Suppose a monopoly firm faces a market demand curve given by Q = 50 – P and a marginal revenue curve given by MR = 50 –

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Suppose a monopoly firm faces a market demand curve given by Q =
50 – P and a marginal revenue curve given by MR = 50 – 2Q. The
marginal cost of production is constant at MC = $4 and there are no
fixed costs.
a. Calculate this firm’s profit-maximizing quantity and
price.
b. Calculate this firm’s profit.
c. What is the deadweight loss from this firm having
monopoly power.
d. Now suppose a second firm enters the market, and we
have a duopoly. Each firm will choose its profit-maximizing output
level on the assumption that the competitor’s output is fixed (as
in the Cournot model). The marginal revenue for Firm 1 is given by
MR1 = 50 – 2Q1 – Q2 and the marginal revenue for Firm 2 is given by
MR2 = 50 – 2Q2 – Q1. Find each firm’s reaction curve.
e. Calculate the Cournot equilibrium price and quantities for
each firm (round your answers to the nearest hundredth). Show all
work.
f. What is the total profit earned in this duopoly in
equilibrium?