This is the second time I am posting this exercise, I have posted it before and it was not answered correctly. Please do not just copy the solutions to a previous, similar exercise posted on here, use the two equalities given in part a). Thank you and Happy New Year!

Agents: Let = 2 and = 1/2 so that agents, characterized by their type {L , H} , have a utility function given by

(, ; , , ) = 2 + + ( + ) (, ),

where is the fixed wage and the bonus rate and where the cost of effort is

(, ) = 1/2 (2 + 2 + ).

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

Setting 2: Consider that several employers are competing for agents. Each employer offers contract (zH, yH) to type H and contract (L , L) to type L . Upon receiving this contract and accepting it, the agent chooses the effort levels and . (Note that in such a context the reservation utility is irrelevant.)

a) Using equalities (H, yH, zH) = 0 <-> (yH) + (b- yH)H = zH; and (L, yL, zL) = 0 <-> (yL) + (b - yL)L= zL; find the contract that would be offered to each type when types are verifiable, and when each employer can perfectly anticipate the efforts exerted by the contracted agent.

b) Explain what will happen if the employers propose the symmetric information contracts when they cannot verify the type. In this case, how must the bonus payments be modified, if at all, to address the incentive compatibility issues?

c) Explain, in a few lines, what are the main conclusions one can draw from this analysis in terms of large bonuses being paid in some sectors of the economy. Show that you understand how contracts are modified to address the asymmetry of information when there is competition and where there is a monopolistic employer.