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# ECON 601 - Microeconomics: Theory and Applications - Final Exam - Question 5: Exchange under incomplete contracts

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Economics 601 -Microeconomics: Theory and Applications

Final Exam

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5.     Exchange under incomplete contracts (40 points) Consider a situation where a Buyer seeks to purchase goods for resale from n small business Suppliers, but cannot contract on the quality q of the goods provided, and hence may only decide to terminate a relationship if quality is too low. Assume the Buyer sets price p and chooses number of suppliers n to maximize profit given by a revenue function r( ) less costs as:

π = r( n q(p) ) – pn a given Supplier’s per period utility is:

u(p,q) = p – δ / (1 – q) and the Supplier’s net present value of the relationship is:

v=(u(p,q)+tz)/(i +t) where t, the Buyer’s termination probability, is t(q) = 1-q;

z, the Buyer’s fallback option, is 0;
and i, the Buyer’s rate of time preference, is 0.

5.1.  Give the value v of the transaction to the Supplier, and solve for the Supplier’s best-response choice of quality to provide to the Buyer for a given price, i.e., q*(p).

5.2.  Give the Buyer’s first order conditions in their two choice variables n and p, and use these and the Supplier’s best response function q*(p) to solve for the equilibrium price offered and quality provided in the transaction.

5.3.  What is the per period utility of the Supplier, how long is the expected duration of transaction relationships, and what is the total value of the relationship to the Supplier? Explain how these three quantities relate to each other, and whether the labor market clears.

5.4.  In some contexts repeated interactions between buyers and sellers may be infeasible. Describe two other means by which cooperation between buyers and sellers may be supported under incomplete contracts, and compare them to the retaliatory / contingent renewal model outlined here.

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