Question 4: (10 points) Consider identical firms competing in a Cournot oligopoly, with cost functions: C(q) = 10q, and corresponding marginal costs…

Question 4: (10 points)

Consider identical firms competing in a Cournot oligopoly, with cost functions: C(q) = 10q, and

corresponding marginal costs of: MC(q) = 10. The market elasticity of demand is: EM = -2.

(note: NOT the firmâs elasticity of demand, which is EF!)

a) Suppose you are a monopolist. Solve for the profit-maximizing price. (hint: a monopoly is

Cournot competition with only one firm, i.e. where N=1).

b) Now suppose another, identical firm, enters the market. Solve for the new profit maximizing

price.

c) As more firms enter, the price falls. How many firms must be in the market for the price

to fall below: P = $11? (hint: you can solve this by trial-and-error, i.e. testing a certain

number of firms, or by solving directly for N. Try solving for N directly. Also, ð must be

an integer.)

1.a) −1( P−MC )=EdP−1( P−10)=2PP=2p-20P=20b)n=2 ( N∗Mc )P= ( N +1 )∗( 1 )Ed(2∗10)= ( 2+1 )∗( 1 )2=13.33c)n=3 firmsTR1=20q1-(10q1+10q2+10q3)…

 
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