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# exam3last - Name Exam 3 ISyE 4803 Spring 2006 Please sign...

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Name__________________________ Exam 3 – ISyE 4803 Spring 2006 Please sign the following statement: I give my word that I will not discuss this exam or any of the content with anyone until after next Wednesday ___________________________________ Sign your name Show all work for partial credit. 1. ( 15 points ) A manufacturer wants to hire a subcontractor to make a component for them. An alternative contract exists for the subcontractor at a value of \$100 if they do not take the offer from the manufacturer. The output for the subcontractor depends on the level of effort (in terms of applying appropriate resources) applied to the project. The manufacturer wants to devise a contract that will pay the subcontractor for performance (in terms of output observed). If the subcontractor applies a high level of effort, then this gives value V H to the manufacturer 70% of the time (the other 30% is shows as V L due to poor support logistics from the manufacturer). If the subcontractor applies a low effort, then it shows as V L 60% of the time (the other 40% of the time it shows as V H ). The subcontractors “utility” is defined by the contract value ( w ) minus the level of effort ( e H or e L ), and the manufacturer desires the subcontractor to have a high level of effort. Write the participation and the incentive compatibility constraints for the contract the manufacturer would need to offer (and label them). There is no need to solve them for w .

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2. ( 25 points ) Two companies (A and B) each have unit cost c=10. The price they get per part is defined by market demand P( Q ) = 200-5 Q , where Q = q A + q B . Answer the following: a. Solve for the Nash output quantities for each firm. b. Determine the market price, and what the total profit for the two firms would be. c. Suppose the three firms merged and became a single firm. What would the output quantity and market price be in this case? Compare this answer to what you found in b.
3. ( 25 points ) A manufacturer sells parts to a store which packages the parts and sells them to the customers. The manufacturer has a cost of \$5 for each part it

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exam3last - Name Exam 3 ISyE 4803 Spring 2006 Please sign...

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