Question 5 For each part that follows, assume I buy only bananas (b) and mangos (m) and have income y. My budget constraint is pbb+ pmm S 1,1. For each case, solve the consumer's choice problem: nd my demand for bananas and mangos as functions of market prices and income. i) Identify the type of preferences: perfect substitutes) perfect complements, or plain old diminishing marginal rate of substitution preferences. ii) For each case, solve the consumer's choice problem: nd my demand for bananas and mangos as functions of market prices and income. a) u(b, m) : 2l7'/Zm'/2 b) u(b, m) : 2b + 2721 c) u(b, m) = min{3b, 5m} Question 6 Describe a situation in which a person's preferences violate: a) Completeness b) Monotonicity (choose something that violates even weak monotonicity; it should also be neither always good nor always bad) c) Convexity (choose something that violates even weak convexity) Question 7 What is the tradeoff represented in the slope of the indifference curve? What is the tradeoff represented in the slope of the budget constraint? How are these different from each other? Question 8 How do you know when you can use the Lagrangian method to solve a consumer choice problem? Question 9 How do these concepts relate to each other: a) Utility, preference, and indifference curves