Yi has preferences over two goods, drinks with quantity d and dollars spent on food, f and has the utility function u(f, d) = 3d + 3f - f2 20 The price per drink is $3 and Yi's income is m dollars. Call dollars spent on food good 1. (a) Explain that the price of good 1 (dollars spent on food) is p1 = $1 per unit. (b) Are the two goods perfect substitutes for Yi? Why or why not? (c) Suppose m = $50. Can Yi afford the bundle (10, 10)? If he can afford it, is there another affordable bundle (give a specific example) that he strictly prefers to (10, 10)? Hint: use monotonicity of preferences). (d) Write down Yi's consumer's problem of maximizing his utility subject to his budget constraint and find his demand function for each of the two goods for any income level m 2 0. Plot Yi's Engel curve for good 1. (e) What is Yi's optimal consumption bundle if m = $50? If his income was $15 instead, what would be his optimal bundle? (f) Let m = $50 and suppose the price of drinks rose to $4. If the government gave Yi a $14 lump-sum income subsidy in addition to his $50, what would be Yi's budget set (plot it on a graph)? What is his new optimal bundle? Is he better off or worse off than in part (e) when he had m = $50 but drinks were cheaper