Question

3) Assuming that firms compete a la Cournot, that all firms have the same marginal cost, and

that demand is linear, when is price most sensitive to changes in marginal cost: in a market

with very few firms or in a market with many firms? Show this formally. [Hint: assume

demand 𝑝 = 𝑎 – 𝑏𝑄]

b) Consider a Bertrand duopoly with differentiated products. Demand curves are given by

𝑝! = 600 − 2𝑞! − 𝑞"

𝑝" = 600 − 𝑞! − 2𝑞"

Suppose that the cost functions are given by (𝑞#) = 60𝑞# , for 𝑖 = 1, 2. Find the equilibrium

outputs, the prices and the profits.

Answer 1

a.

Price is most when demand is elastic. It can be expressed as p=a-bQ meaning consumers will buy consume more when price is less .

b.

$\frac{dTC}{Q}=\frac{60Q}{Q}=60$

Price =$600-60-120=420$

Profit$P×Q=420×60=25,200$