qp*14. The market for nutmeg is controlled by two small islandeconomies, Penang and Grenada. The market demand forbottled nutmeg is given by P=100-9p - 9G, whereis the quantity Penang produces and qG is the quantityGrenada produces. Both Grenada and Penang producenutmeg at a constant marginal and average cost of $20 perbottle.a. Verify that the reaction function for Grenada is givenby qG=40-0.5qp. Then verify that the reactionfunction for Penang is given by qp = 40-0.5qG.b. Find the Cournot equilibrium quantity for eachisland. Then solve for the market price of nutmeg andfor each firm's profit.c. Suppose that Grenada transforms the nature of com-petition to Stackelberg competition by announcing its production targets publicly in an attempt to seize afirst-mover advantage.i. Grenada must first decide how much to produce,and to do this, it needs to know the demand con-ditions it faces. Substitute Penang's reactionfunction into the market demand curve to find thedemand faced by Grenada.ii. Based on your answer to the problem above, findthe marginal revenue curve faced by Grenada.iii. Equate marginal revenue with marginal cost tofind Grenada's output.iv. Plug Grenada's output into Penang's reactionfunction to determine Penang's output.v. Plug the combined output of Grenada and Pen-ang into the market demand curve to determinethe price. How do the industry quantity and pricecompare to those under Cournot competition?vi. Determine profits in Grenada and Penang. Howdo the profits of each compare to profits underCournot competition? Is there an advantage tobeing the first-mover?

DISCLAIMER “Since you have asked many questions, we will solve the first three sub-parts question…

9P 4. The market for nutmeg is controlled by two small island economies, Penang and Grenada. The market demand for bottled nutmeg is given by P=100-9p - 9G, where is the quantity Penang produces and qG is the quantity Grenada produces. Both Grenada and Penang produce nutmeg at a constant marginal and average cost of $20 per bottle. a. Verify that the reaction function for Grenada is given by qG=40-0.5qp. Then verify that the reaction function for Penang is given by qp = 40-0.5qG. b. Find the Cournot equilibrium quantity for each island. Then solve for the market price of nutmeg and for each firm's profit. c. Suppose that Grenada transforms the nature of com- petition to Stackelberg competition by announcing its

9P 4. The market for nutmeg is controlled by two small island economies, Penang and Grenada. The market demand for bottled nutmeg is given by P=100-9p - 9G, where is the quantity Penang produces and qG is the quantity Grenada produces. Both Grenada and Penang produce nutmeg at a constant marginal and average cost of $20 per bottle. a. Verify that the reaction function for Grenada is given by qG=40-0.5qp. Then verify that the reaction function for Penang is given by qp = 40-0.5qG. b. Find the Cournot equilibrium quantity for each island. Then solve for the market price of nutmeg and for each firm's profit. c. Suppose that Grenada transforms the nature of com- petition to Stackelberg competition by announcing its

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter19: Externalities And Public Goods

Section: Chapter Questions

Problem 19.3P

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