employee farms and applies effort,

employees's outside option is 0 , andemployee has wealth w

Thecompany cannot observee

Effort is costly. The cost of effort is 1/2ce^2

Two things can happen:

With probability : Output is H

With probability : Output is 1-e output is zero

company to employee

Payment of h if output is H

Payment of l if output is 0

please answer 'questions:'

question Qc :

max h,L[eH+(1e)0(eh+(1e)L)]

such that

e argmaxeh+(1e)L1/2ce^2 ,

(eh+(1e)L1/2ce^2>=0)

question:

Solve for h andL in terms of H and c . To do so, plug your answers to Q3 and Q4 into the two constraints in Qcand solve.

P(e) = e*h + (1-e)*L (employee maximises his pay off)

Q3 answer result (h-l)/c

Now assume that effort is not contractible. That is, the company cannot specify what level ofmust the employee can put. The company offers a contract that offers payment h when output is H and payment L when the output is 0. Given this contract, set up employee's utility maximization problem and find his chosen level of effort.

Question 4 answer result H

she wants to set h and L such that the employee will always choose the first best level of effort. What will h-L ? Express your answer in terms of

question?

What is the employee utility under this contract? Write the utlity as a function

PART C OPTIMAL CONTRACT WITH LIMITED LIABILITY

company cannot take more than employees wealth (L >= -w)

also suppose that L you found inprevious question is smaller than -w

question:

WHAT IS L chosen by the company?

question:

max h,L[eH (eh+(1e)L)]

e = (h-L)/c

L =L*(previous L from the previou question WHAT IS L chosen by the company)

where the first constraint is the employee ICC and the second is the limited liability constraint (LLC). Ignore the participation constraint for now. Solve the optimization problem and findCall itand express it in terms of

H c w

question

question find the optimal e?,

in terms of h L

question

How much utility will the tenant get from this contract? Express the utility in terms of H c w

question

When will the tenant accept this contract?

options:

(H^2)/8c - w <= 0

(H^2)/8c - w >= 0

(H)/2c - w >= 0

they will accept the contract without conditions

question

Suppose the tenant accepts the contract. Is the tenant better off under the contract with or without limited liability?

The tenant is better off with the contract without limited liability (fixed rent contract)

The tenant is (weakly) better off with this limited liability contract