• Columbia University

• ECON V3265

Question 1 [16 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 $8 at T=2. The project can be liquidated at T=1 but early liquidation yields $1 at T=1. An agent has $1 and can be of two types. With probability 0.5 the agent is a type-1 consumer and with probability 0.5 the agent is a type-2 consumer. If an agent is a type1-consumer, he only values consumption at T=1 and his utility function is 1 1 1 2 c u   where c1 is the amount consumed at T=1. If an agent is a type-2 consumer, he values consumption at both T=1 and T=2 according to the utility function 1 2 2 1 2 c c u    where c1 and c2 are the amounts consumed at T=1 and T=2, respectively. The agent maximizes expected utility