An agent must pick one of two possible designs (A or B) for a new device. The agent knows that the value of the device when using design k {A,B} is a random variable xk [0,1], where xk is an independent draw from a uniform distribution in [0,1]. The agent can learn the realization of the random variable xk by paying a cost c 0.

1. (a)What is the expected payoff of picking A or B without paying the cost c to learn the value of either of the alternatives?
2. (b)Suppose the agent knows that the value of design A is xA. At this point, the agent could implement design A, implement design B without paying to learn its value, or pay c to learn the value of design B, and then implement the design with the highest value. Compute the agent's payoff in each one of these cases.
3. (c)Suppose the agent knows that the value of design A is xA. Under what condition will the agent pay c to learn the value of design B?

(d) Assume that c = 1/32. Suppose that the agent does not the value of A or B and she decides to learn the value of some design, she always learns the value of A first and subsequently decides whether to learn the value of B. Under what condition will the agent pay the cost c to learn the value of A?