Answer to Question #63688 in Microeconomics for Aisha

Question

A FIRM’S MARKET DEMAND IS P = 26 - Q. TWO IDENTICAL FIRMS HAVE COST FUNCTIONS C = 64 + 2Q, WHERE Q IS EACH FIRM'S INDIVIDUAL OUTPUT. (SO MC = 2.) THE FIRMS PRODUCE IDENTICAL PRODUCTS.
A. WHAT IS THE COURNOT-NASH EQUILIBRIUM MARKET PRICE AND OUTPUT? (8 PTS)
B. WOULD A THIRD IDENTICAL FIRM WANT TO ENTER? (6 PTS)
C. WHAT IS THE EQUILIBRIUM (MARKET PRICE AND QUANTITY OF EACH FIRM) IF THE FIRMS COLLUDE AND SPLIT THE MARKET EQUALLY? (6 PTS)

Answer 1

P = 26 - Q, C = 64 + 2Q, MC = 2.
A. The COURNOT-NASH EQUILIBRIUM market price and output are:
The output is optimal, when P = MC, so:
26 - Q = 2,
Q = 24 units.
P = 26 - 24 = $2.
B. A third identical firm would not want to enter, because both these firms are receiving zero profits at the market price and output.
C. WHAT IS THE EQUILIBRIUM (MARKET PRICE AND QUANTITY OF EACH FIRM) IF THE FIRMS COLLUDE AND SPLIT THE MARKET EQUALLY?
If the firms collude and split the market equally, then the equilibrium price and quantity will be:
The output is optimal, when MR = MC, so MR = TR' = (P*Q)' = 26 - 2Q,
26 - 2Q = 2,
Q = 12 units,
P = 26 - 12 = $14.