Question

2. Mike's preferences are represented by the utility function U(A, B)- A+2B. He has an income of $20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ii) graph the budget lines for each combination of prices, (iii) calculate and label the optimal consumption choice(s) for each combination of prices, and (iv) calculate the utility Mike derives from consuming the optimal consumption choice bananas

Answer 1

a) U (A, B) = A + 2 B P_A = 1 P_B = 2 M = 20 rightarrow A + 2 B = 20 Any level of apple & which satisfy A + 2 B = 20 in an optimal choice U (A, B) = A + 2 B = 0 b) U (A, B) = A + 2 B P_A = 2 P_B = 2 M = 20 rightarrow 2c A + 2 B = 20 rightarrow A + B = 10 If I an investing every thing n apple A = 10 7 U = 20 If I invest everything on B = 10 & U = 20 rightarrow optimal consumption choice (0, 10) U (A, B) = 20 c) U (A, B) = A + 2 B P_a = 1 P_B = 5 M = 20 rightarrow A + 5 B = 20 If A = 0, B = 4, U (A, B) = 0 + 2 times 4 = 8 If B = 0, A = 20, U (A, B) = 20 + 2 times 0 = 20 rightarrow optimal consumption choice = (20, 0) U (A, B) = 20 d) U (A, B) = A + 2 B P_A = 1 P_B = 0 M = 20 If (A, B) = (20, 0) i e spend all inverse n buying U (A, B) = 20