The Principal hires an agent to work. There are 2 possible effort levels that the worker can exert -high effortehand low effort,where eh >el. The agent is risk averse and his utility is given by u=phsh+plslce,

whereceis the worker's cost for exerting efforte=h, l. High effort increases the probability of success, but is more costly to the worker:ch= 9 andcl= 6.shis the wage in the high output state andslis the wage in the low output state.u = 10 is the worker's outside utility from some other job. There are 2 possible output levels:yh= 1000,yl= 600.

The probabilities of high output state and low output state are given as before.

	y=yh	y=yl
e=eh	0.7	0.3
e=el	0.4	0.6

A) Write down the maximization problems for the Principal when effort is observable under high effort and low effort.

b) Construct the Lagrangians and write down the First Order Conditions.

c) Find the wage ratessh,sl.

d) Find the Lagrange multipliers and interpret them.

e) Write down the maximization problems (with participation and incentive constraints) for the Principal when the worker's effort is unobservable.

f) Find the wage ratessh, sl.

g) Find the Lagrange multipliers and interpret them.

h) Will the Principal ask for a high effort from the worker when the effort level is unobserv- able? Why or why not? Show your work. Hint: calculate the Principal's expected profits under observable and unobservable efforts.