4. (30 points) Consider a principal agent model with hidden effort effort. The principal can choose the wage for project success p5 and the wage for project failure pf. After the wages are chosen, the agent chooses an effort level 7'. One unit of wages directly transfers one unit of utility from principal to agent. A successful project produces 10 units of utility for the principal. The cost of effort to the agent is 2T2. A. Write down the utility function for both players as a function of p f, p3, and 'r. B. Find effort as a function or ps and p f. C. Find equilibrium effort and wages assuming a limited liability constraint. D. What is the efcient effort level in the sense of maximizing total utility