Question: Sarada owns a firm with a technology in whichx=e, whereeis the effort of her agent andxis the level of output, both measured per day.She can sell output for a constant unit price of $10, and pays her agent an incomew.Her utility function is V(x,w) = 10x - w.

There are two types of agents in the world, differentiated by their disutility of effort.An agent's utility function is given by Ui(w,e) = w - vi(e),i=1,2, wherewis income and v1(e) e: that is, type-1 agents have less disutility of effort than type-2 agents.All agents have a maximum level of effort of 2, and reservation utility of 0.

Sarada can observe the output level at the end of each day, and she has all the bargaining power in her negotiations with any agent.

a) Identify the principal and the agent(s) in this situation.

b) If Sarada knows the type of agent she hires, what constraints must be satisfied at the contract she designs for type-1 workers?For type-2 workers?

Suppose now that Sarada cannot distinguish between agents of different types, but knows that proportionqof all agents are of type 1.

c) What further restrictions does this asymmetric information impose on the feasible contracts?Explain briefly.

d) Will the contracts in (a) satisfy these restrictions?Explain why or why not.

e) Is an "information rent" a component of any contract offered by Sarada under asymmetric information?Explain why or why not.