In: Economics

Suppose two firms, "A" and "B," form a duopoly in the market for a special type of computer chip. Each firm has a constant marginal cost of $2. The daily market demand for this chip is given by the following equation:

P = 8 – 0.005 Q = 8 – 0.005 (qA+qB).

a. Find an expression for firm #A's revenue, as a function of its own quantity and firm B’s quantity: RevA(qA,qB). [Hint: By definition, RevA = P qA. Here, replace P by the equation for the demand curve.]

b. Find an expression for firm A's marginal revenue, as a function of its own quantity and firm B’s quantity: MRA(qA,qB). [Hint: MRA(qA,qB) = d RevA(qA,qB) / dqA., where the derivative is taken holding qB constant.]

c. Find an expression for firm #A's reaction function, showing how much firm A will produce for any given level of quantity set by the other firm: qA* = f(qB). [Hint: Set MRA = MC and solve for qA as a function of qB .]

d. Since both firms have the same cost, you may assume the equilibrium is symmetric (that is, assume qA* = qB*). Compute firm A's equilibrium quantity qA*.

e. Compute total market quantity Q* and the Cournot equilibrium price P*.

f. Assume marginal cost equals average cost and compute the total profit of both firms together.

g. Compute the social deadweight loss. [Hint: Sketch a graph first.]

Consider the given problem here there are two firms “A” and “B” each have same “MC = 2” and the market demand curve is given by, “P = 8 – 0.005*Q”, where “Q = Qa+ Qb”.

a).

So, the revenue function of “A” is given by, “Ra= P*Qa = (8 – 0.005*Q)*Qa = 8*Qa – 0.005*(Qa+Qb)*Qa.

=> Ra = 8*Qa – 0.005*Qa^2 – 0.005*Qb*Qa.

So, the above equation show the “Revenue function” of “A” as function of “Qa” and “Qb”.

b).

So, the “marginal revenue” function of “A” is given below.

=> ?Ra/?Qa = 8 – 2*0.005*Qa – 0.005*Qb => MRa = 8 – 0.01*Qa – 0.005*Qb.

So, the above equation shows the “MR” of “firm a”.

c).

Here we will get the “reaction function” of “A” by equating “MRa” with “MC”. So, the reaction function of “A” is given by.

=> MRa = MC, => 8 – 0.01*Qa – 0.005*Qb = 2, => 6 – 0.005*Qb = 0.01*Qa.

=> Qa = 600 – 0.5*Qb, be the reaction function of “firm A”.

d).

Now, both the firms have same cost function ,=> “Qa=Qb. SO, by plugging this condition into the above “Reaction function” we will get the optimum quantity production.

=> Qa = 600 – 0.5*Qb, => => Qa = 600 – 0.5*Qa, => 1.5*Qa = 600, => Qa = 600/1.5 = 400.

So, the quantity production by each firm is “Qa=Qb=400”.

e).

So, here the total production is given by, “Q= QA+QB = 2*400 = 800. So, at this quantity the corresponding “P” is given by, “P = 8 – 0.005*Q = 8 – 0.005*800 = 4. So, the quantity and the price combination is given by, (Q, P)=(800, 4).

f).

So, the profit function of “A” is given below.

=> ?A = P*QA - ACa*QA = (P – AC)*QA = (4-2)*400 = 2*400 =800.

Similarly, the profit function of “B” is given by, “=> ?B = P*QB - ACb*QB = (P – AC)*QB = (4-2)*400 = 2*400 =800”.

g).

Now, to find out DWL, we 1^{st} have to find out the “Q”
corresponding to “P=MC=2”. So, at MC=2, the corresponding “Q” is
“1200”.

So, the DWL is given by the area ABC in the fig. SO, the DWL = (1/2)*(4-2)*(1200-800) = 400.

Suppose in a duopoly market there are two firms, 1 and 2, each
with a cost function given as TC1 = 10Q1 and
TC2 = 10Q2. The inverse demand in the market
is P = 100 – 2(Q1 + Q2). The firms are
homogeneous product duopoly.
Suppose the market is characterized by Cournot oligopoly.
Calculate each firm’s profit-maximizing output, price, and profit.
Be sure to show all steps needed for this question.
Now suppose the market is characterized by Stackelberg...

Two firms, Firm A and Firm B, operate in a duopoly market. Firm
A has been a leader in the industry for years and has observed how
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units. Marginal costs are assumed to be constant and equivalent
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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.

Two firms are participating in a Stackelberg duopoly. The demand
function in the market is given by Q = 2000 − 2P . Firm 1’s total
cost is given by C1(q1) = (q1)^2 and Firm 2’s total cost is given
by C2(q2) = 100q2. Firm 1 is the leader and Firm 2 is the
follower.
(1) Write down the inverse demand function and the maximization
problem for Firm 1 given that Firm 2 is expected to produce
R2(q1).
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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?

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 = $77.
The cournot-duopoly
equilibrium profit for each firm is _____.

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...

5. 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
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graph i. What is the profit for each firm?
6. Now assume the same market demand curve as...

Problem 1: Consider the following Bertrand
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market demand can be written as ? = 50 − ?. Assume that neither
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market demand at any price. Suppose further that the profit
function for each firm can be written as ? = ?? − ?? = (? −...

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