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 - qP - qG, where qP 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 - 0.5 qG.
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 competition to Stackelberg competition by announcing its production targets publicly in an attempt to seize a first-mover advantage.
i. Grenada must first decide how much to produce, and to do this, it needs to know the demand conditions it faces. Substitute Penang's reaction function into the market demand curve to find the demand faced by Grenada.
ii. Based on your answer to the problem above, find the marginal revenue curve faced by Grenada.
iii. Equate marginal revenue with marginal cost to find Grenada's output.
iv. Plug Grenada's output into Penang's reaction function to determine Penang's output.
v. Plug the combined output of Grenada and Penang into the market demand curve to determine the price. How do the industry quantity and price compare to those under Cournot competition?
vi. Determine profits in Grenada and Penang. How do the profits of each compare to profits under Cournot competition? Is there an advantage to being the first-mover?