Question

In: Economics

Two firms, a and b, compete in a market to sell homogeneous products with inverse demand...

Two firms, a and b, compete in a market to sell homogeneous products with inverse demand function P = 400 – 2Q where Q = Q_a + Q_b. Firm a has the cost function C_a = 100 + 15Q_a and firm b has the cost function C_b = 100 + 15Q_b. Use this information to compare the output levels, price and profits in settings characterized by the following markets:

Cournot
Stackelberg
Bertrand
Collusion

Solutions

Expert Solution

Answer:

Given that,

Cournot
Stackelberg
Bertrand
Collusion

P = 400 – 2Q , Q = Q_a + Q_{b , MC=15.}

(1) Cournot:

Symmetric equation,

So, 6q=385

q=385/6=64.167

Q=2q=385/3=128.33

p=400-2(128.33)=143.33

(p-MC)q-100

=(143.33-15)(64.167)-100

Answer=8134.76

(2) Stackelberg:

Max ,, st

Let a is leader ,b is follower

=(385-2q_a)/4

So , =(400-15-2q_a-2q_b)q_a

=(385-2q_a-2(385-2q_a)/4)q_a

=(385-2q_a-385/2+q_a)q_a

=(385/2-q_a)q_a=385/2q_a-q_a^2

385/4=96.25

48.125

144.375,

400-2

=111.25

=(111.25-15)96.25=9264.0625

=(111.25-15)(48.125)=4632.03125

(3) Bertrand:

=(400-15)/2=192.5

(4) Collusion:

MR=MC, 400-4Q=15

385=4Q

=96.25, 207.5

(207.5)(96.25)

=18528.125

***Please comment on any doubt.Please give up vote.

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

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 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...

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 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...

1. Consider a market of homogeneous products in which firms compete on price. Demand in this...

1. Consider a market of homogeneous products in which firms compete on price. Demand in this market is given by q(p) = 50 -10p Consumers buy from the producer with the lowest price. If the prices of both firms are the same then they purchase from E. There are both an incumbent firm M and a potential entrant E which can produce the good at marginal costs 3 and 2 , respectively. Prior to entry, E must incur an entry...

Two firms compete in a market with inverse demand P(Q) = a − Q, where the...

Two firms compete in a market with inverse demand P(Q) = a − Q, where the aggregate quantity is Q = q1 + q2. The profit of firm i ∈ {1, 2} is πi(q1, q2) = P(Q)qi − cqi , where c is the constant marginal cost, with a > c > 0. The timing of the game is: (1) firm 1 chooses its quantity q1 ≥ 0; (2) firm 2 observes q1 and then chooses its quantity q2 ≥...

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)...

Two firms, A and B, compete as duopolists in an industry. The firms produce a homogeneous...

Two firms, A and B, compete as duopolists in an industry. The firms produce a homogeneous good. Each firm has a cost function given by: C(q) = 30q + 1.5q2 The (inverse) market demand for the product can be written as: P =300−3Q, where Q = q1 + q2, total output. (a) If each firm acts to maximize its profits, taking its rival’s output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected...

Two firms, A and B, compete as duopolists in an industry. The firms produce a homogeneous...

Two firms, A and B, compete as duopolists in an industry. The firms produce a homogeneous good. Each firm has a cost function given by: C(q) = 30q + 1.5q2 The (inverse) market demand for the product can be written as: P = 300 − 3Q , where Q = q1 + q2, total output. Question: If each firm acts to maximize its profits, taking its rival’s output as given (i.e., the firms behave as Cournot oligopolists), what will be...

Consider two firms competing to sell a homogeneous product by setting price. The inverse demand curve...

Consider two firms competing to sell a homogeneous product by setting price. The inverse demand curve is given by P = 6 − Q. If each firm's cost function is Ci(Qi) = 6 + 2Qi, then each firm will symmetrically produce _________ units of output and earn ___________. Multiple Choice 2 units; profits of $2 4 units; profits of $6 4 units; losses of $2 2 units; losses of $6

Subjects