Market with market demand
1. Consider a market with market demand P(Q) = 68−2Q
and each firm in the market faces a total cost T C(Q) =
32Q.
Suppose there is only one firm in the market.
(a) What is the profit-maximizing price and quantity
be in the market?
(b) What are the profits and consumer surplus?
Now suppose we have a Cournot duopoly where
firms choose quantities.
(c) What is the equilibrium price and market quantity?
(d) What is the consumer surplus and profits for each
firm?
(e) What happens to total market profits and consumer
surplus as we increase from one to two firms?
2. Consider a market with demand P(Q) = 82−2Q in which
two firms compete. Firm 1 faces T C1(Q) = 26Q and firm
2 faces T C2(Q) = 18Q.
(a) Find the reaction function for firm 1.
(b) Find the reaction function for firm 2.
(c) Find the Cournot equilibrium (Q∗
1
, Q∗
2
, P∗
).
(d) Determine profits for each firm and consumer surplus.
3. Consider a market with demand P(Q) = 85−2Q in which
8 identical firms compete. All firms face T C(Q) = 31Q.
Let X = Q2 + Q3 + · · · + Q8.
(a) Write out the residual demand curve for firm 1 in
terms of X and Q1.
(b) Find the corresponding marginal revenue.
(c) What is the reaction function for firm 1 (in terms
of X).
(d) Find the Cournot equilibrium (market quantity
QM∗
, P∗
).
(e) Determine profits for each firm.