increase in Pg? 5.8. David has a quasilinear utility function of the form U(z,y) = /x + y, with associated marginal utility functions MU, = 1/(2+/x) and MU, = 1. a. Derive David's demand curve for x as a function of the prices, Py and P;,. Verify that the demand for x is independent of the level of income at an interior optimum. b. Derive David's demand curve for y. Is y a normal good? What happens to the demand for y as P, increases