Question 1 [22 points] Consider an economy with three dates (T=0, 1, 2) and the following investment opportunity. If an agent invests $1 in a project at T=0, the project yields $4 at T=2. The project can be liquidated at T=l but early liquidation yields $1 at T=l. An agent has $1 and is risk avers and can be of two types. With probability 0.2 an agent is a type-l consumer and with probability 0.8 an agent is a type-2 consumer. If an agent is a typel-consumer, he only values consumption at T=1 and his utility function is 111:2i C] where c] is the amount consumed at T=l. If an agent is a type-2 consumer, he values consumption at both T=l and T=2 according to the utility function 1 u2=2 c1+c2 where c1 and 02 are the amounts consumed at T=l and T=2, respectively. a) What is the expected utility of the agent? [3 Points]