A farmer produces goods with the production function x 10e, where e is the amoun

Question

A farmer produces goods with the production function x 10e, where e is the amount of time the farmer works and x is the amount of output. The farmer values goods and finds work onerous according to the following utility function: where y is the farmer's income (a lfy r-R, where R is a fixed rent that must be paid to the landowner, so that the farmer ir the residual claimant on the crop, how much labor (e) will he chooce to do? (Hint maximize the farmer's utility) Answer: Say true or false If the farmer is a wage-worker whose falback utility is 0 and e is contractible (it is possible to write a contract specify ing a certain amount of e), the farmer's profit- maximizing employer will offer a contract implementing the same level of labor as in the case where the famer was a residual claimant Select one: True Faise e) Now suppose that a contracts that specifies an exact amount of e canmot be writen. The landowner, anstead, offers the farmer a shaze contract, according to which the farmer gets to keep a part of the production for him berself The share of the produce that the farmer will be able to keep is equal to y-, with 0sssl. ·The farmer's utility function wil now be:u-s( Choose. ).Ooos. e. " How much labor will the farmer now do as a function ofthe share?! Choose . The profit function 6f the landlord will now be: P- Choose Choose , the landlord v ller s dint te la dodeille eriheth ithat nar epts bengthyezne dt Inte Nash Equili Choose responce function)

Explanation / Answer

a. The R should be when utlity is maximum =

y = x- R            1

and u = y- 1/2e2             2

Put value of y in equ 2

u = x-R-1/2e2. and x= 10e

So U = 10e- R - 1/2e2.

b. The answer of second page is True.

c. 1. The answer would be 10e.

2. The answer would be 4s.
3. The answer would be 1/2xe.
4. The answer would be 10s.

d. 1. equal to, less than.

2. efficient.

3. inefficient.

4. suprerior.

5. efficient.

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