Question: Optimal Contracting

The yearly demand for Thelma's pumpkins is P =1,000 − 0.1 Q , where P is the price per

ton and Q is the quantity demanded in tons.

Thelma's fixed cost is $500,000 a year.

Thelma's total crop is given and equals 6,000 tons.

1. Thelma transports her crop to the market by herself at a cost of $120 per ton. What price should Thelma set in order to maximize her profit? What would her profit be in this case?
   Instead of transporting the goods by herself, Thelma is considering using Louise's transportation services. Louise's only cost is $40 per ton.
2. Suppose that Louise charges Thelma $100 per ton? Should Thelma use Louise's service in this case? What will be Louise's profit and what will be Thelma's profit, in this case?
3. Instead of paying $100 per ton, Thelma offers to pay Louise the exact amount she paid in part b above (i.e., a lump sum payment). Should Louise accept Thelma's offer?
4. What is the minimum lump sum payment that Thelma should pay Louise, in order for Louise to make the same profit as she made in part b above? Would Thelma be willing to pay such an amount?
5. Can you suggest some other arrangements between Thelma and Louise that would give both of them a higher profit, relative to the profit they made in part d above?

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Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document