Suppose you are given the following information: Market Demand: P 60 - Q where Q

Question

Suppose you are given the following information: Market Demand: P 60 - Q where Q is the total amount of the good supplied in the market. 1. (25pts) Assume that there are two firms in this market Firm A and Firm B Furthermore, Firm A's total cost function is given by C(%) = 10 + and Firm B's total cost function is given by CB(4a) = 10 + that the two firms decide to collude (i.e. split output and production evenly) and work as a monopolist. Find the market price, output, and profits of each firm, Explain. a. Suppose b. (5pts)Explain precisely why this is not a Nash equilibrium in this market under quantity (Cournot) competition.

Explanation / Answer

a) When the two firms collude there will be a single marginal cost.

MCA = 2qA and MCB = 2qB

qA = MCA/2 and qB = MCB/2

Total quantity produced = Q = MCA/2 + MCB/2 = MC

Hence MC = Q

MR = 60 - 2Q

Find the profit maximizing quantity

MR = MC

60 - 2Q = Q

Q* = 20 and so qA = qB = 10 units, price is P = 60 - 20 = 40. Profits for each firm is = TR - TC = (40*10 - 10 - 10^2) $290

b) Cournot outcome has both firm using their best response functions as

MRA = MCA MRB = MCB

60 - 2qA - qB = qA 60 - 2qB - qA = qB

qA = 20 - (1/3)qB and qB = 20 - (1/3)qA

Solve them to get qA = qB = 15 units and price = 60 - 30 = $30. Profits are (30*15 - 10 - 15^2) = $215. See that Cournot equilibrium has lower profit per firm so it is not preferred over collusion.

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