A farmer needs a worker (called harvest hand) to help her bring in the harvest.

Question

A farmer needs a worker (called harvest hand) to help her bring in the harvest. A great harvest hand adds £5000 to the farmer’s revenue. A good harvest hand adds £4000, a decent harvest hand adds £3000 and a bad harvest hand adds £2000 to the farmer’s revenue. A harvest hand’s outside option is equal to half the revenue he would add, i.e. the outside option for a great harvest hand is £2500, £2000 for good harvest hand, £1500 for a decent harvest hand and £1000 for a bad harvest hand.

a. Assume the farmer knows the quality of a harvest hand before she hires him. What quality of harvest hand does she hire and why? How much does the farmer pay him?

b. Assume the farmer does NOT know the quality of a harvest hand before she hires him. Assume additionally that 5% of all harvest hands are great, 15% are good, 50% are decent and 30% are bad. What is the expected profit maximizing contract offer?

c. An agency offers to provide information to the farmer that allows her to identify decent and bad harvest hands. How much would the farmer pay for this information at most? Explain your answer. If you are stuck, think about what the farmer could do with this information.

Explanation / Answer

a. She will hire a great harvest hand as it adds maximum to her's revenue.

She will pay great harvest hand atleast equal to his second option = 2500

b.  expected profit maximizing contract offer will be one which maximizes revenue

Expected value of revenue = 0.05*5000 + 0.15*4000 + 0.50*3000 + 0.30*2000

= 250 + 600 + 1500 + 600

= 2950

So, expected profit maximizing contract offer = 1/2Expected value of revenue = 2950 = 1475

c.

As, Farmer now can identify Decent harvest hand

So increase revenue of Farmer = Addition by decent harvest = 5000

Increase in Profit in case of decent = 5000 - 2500 = 2500

Increase in Profit in case of quality n't known = 2950 - 1475 = 1475

Max. Amount farmer pay for information = difference in Profit = 2500 - 1475 = 1025

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