Steve consumes only two goods, food and clothing. Let x be his consumption of food, and y be his consumption of clothing. Steve's preferences can be represented by the utility functionu(x; y) = x2y. He has an income m = 30. The market prices are px = 1 and py = 2.

(a) What is Steve's optimal choice?

Suppose that the income increases to m0 = 60. What is Steve's new optimal choice? Is clothing normal or inferior?

(b) Suppose that the government imposes a 50% value tax on food, and gives Steve a lump-sum subsidy of 15. What is Steve's new optimal choice? Is he better off or worse off, compared to part (a)?

(c) Fix m = 15 and px = 1. Derive Steve's demand function for clothing. Is clothing ordinary or Giffen?

Suppose that the price of clothing increases from py = 2 to py1 = 3. Draw on a graph the change in consumer surplus caused by it.

(d) Suppose that Steve's utility function is now u(x; y) = minfx; 2yg. His income is still m = 30.

The prices are still px = 1 and py = 2. What is Steve's optimal choice?