1 Agents: Let v = 2 and y = 1/2 so that agents, characterized by their type E {H, L}, have a utility function given by 2 U(a, b; , y, z) = 2a +z+y( + b) C(a, b), where z is the fixed wage and y the bonus rate and where the cost of effort is C(a, b) 1/2 (a² + b² + ab).

2. Firms Assume A= 2 and B = 4 so that the profits they get from contracting an agent Firms: Assume that A is given by (, y, z) = 2a + (4 y)(b + ) z.

Consider a monopsony employer. This employer offers contract (Z_H, Y_H) to type _H and contract (Z_L, Y_L) to type _L. Upon receiving this contract and accepting it, the agent chooses the effort levels a and b.

i. Find the optimal effort levels exerted by the agent. Comment on whether, in this setting, the more productive agent, type _H, exerts a higher effort than the less productive agent, type _L.

ii. Assume that the type is verifiable and that the reservation utility is such that = 140/3 Solve for the optimal contracts (Z_H, Y_H) and (Z_L, Y_L), keeping in mind that the employer can perfectly anticipate the effort levels found in i.. Describe the optimal contracts in a few words comparing the bonus rates and the fixed wages. [Tip: For each type, start by writing the optimization problem and the constraint that must bind.]

iii. Assume that the type is not verifiable. Write the optimization problem that the employer must solve assuming that there is a 50% that he faces a high type. Make sure that you specify what effort levels are perfectly anticipated.

iv. Explain what will happen if the employer uses the symmetric information contracts when it cannot verify the type.