Yi has preferences over two goods, drinks with quantity d and dollars spent on food, f and has the utility function f u(f, d)=3d+3f- 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 p = $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 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? Yi has preferences over two goods, drinks with quantity d and dollars spent on food, f and has the utility function f u(f, d)=3d+3f- 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 p = $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 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?