Homework # 3 - ISyE 6230 – Economic Decision Analysis II – Spring 2010 Due Thursday Mar 11, 2010 Grading: Up to 10 points per problem for completing each problem; the remaining 50 points will come from grading one randomly selected problem for correctness. 1. In a small town, there are three firms producing automobile tires. Firm A is the leader in the market; while firm B and C are the followers. Current demand is characterized by 200PQ=− , where P is the price of the tire and Q is the total quantity produced. A firm’s total cost function is 2()2qCq = . In this industry, firm A determines the optimal quantity to produce. Firm B and firm C realize firm A’s quantity and then choose their own quantities (without observing each other’s decision). (i) What are the optimal quantities of each firm? (ii) What is the total demand produced in this market, and at what price? (iii) What are profits of each firm in this market? (iv) Suppose they are no leaders in this market and all three firms determine their quantities simultaneously. What are the quantity and profit of each firm? Discuss how it is different than the previous case. 2. Consider the following market with three companies, Sunny, Windy and Rainy Inc. From previous years, it has been recorded that the market price as a function of quantity is as followed, 120 ( )sunny windy rainyPqqq=− + +. Each firm has a marginal cost of production, 10, per unit produced. All of them determine their quantities simultaneously. Consider the infinitely repeated Cournot game. What is the lowest value of the discount factor δ such that they are able to apply the trigger strategies, in which each of them will corporate to produce one third of the monopoly output? 3. Find an industry article on supply chain coordination and/or contracting and analyze the situation. In particular, discuss the structure of the contract and whether or not the supply chain would yield different product flows and prices from a centralized channel, comment on the distribution of risk, and the distribution of power and profit. Be sure to give the full reference of the article. Be prepared to discuss article in class on the date the homework is due.4. A skin care company from Asia, named Alyn, is trying to reach a new market in Australia. The cost of producing and shipping a bottle of special formula lotion are $3 and $1, respectively. The Australian distributor, named Roxel, is buying the skin care product from Alyn at a wholesale price of $w per bottle. From statistics of similar products in Australia, if the selling price is $15, demand can be estimated to be 9,000. If the price is $5, demand will be 18,000. Note that demand is assumed to be linear function in this case. (i) Suppose Roxel and Alyn were a single company, what is the optimal price and quantity to be sold in Australia and what is its centralized profit? (ii) In the case that they are separate companies and each of them wants to maximize its own profits, what are the wholesale price and the quantity ordered? (iii) How are the total profit and the consumer surplus under the wholesale price contract in case (ii) compared to those of the centralization in case (i)? 5. Revenue Sharing Contract: Suppose from Problem 4, there is an option that Alyn and Roxel can apply a revenue sharing contract in which Roxel agrees to share 45% of the profit with Alyn, and Alyn will sell the lotion to Roxel at only $2 per bottle. (i) What is the optimal order quantity for Roxel, and what is the profit for each party in this type of contract? (ii) Is this revenue sharing contract desirable to Alyn and Roxel, compared to the wholesale contract? Explain why or why not. (iii) Does this contract coordinate the supply
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