UWJJ. dilDWULD. 11.11 GLLDWULD' 111mm. Ul': buUbbdllbldqu. Question 1: Consider an economy with two goods, and an agent with income I = 100. The unit price of good 1 is 331 = 2, While the unit price of good 2 is p2 = 1. However, in order to purchase any quantity of good 2, the consumer must rst pay an up-front xed fee of 20. 1.1 Describe the feasible set, and sketch it in a gure. 1.2 Is the feasible set a convex set? Explain your answer. 1.3 Assuming preferences are strictly monotonic and strictly convex or equivalently that the utility function is strictly increasing and strictly quasiconcave is it possible to say Whether or not there is a unique bundle in the feasible set that is optimal for the consumer? Explain your answer. In the remainder of the question, assume that the agent has utility function Ma, 3%) = 2,/:c1 + 2041/5122, where a > 0 is an exogenous constant. 1.4 Assuming that the utility-maximizing bundle is interior, What is the optimal bundle as a function of oz? What is the consumer's utility? Simplify the latter as much as possible. 1.5 For what values of 04 is the optimal bundle interior? Do you agree that it may be optimal to only consume good 1 but that it is never optimal to consume only good 2? Carefully explain your answer and the economic intuition