In: Economics

Demand in a market
dominated by two firms (a Cournot duopoly) is determined according
to: P = 300 – 4(Q_{1} + Q_{2}), where P is the
market price, Q_{1} is the quantity demanded by Firm 1, and
Q_{2} is the quantity demanded by Firm 2. The marginal cost
and average cost for each firm is constant; AC=MC = $77.

The cournot-duopoly equilibrium profit for each firm is _____.

P = 300 – 4(Q_{1} + Q_{2}) = 300 -
4Q_{1} - 4Q_{2}

Each firm maximizes profit according to the rule, MR = MC

Firm 1: Total revenue, TR1 = P*Q_{1} = (300 -
4Q_{1} - 4Q_{2})*Q_{1} = 300Q_{1} -
4Q_{1}^{2} - 4Q_{1}Q_{2}

So, Marginal Revenue, MR1 =

Now, MR1 = MC gives,

300 - 8Q_{1} - 4Q_{2} = 77

So, 8Q_{1} = 300 - 77 - 4Q_{2} = 223 -
4Q_{2}

So, Q_{1} = (223/8) - (4Q_{2}/8)

So, Q_{1} = 22.875 - 0.5Q_{2}

This is the best response function of firm 1. As demand function
and MC is same for both firms, so best response funtion of firm 2
can be written as:

Q_{2} = 22.875 - 0.5Q_{1}

Now, we substitute Q1 into Q2. We get,

Q_{2} = 22.875 - 0.5(22.875 - 0.5Q_{2}) = 22.875 -
11.4375 + 0.25Q_{2}

So, Q_{2} - 0.25Q_{2} = 0.75Q_{2} =
11.4375

So, Q_{2} = 11.4375/0.75

So, Q_{2} = 15.25

Now, Q_{1} = 22.875 - 0.5Q_{2} = 22.875 -
0.5(15.25) = 22.875 - 7.625 = 15.25

So, Q_{1} = 15.25

P = 300 – 4(Q_{1} + Q_{2}) = 300 -
4(15.25+15.25) = 300 - 122 = 178

So, P = 178

Profit for firm 1 = Profit for firm 2 = Total revenue - Total
cost = P*Q_{1} - AC*Q_{1} = (P - AC)*Q_{1}
= (178-77)*15.25 = 101*(15.25) = 1,540.25

**The cournot-duopoly equilibrium profit for each firm is
$1,540.25**

Demand in a market dominated by two firms (a Cournot duopoly) is
determined according to: P = 300 – 4(Q1 +
Q2), where P is the market price, Q1 is the
quantity demanded by Firm 1, and Q2 is the quantity
demanded by Firm 2. The marginal cost and average cost for each
firm is constant; AC=MC = $68.
The cournot-duopoly equilibrium profit for each firm is
_____.
Hint: Write your answer to two decimal places.

1)
Demand in a market dominated by two firms (a Cournot duopoly) is
determined according to: P = 300 – 4(Q1 +
Q2), where P is the market price, Q1 is the
quantity demanded by Firm 1, and Q2 is the quantity
demanded by Firm 2. The marginal cost and average cost for each
firm is constant; AC=MC = $65.
The cournot-duopoly equilibrium quantity produced by each firm
is _____.
Hint: Write your answer to two decimal places.
2)
Demand...

Two firms are participating in a Cournot duopoly. The demand
function in the market is given by Q=430−2P. Each firm’s total cost
is given by C(q)=5q+q2.
(1) Write down the inverse demand function and the maximization
problem for Firm 1 given that Firm 2 is expected to produce
q2^e.
(2) Write down the reaction function q1(q2^e) for Firm 1.
(3) Find the market price, quantities supplied, and firms’ profits
in the Cournot
equilibrium of this game.

a.) Two identical firms compete as a Cournot duopoly. The market
demand is P=100-2Q, where Q stands for the combined output of the
two firms, Q=q1 +q2. The marginal cost for each firm is 4. Derive
the best-response functions for these firms expressing what q1 and
q2 should be.
b.) Continuing from the previous question, identify the price
and quantity that will prevail in the Cournot duopoly market
c.) Now suppose two identical firms compete as a Bertrand
duopoly. The...

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.

Two firms, firm 1 & firm 2, in a Cournot duopoly are facing
the market demand given by P = 140 – 0.4Q, where
P is the market price and Q is the market quantity
demanded. Firm 1 uses old technology and has (total) cost of
production given by C(q1) = 200 + 15q1,
where q1 is the quantity produced by firm 1. Firm 2 has
managed to introduce a new technology to lower the per unit cost,
and its...

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

Assume that two firms are in a Cournot oligopoly market. Market
demand is P=120 - Q where Q isthe aggregate output in the market
and P is the price. Firm 1 has the cost function
TC(Q1)=30 + 10Q1 and Firm 2 has the cost
function TC(Q2)=15 + 20Q2.
a) Write down the
Profit function of Firm 1:
Profit function of Firm 2:
b) Using the profit functions in part (a), obtain the reaction
function of Firm 1 to Firm 2....

In a duopoly market with two identical firms, the market demand
curve is: P=50-2Q And the marginal cost and average cost of each
firm is constant: AC=MC=2 a. Solve for firm 1’s reaction curve and
graph b. Solve for firm 2’s reaction curve and graph c. Solve for
each firm’s Q and P in a cournot equilibrium and show on your graph
i. What is the profit for each firm?

Consider a Cournot duopoly where P = 400 - 4Q1 - 4Q2. The two
firms are identical. Each firm treats the other firm’s production
quantity as a constant. The marginal cost of production is 16 for
every unit. What is the best production level for Firm 1?

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