Question 3 (36points)

3. (36 points) Consider the utility function rig-hm?) = tins-1- Let the prices of good 1 and good 2 be 131 and p1: and let the consumer's income be m. a. State the consumer's maximization problem and use this problem to derive his demand functions for the two goods. (8 points) b. Is good 1 ordinary or Gi'en'.' Is good 1 normal or inferior? Is good 1 luxury or necessary? Justify your answers. (6 points) c. Suppose the prices per unit for the two goods are m = p: = $2 and the consumer's income is m - $100. Calculate his optimal consump- tion bundle- (6 points) d. Now suppose the price of good 1 increases to pi = $4 per unit. \""hat is his new optimal consumption bundle? {6 points} e. Calculate the substitution eect and the income eEect of the price change in demand of good 1. Illustrate them on a graph. {10 points)