Q.1There are two firms in the market. One has lower costs than the other. Assume they compete within the market in a Cournot game. Find the equilibrium output of both firms, the market-clearing price, the profit each firm earns, and consumer surplus.
Demand: Q = 200 − 4P
MC1 = AC1 = 8, MC2 = AC2 = 5
Note: The firms’ costs are different, therefore their best response functions must look different (MR1 = MC1 will not be the same MR2 = MC2).
1.bImagine you are a social planner. Firm 2 wishes to buy firm 1. This will create a monopoly in the market with Firm 2’s marginal and average costs. As a social planner, your goal is to maximize social welfare. In order to do so you can approve or deny the merger. Firm 2 argues that this merger will mean that all the products in the market will be produced with their more efficient technology, thus improving welfare. Calculate monopoly quantity, price, and total welfare that will occur if you approve the merger. Should you approve the merger?
Q2Suppose the two firms from question 1.a compete in a Bertrand game instead. Find the equilibrium prices of both firms, the quantity demanded and the profit each firm earns
2.bSeeing the difference in the market outcomes between question 1 and question 2.a, describe “Bertrand’s Paradox”.
Q.3Suppose there is a different market in which three identical firms compete in a Cournot game. Find the output of each firm, consumer surplus and profit each firm earns.
Demand: Q = 220 − 2P MC = AC = 5
(Hint: You do not have to use solve MR=MC for every single firm.)