Firms in a duopoly face the inverse market demand function P= 150-Q where P= pri
ID: 1113218 • Letter: F
Question
Firms in a duopoly face the inverse market demand function P= 150-Q where P= price per unit (€) and Q = market demand (millions of units) and each faces a constant cost of €60 per unit.
If the industry is a Cournot duopoly, derive the equations for the reaction functions for each firm. In the long-run what level of output would be produced by each firm? At what price will this output sell?
If the industry is a Stackelberg duopoly, with one firm the leader and the other the follower, what level of output would be produced by each firm? At what price will this output sell?
(c) If instead this industry was a monopoly, calculate its profit maximising output level and price.
(d) If this industry was perfectly competitive, what would be the equilibrium price and output?
(e) Compare the output levels and price under the various models in (a)-(d) above and discuss the differences in terms of competition and strategy.
Explanation / Answer
We have market demand P = 150 - Q and MC = 60 per unit
a) For the two firms acting as duopolist, the marginal revenue functions are MR1 = 150 - 2Q1 - Q2 and MR2 = 150 - 2Q2 - Q1. With MC = 60, reaction functions are
MR1 = MC and MR2 = MC
150 - 2Q1 - Q2 = 60 150 - 2Q2 - Q1 = 60
Q1 = 45 - 0.5Q2 Q2 = 45 - 0.5Q1
Solve them to get Q1 = Q2 = 30 and price = 150 - (30 + 30) = $90.
b) Stackelberg leader produces (150 - 60)/2 = 45 units and follower produces (150 - 60)/4 = 22.5. The price is P = 150 - (45 + 22.5) = 82.5.
c) Monopoly produces an output determined by MR = MC
150 - 2Q = 60
Q* = 45 units. Price = 150 - 45 = $105 per unit
d) Perfectly competitve firm produces at P = MC
150 - Q = 60
Q* = 90 and price P = 150 - 90 = $60 per unit.
e) Perfectly competitive firm produces the maximum and charges the lowest. Monopolist charges the highest price and produces the lowest quantity.
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