Question

In: Economics

The inverse market demand in a homogeneous-product Cournot duopoly is P = 140 – 2(Q1 +...

The inverse market demand in a homogeneous-product Cournot duopoly is P = 140 – 2(Q1 + Q2) and costs are Company 1, C1(Q1) = 18Q1 and Company 2 C2(Q2) = 17Q2. Calculate the equilibrium output for Company 1 Round all calculations to 1 decimal

The inverse market demand in a homogeneous-product Cournot duopoly is P = 133 – 1(Q1 + Q2) and costs are Company 1, C1(Q1) = 10Q1 and Company 2 C2(Q2) = 21Q2. Calculate the equilibrium output for Company 2 Round all calculations to 1 decimal

Solutions

Expert Solution

P = 140 - 2(q1+q2)

Company 1:

Total Revenue TR = P*q1 = 140q1 - 2q12 - 2q1q2

Marginal Revenue = dTR/dq1 = 140 - 4q1 - 2q2

Marginal Cost = 18

The firm equates MR and MC

140-4q1-2q2 = 18

4q1 = 122-2q2

q1 = 30.5 - 0.5q2 ...........1

Company 2:

Total Revenue TR = P*q2 = 140q2 - 2q22 - 2q1q2

Marginal Revenue = dTR/dq1 = 140 - 4q2 - 2q1

Marginal Cost = 17

The firm equates MR and MC

140-4q2-2q1 = 17

4q2 = 123-2q1

q2 = 30.75 - 0.5q1............ Put this value in equation 1 above,

q1 = 30.5 - 0.5q2

q1 = 30.5 - 0.5(30.75 - 0.5q1)

q1 = 30.5 - 15.375 + 0.25q1

0.75q1 = 15.125

q1 = 20.17

Second question:

P = 133 - 1(q1+q2)

Company 1:

Total Revenue TR = P*q1 = 133q1 - q12 - q1q2

Marginal Revenue = dTR/dq1 = 133 - 2q1 - q2

Marginal Cost = 10

The firm equates MR and MC

133 - 2q1 - q2 = 10

2q1 = 123-q2

q1 = 61.5 - 0.5q2 ...........2

Company 2:

Total Revenue TR = P*q2 = 133q2 - q22 - q1q2

Marginal Revenue = dTR/dq1 = 133 - 2q2 - q1

Marginal Cost = 21

The firm equates MR and MC

133 - 2q2 - q1 = 21

2q2 = 112-q1

q2 = 56 - 0.5q1. Put this value in equation 2 above we get,

q1 = 61.5 - 0.5q2

q1 = 61.5 - 0.5(56 - 0.5q1)

q1 = 61.5 - 28 + 0.25q1

0.75q1 = 33.5

q1 = 44.67

Please give a thumbs up if you found the answer helpful.

Rahul Sunny answered 1 year ago
Next > < Previous

Related Solutions

Consider a homogeneous good Cournot duopoly with inverse demand function given by p = 1 –...
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?
The inverse demand for a homogeneous-product Stackelberg duopoly is P = 12,000 -5Q. The cost structures...
The inverse demand for a homogeneous-product Stackelberg duopoly is P = 12,000 -5Q. The cost structures for the leader and the follower, respectively, are CL(QL) = 3,000QL and CF (QF) = 6,000QF.. a. What is the follower’s reaction function? QF= ____ - _____ QL b. Determine the equilibrium output level for both the leader and the follower. Leader output:​ _______ Follower output: _______ c. Determine the equilibrium market price. $________ d.  Determine the profits of the leader and the follower. Leader...
The inverse demand for a homogeneous-product Stackelberg duopoly is P = 18,000 -5Q. The cost structures...
The inverse demand for a homogeneous-product Stackelberg duopoly is P = 18,000 -5Q. The cost structures for the leader and the follower, respectively, are CL(QL) = 2,000QL and CF (QF) = 4,000QF.. a. What is the follower’s reaction function? QF=_____ - ______ QL b. Determine the equilibrium output level for both the leader and the follower. Leader output: Follower output: c. Determine the equilibrium market price. $ d. Determine the profits of the leader and the follower. Leader profits: $...
Firms A and B are Cournot duopolists producing a homogeneous good. Inverse market demand is P...
Firms A and B are Cournot duopolists producing a homogeneous good. Inverse market demand is P = 100 − Q , where P is market price and Q is the market quantity demanded. Each firm has marginal and average cost c = 40. (a) The two firms propose to merge. Derive total output, market price, profit and consumer surplus before the merger and after the merger. Explain intuitively any changes you see to these variables when the merger occurs. (b)...
Let the equation of the inverse demand curve for a Cournot duopoly be p = 88...
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...
Two firms operate in a Cournot duopoly and face an inverse demand curve given by P...
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 compete in a homogeneous product market where the inverse demand function is P =...
Two firms compete in a homogeneous product market where the inverse demand function is P = 10 -2Q (quantity is measured in millions). Firm 1 has been in business for one year, while Firm 2 just recently entered the market. Each firm has a legal obligation to pay one year’s rent of $0.5 million regardless of its production decision. Firm 1’s marginal cost is $2, and Firm 2’s marginal cost is $6. The current market price is $8 and was...
Two firms compete in a market to sell a homogeneous product with inverse demand function P...
Two firms compete in a market to sell a homogeneous product with inverse demand function P = 600 − 3Q. Each firm produces at a constant marginal cost of $300 and has no fixed costs. Use this information to compare the output levels and profits in settings characterized by Cournot, Stackelberg, Bertrand, and collusive behavior.
Two firms compete in a homogeneous product market where the inverse demand function is P =...
Two firms compete in a homogeneous product market where the inverse demand function is P = 20 -5Q (quantity is measured in millions). Firm 1 has been in business for one year, while Firm 2 just recently entered the market. Each firm has a legal obligation to pay one year’s rent of $1 million regardless of its production decision. Firm 1’s marginal cost is $2, and Firm 2’s marginal cost is $10. The current market price is $15 and was...
Two firms compete in a market to sell a homogeneous product with inverse demand function P...
Two firms compete in a market to sell a homogeneous product with inverse demand function P = 400 – 2Q. Each firm produces at a constant marginal cost of $50 and has no fixed costs -- both firms have a cost function C(Q) = 50Q. If the market is defined as a Bertrand Oligopoly, what is the market price? Refer to the information above. What is the total amount of Q produced in this market? How much does firm 1...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT