Question

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.

Answer 1

Answer:

Explanation:

We need to find the function of firm 1 and firm 2 which we have as

PQ1/Q1= 300

600Q1– 3Q21 – 3Q1Q2/ = 300

300 – 6Q1 – 3Q2= 300

Q1 = 1/6(600 -300 – 3Q2)

Q1 = 50 – 1/2Q2 Reaction function for firm 1

Q2 = 50 – 1/2Q1 Reaction function for firm 2

Cournot which we have as;

Q2 = = 1/6(600 -300 – 3Q1)

Q2 = 50 – 1/2Q1

Q2 = 50 – ½(50 – 1/2Q1)

Q2 = 50 – 25 + 1/4Q1

Q1 = 100/3 = 33.33 Output

Q2= 100/3 = 33.33 Output

Equilibrium market price which is

P = 600 – 3(Q2+ Q2)600 – 3(100/3 + 100/3)= 400

Profits for firm 1

Π1 = TR1– C1= PQ1 – C1=400 * 100/3 – 300 * 100/3= 10000/3 = $3,333.33 For firm 1

Profits for firm 2

Π2 = TR2– C2= PQ2 – C2=400 * 100/3 – 300 * 100/3= 10000/3 = $3,333.33 For firm 2

Stackelberg is given as ;

QL= (600 – 300)/2*3 = 50 Firm 1 output is QL = 50

QF= (600 – 300)/4*3 = 25 Firm 2 output is QF =25 P = 600 – 3*75 = 375

Π1 = (375-300) * 50 = 3750Profit for firm 1

Π2 = 75*25 = 1875 Profit for firm 2

Bertrand is given as ;

Under this competition, price is the same to marginal cost and profits are zero

600 – 3Q = 300

Q = 100 Output = 100

P = Zero

Collusive Behavior is given as;

MR=MC600 - 6Q = 300

300 = 6QQ = 50 Output

P = 600 – 3*50 = 450

Π = (450 – 300) * 50 = 7,500profit