Answer each of the following questions neatly and thoroughly. Use graph paper to
ID: 1198919 • Letter: A
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