In: Economics

Two firms operate in a Cournot duopoly and face an inverse demand curve given by P = 200 - 2Q, where Q=Q1+Q2 If each firm has a cost function given by C(Q) = 20Q, how much output will each firm produce at the Cournot equilibrium?

a. Firm 1 produces 45, Firm 2 produces 45.

b. Firm 1 produces 30, Firm 2 produces 30

c. Firm 1 produces 45, Firm 2 produces 22.5

d. None of the above.

The inverse demand function is given as:

P = 200 - 2Q1 - 2Q2

The cost function is given as:

C(Q) - 20Q

The marginal cost (MC) is:

MC(Q) = 20

The total revenue for firm 1 is:

PQ1 = (200 - 2Q1 - 2Q2)(Q1)

TR1 = 200Q1 - 2Q1^{2} - 2Q1Q2

The marginal revenue for firm 1 is:

MR1 = 200 - 4Q1 - 2Q2

Similarly, the total revenue for firm 2 is:

PQ2 = (200 - 2Q1 - 2Q2)(Q2)

TR2 = 200Q2 - 2Q2^{2} - 2Q1Q2

The marginal revenue for firm 2 is:

MR2 = 200 - 4Q2 - 2Q1

Equating MR1 and MC1:

200 - 4Q1 - 2Q2 = 20

4Q1 + 2Q2 = 180

2Q1 + Q2 = 90

Q2 = 90 - 2Q1 (Equation 1)

Equating MR2 and MC2:

200 - 4Q2 - 2Q1 = 20

4Q2 + 2Q1 = 180

2Q2 + Q1 = 90 (Equation 2)

Solving equation 1 and equation 2:

2(90 - 2Q1) + Q1 = 90

180 - 4Q1 + Q1 = 90

-3Q1 = -90

Q1 = 30

Substituting Q1 = 30 in equation 1:

Q2 = 90 - 2Q1

Q2 = 90 - 2(30)

Q2 = 90 - 60

Q2 = 30

Answer: Q1 = Q2 = 30.

So, the firm 1 will produce 30 units and firm 2 will also produce 30 units. Therefore, the correct answer is 'Option B'.

Let the equation of the inverse demand curve for a Cournot
duopoly be p = 88 - 2 (q1 + q2). where q1 is the output of firm 1
and q2 is the output of firm 2. Firm i's cost function is c(qi) =
8qi .
(a)What are the Cournot duopoly equilibrium outputs, price and
profit per firm for this market?
(b) Suppose that for a market with the inverse demand equation
and cost functions of part (a), firm 1...

A) Two firms operate as Cournot competitors. Inverse demand is P
= 120 - 2Q. Firm 1 has total cost function c(q1) = 10q1 and Firm 2
has total cost function c(q2) = 20q2. Solve for the Nash
equilibrium in quantities and determine the equilibrium price. B)
Now assume the rms are Bertrand competitors, simultaneously
choosing prices. Solve for the Nash equilibrium in prices and
determine the equilibrium quantities.

Consider a Cournot duopoly, the firms face an (inverse) demand
function: Pb = 128 - 3 Qb. The marginal cost for firm 1 is given by
mc1 = 4 Q. The marginal cost for firm 2 is given by mc2 = 6 Q.
(Assume firm 1 has a fixed cost of $ 65 and firm 2 has a fixed cost
of $ 87 .) How much profit will firm 2 earn in the duopoly
equilibrium ?

2) Two firms, a and b, in a Cournot oligopoly face the inverse
demand function p = 500 – 2Q. Their cost function is c
(qi) = 20 + 4qi2 for i = a, b.
Calculate the profit maximizing price output combination. (3)

3) Two firms, a and b, in a Cournot oligopoly face the inverse
demand function p = 25 – Q. Their cost function is c
(qi) = 0.5*qi for i = a,
b. Calculate the profit maximizing price output
combination. (3)

Two firms compete as a Stackellberg duopoly. The inverse
market demand function they face is P = 65 – 3Q. The cost function
for each firm is C(Q) = 11Q. The outputs of the two firms
are

Two firms compete as a Stackelberg duopoly. The inverse market
demand function they face is P = 65 – 3Q. The cost function for
each firm is C(Q) = 11Q. The outputs of the two firms are
QL = 9, QF = 4.5
QL = 9, QF = 10.5
QL = 6, QF = 3
QL = 4, QF = 2
Please help/ explain. Thank you

Question #5: Consider a Cournot duopoly, the firms face an
(inverse) demand function: Pb = 110 - 7 Qb. The marginal cost for
firm 1 is given by mc1 = 5 Q. The marginal cost for firm 2 is given
by mc2 = 7 Q. (Assume firm 1 has a fixed cost of $ 112 and firm 2
has a fixed cost of $ 148 .) How much profit will firm 2 earn in
the duopoly equilibrium ?

1. Two firms compete in Cournot competition. Inverse demand in
the market is given by P = 1500 − 3 Q and each firm has constant
marginal cost c = 420.
a) Assuming there are no fixed costs, find the Cournot
equilibrium market price and quantities produced by each firm.
(20 points)
b) Now suppose that each firm faces a non-sunk fixed cost of
20,000 if they produce at all. Would the firms still want to
produce the amounts you...

Consider a homogeneous good Cournot duopoly with inverse demand
function given by p = 1 – Q. The two firms have identical marginal
costs equal to 0.4 and propose a merger. The firms claim that the
merger will result in a decrease of the marginal cost of the merged
firm by x per cent. How large would x need to be for welfare to
increase rather than decrease as a result of the merger?

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