Question

In: Economics

Two oligopolies (Firm A and Firm B) have access to the same the same technology and...

Two oligopolies (Firm A and Firm B) have access to the same the same technology and have similar costs. FC = 0 MC = AVC = ATC = $100 Assume the demand of the product is given below: P=1000-Q Remember Q= q_A+ q_B Where q_(A ) is production by firm A and q_B-is production by firm B c) Now assume that the firms compete by setting quantities and they both move at the same time. Assume that the reaction functions for Firm A and B are given below. qa=450-.5qb reaction function firm AbPPposarQtS4PrK0P6AsfNa5J0CBpuMSTmpTMCGY qa=900-2qb reaction function firm BT79B8Hf9vkAAAAAASUVORK5CYII= i. Obtain the Nash-Cournot equilibrium and illustrate it in a diagram ii. Obtain the price of this product under these conditions iii. Obtain the profits of each firm. d) Now assume firm B is going to move first. Assume that once firm B moves, firm A will respond using their reaction function. i. Obtain qa and qb. ii Obtain the P of the market. iii Obtain economic profit of firm A and firm B iv. Who has the advantage the first mover or the second mover?

Solutions

Expert Solution

Demand Function: P = 1000 - Q, Where Q = q_a + q_b

Reaction function of Firm A: q_a = 450 - 0.5q_b

Reaction function of Firm : q_a = 900 - 2q_b

ii.

Equating reaction function of firm B in reaction function of firm A, we get

450 - 0.5q_b = 900 - 2q_b

=> 1.5q_b = 450

=> q_b = 300, q_a = 300

P = 1000 -(q_a + q_b) = 1000 - (300 + 300) = 400

iii.

Total profit of both firm = TR - TC

=> P*Q - ATC*Q

=> 400*600 - 100*600

=> 240000 - 60000

=> 180000

Each firm profit = 90000

d) Now the firm B is going to move first. Once firm B moves, firm A will respond using their reaction function.

i. The demand function is P = 1000 - q_a - q_b

Profit for Firm B (_b)= TR - TC

= 1000q_b - q_aq_b - q_b² - 100q_b

= 900q_b - q_aq_b - q_b²

= 900 - q_a - 2q_b

=> q_b = 450 -0.5q_a

Substituting the reaction function of firm B in the profit function of firm A

Profit for Firm A (_a)= TR - TC

= 1000q_a - q_a² - q_aq_b - 100q_a

= 900q_a - q_a² - q_aq_b

= 900q_a - q_a² - q_a(450 -0.5q_a)

= 900q_a - q_a² - 450q_a + 0.5q_a²

= 450q_a - 0.5q_a²

= 450 - q_a

=> q_a = 450, q_b = 450 - 0.5(450) = 450 -225 = 225

ii.

P =1000 - (450 + 225) = 1000 - 675 = 325

iii.

Profit for Firm B (_b)= TR - TC

= 900q_b - q_aq_b - q_b²

= 900*225 - 450*225 - (225)²

= 50625

Profit for Firm A (_a)= TR - TC

= 900q_a - q_a² - q_aq_b

=900*450 - (450)² - 450*225

= 101250

iv.

The second mover has the advantage, here it is Firm A.

Rahul Sunny answered 11 months ago

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