Consider a standard hidden-action agency model. Let the agent's utility be U(w, a) = u(w) - ca), where u : w, co - R is strictly increasing and strictly concave, w 2 -00, lime-wu(w) = -co, and c: A - R. Assume the action space A consists of two elements, 0 and 1, with c(1) = c > c(0) = 0. Normalize the agent's reservation utility to zero and assume the principal offers a contract on a TIOLI basis. There are two possible outcocmes, failure (f) and success (s), where Pr{sa} = qp if a = 0 if a = 1. Assume pe (0, 1) and q e (0, 1). The principal's utility is a - w, where w is the payment to the agent and * 6 { #, 1 } CR, where x, is realized if T is the outcome. Assume Is > If.(5 marks) Suppoose now that u(w) = log(w), c(a) = a and q = 0. Suppose you observe the principal offering the contract (wy, w ) in which W: >w. What is the minimum value of Is - If as a function of the other parameters such that the contract you see offered is consistent with the principal being rational