Answer each of the following questions neatly and thoroughly. Use graph paper to

Question

Answer each of the following questions neatly and thoroughly. Use graph paper to plot or sketch
curves when requested, use complete sentences when providing explanations, and show your
work; points are deducted if these instructions are not followed. Typing is optional but
encouraged if your handwriting is poor.
1. Consider an industry with a market demand curve of P = 100 – Q and MC = 0.
a. Assume this industry is perfectly competitive; find the profit-maximizing output, price,
and profit.
b. Assume this industry is monopolistic; find the profit-maximizing output, price, and profit.
c. Assume this industry is a duopoly but the firms act jointly as a monopolist; find the
profit-maximizing output, price, and profit for each of the two firms.
d. Assume this industry is a Cournot duopoly:
i. derive the reaction curves for each of the two firms;
ii. find the profit-maximizing output, price, and profit for each of the two firms.
e. Assume this industry is a Betrand duopoly:
i. Find the profit-maximizing output, price, and profit for each of the two firms.
f. Assume this industry is a Stackleberg duopoly, with firm 1 as the leader and firm 2 as the
follower:
i. derive the reaction curves for each of the two firms;
ii. find the profit-maximizing output, price, and profit for each of the two firms.
g. Summarize the results in the table (or a similar one of your own creation) below.

Market                Q1    Q2    P1 P2   Profit1 Profit2

Perf. Comp. (a)             -                 -                    -
Monopoly (b)               -                 -                    -
Duopoly (c)
(acting jointly)
Cournot (d)
Bertrand (e)
Stackleberg (f)

Explanation / Answer

a)

When MC=0, the perfectly competitive output will have a P=MC=0 and Q=100

The good will be provided at no cost, like a public good.

b)

In case of a monopoly, profit maximization occurs at the point MR=MC

From the given demand function, MR=100-2Q and MC=0 (given)

Therefore, equating MR=MC will give Q=50 and P=50

c)

Demand curve: P = 100-Q1-Q2

MC1 = MC2 = 0

Equate MR1=MC1 and MR2=MC2

Substitute the resultant equations to find Q1=Q2=33.33 and P=33.33

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