Consider a homogeneous-product duopoly model in which Q is the market
output, P is the price, and Q1 and Q2 are the output levels produced by firms 1 and 2, respectively.
The inverse market demand function is P = 310 - 3Q
The marginal cost is constant and equal to $10 for both firms. There are no fixed costs.
a) Determine each firm's best-response function. (4 marks)
b) Explain what a best-response function shows, and why it is downward sloping.
c) Draw the two best-response functions on a carefully-labeled diagram.
d) Determine the equilibrium output level and the profit for each firm in a Cournot duopoly.
e) Determine the collusive output level and show it on your graph. Explain whether collusion is sustainable if the firms only interact once.
f) Explain what would happen if the two firms decided to compete over prices instead of quantities.
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