Question

Two Cournot firms produce slightly different products. Product
prices depend on both firms' outputs and are determined by the
following equations P_{1} = 70 - 2Q_{1} -
Q_{2,} P_{2} = 100 - Q_{1}- 2Q_{2.}
Both Firm 1 and Firm 2 have constant marginal cost of $10 and zero
fixed cost. Firm 1 chooses Q_{1} and Firm 2 chooses
Q_{2.}

- (3pts) Find Firm 1's best response as a function of Firm 2's
output Q
_{2}. - (3pts) Find Firm 2's best response as a function of Firm 1's
output Q
_{1}. - (6pts) Use the two best response functions to find the Nash equilibrium. In equilibrium, how much profit will each firm earn?

Answer #1

Consider an asymmetric Cournot duopoly game, where the two firms
have different costs of production. Firm 1 selects quantity q1 and
pays the production cost of 2q1 . Firm 2 selects quantity q2 and
pays the production cost 4q2 . The market price is given by p = 12
− q1 − q2 . Thus, the payoff functions are u1 (q1,q2) = (12 − q1 −
q2 ) q1 − 2q1 and u2 ( q1 , q2 ) = (12...

There is a Cournot game consisting of two different firms that
produce the same goods.
Quantity produced by firm one = q
Quantity produced by firm two = q2
The marginal cost for firm one equals average cost, which is
3.
The marginal cost for firm two equals average cost, which is
4.
The formula for the inverse demand curve of the market is P = 70
- (q1 +q2).
Answer the following questions with work:
1. What is the...

Two firms in a Cournot duopoly produce quantities Q 1 and Q 2
and the demand equation is given as P = 80 - 2Q 1 - 2Q 2. The
firms' marginal cost are identical and given by MCi(Qi) = 4Qi,
where i is either firm 1 or firm 2.
a. Q1 = 80 - 4Q2 and Q2 = 80 - 4Q1.
b. Q1 = 10 - (1/4)Q2 and Q2 = 10 - (1/4)Q1.
c. Q1 = 80 - 2Q2...

Q1.
Consider a Cournot oligopoly in which the market demand curve is
Q = 60 - P. There are two firms in this market, so Q =
q1 + q2. The firms in this market are not
identical: Firm 1 faces cost function c1(q1)
= 2q12, while firm 2's cost function is
c2(q2) = 28q2.
In the space below, write down a function for Firm 1's profit,
in terms of q1 and q2.
Q2.
Refer back to the Cournot oligopoly...

A product is produced by two profit-maximizing firms in a
Stackelberg duopoly: firm 1 chooses a quantity q1 ? 0, then firm 2
observes q1 and chooses a quantity q2 ? 0. The market price is
determined by the following formula: P ( Q ) = 4 ? Q , where Q =
q(1) +q(2) . The cost to firm i of producing q i is Ci( qi ) =
q^2)i . (Note: the only difference between this problem and...

Question 4 Consider the following game. Firm 1, the leader,
selects an output, q1, after which firm 2, the follower, observes
the choice of q1 and then selects its own output, q2. The resulting
price is one satisfying the industry demand curve P = 200 - q1 -
q2. Both firms have zero fixed costs and a constant marginal cost
of $60. a. Derive the equation for the follower firm’s best
response function. Draw this equation on a diagram with...

1.Both firms in a Cournot duopoly would enjoy lower profits
if:
Multiple Choice
one firm reduced output below the Cournot Nash equilibrium level,
while the other firm continued to produce its Cournot Nash
equilibrium output.
None of the answers is correct.
each firm simultaneously increased output above the Nash
equilibrium level.
the firms simultaneously reduced output below the Nash equilibrium
level.
2.Both firms in a Cournot duopoly would enjoy higher profits
if:
Multiple Choice
the firms simultaneously reduced output below...

Consider a Cournot market with two firms that have TC(Q) =5Q.
Demand is given by P= 200−2(Q1+Q2).
A) Find firm 1’s profit as a function of Q1 and Q2
B) Find the equilibrium price, quantity sold by each firm, and
profit for each firm.

2. Consider two identical firms in a Cournot competition. The
market demand is P = a – bQ. TC1 = cq1 = TC2 = cq2 . a. Find the
profit function of firm 1. b. Maximize the profit function to find
the reaction function of firm 1. c. Solve for the Cournot-Nash
Equilibrium. d. Carefully discuss how the slope of the demand curve
affects outputs and price.

Consider a market with two firms whose products are identical.
The market demand curve is p = a − bq where a > 0 and b > 0,
and where q = q1 + q2. Firm i’s profits are πi(q1, q2) = pqi − cqi
. Assume that the firms move in sequence, with firm 1 choosing q1
first, and then firm 2 choosing q2; however, assume firm 2 observes
q1 before choosing q2.
(a) What is a Nash equilibrium...

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