Consider a competitive industry with a linear demand P 200

Consider a competitive industry with a linear demand P = 200 - Q and a constant average and marginal cost AC = MC = 50. Provide the industry output and price and the implied consumer surplus. Due to a series of mergers, the industry has now been monopolized but faces a lower marginal cost AC = MC = 40. Did these mergers improve welfare as measured by the sum of consumer surplus and firm profit?

Solution

Price is nothing but Average revenue of the firm and hene if AR = 200-Q

TR = 200Q-Q²

MR = 200-2Q

Equilibrium is established where MR =MC

200-2Q = 50

2Q = 150

Q = 75

P = 200-75 = 125

Consumer surplus (Intercept of Y axis-equilibrium Price) *(Equilibrium quantity -0)

(200-125)*(75-0) = 75*75 = 5625

Profits = TR-TC

TR = 200(75)-(75)²

9375

TC = 75*50 = 3750

Profits = 5625

b) After merger,

TR = 200Q-Q²

MR = 200-2Q

Equilibrium is established where MR =MC

200-2Q = 40

2Q = 160

Q = 80

P = 200-80 = 120

Consumer surplus (Intercept of Y axis-equilibrium Price) *(Equilibrium quantity -0)

(200-120)*(80-0) = 80*80 = 6400

Total profits

TR = 16000-6400 = 9600

TC = 3200

Profts = 6400

Welafare has increased in terms of consumer surplus and profits.