Problem 1 The figure below illustrates consumer's indifference curve and budget constraint in a two- good economy of apples and bananas as we discussed in class. Let P, and p, denote the unit prices of apples and bananas. Suppose that consumer's utility function takes the form au(ca) + (1 - a)uc), where u is an increasing and concave function, Ca and C are the quantities of apples and bananas that consumed by the consumer, and parameter a (0,1) measures how much the consumer likes apples relative to bananas. The consumer's total income is Y >0. Blue lines are indifference curves with different levels of utilities. The red line represents the budget constraint. A Bananas Apples a. In the graph, there are three consumption bundles denoted by A, B and C. Which one is the optimal? Why. b. Let cand c denote the number of apples and bananas included in the optimal bundle. Please write down two conditions that these quantities should satisfy. c. Assume the utility function is a natural log function, i.e., u(x) = In(x). Solve the optimal consumptions in terms of income Y. 1