Question 4 Suppose that the consumer's utility maximization problem is given by: max (m: + by subject to 1953.1: l pyy = m, with :c 2 0 and y may 20. Suppose that equal quantities of butter and margarine are perfectly substitutable. Butter costs $2 per stick and margarine costs $1 per stick and the consumer has 20 dollars. 4-1 If x denotes one stick of margarine and y denotes one stick of butter, what are the values of a and b? For the rest of the question, let X denote one stick of margarine and y denote one stick of butter. 4.2 Carefully draw a diagram with two or three indifference curves. Your diagram should have margarine on the horizontal axis and butter on the vertical axis. What is the marginal rate of substitution of butter for margarine? 4.3 On the same plot, graph the budget set and label the utility maximizing point carefully. What is the intuition? Suppose now that the supermarket made a mistake and the price of a stick of margarine shouid be $2, whiie the price of a stick of butter should be $1. 4.4 , Plot the indifference curves, the new budget constraint, and the optimal point on a separate graph. 4.5 Compare both graphs and explain why they are different. Make sure that you explain the economic intuition carefully