5. (6 pts). Boron Industries is a monopolist that owns two mines. Mine B is smal

Question

5. (6 pts). Boron Industries is a monopolist that owns two mines. Mine B is smaller and has less capacity, thus its marginal costs rise more steeply than Mine A’s. Mine A has TCa = 5000 + 50*qa + 2 qa2 Mine B has TCb = 8000 + 50*qb + 3qb2 a. (1) Before knowing demand, can you tell whether the firm might choose to operate just one of the two mines? Explain. b. (5) Now assume inverse demand for the firm’s output is P = 1150 - Q. Find optimal output at each plant, the monopolist’s total output, price, and profit or loss.

Explanation / Answer

1)The firm might chose to only operate in Mine A since marginal costs of Mine B are rising and the firm will experience diseconomies of scale, lower than proportionate output for a proportional increase in inputs.

2) The Marginal Revenue curve has twice the slope of the demand curve:

Therefore, P = 1150-Q

and, MR=1150-2Q

MC is the slope of each mines' TC function :

MCa= 50+4Qa

Equating MC=MR for profit maximization:

50+4Qa=1150-2Qa

Qa= 1100/6=183

Similiarly, 50+6Qb=1150-Qb

Qb= 1100/7= 157

At Plant A:

Profit maximizing price = 1150-2*(183) = $783

Total Maximum profit= TR-TC = (1150Q-Q^2)- (5000+50Q+2Q^2)

At Q=183:

Profit = $95833

At plant B:

Profit maximizing price = 1150-2*(157) = $836

Total Maximum profit= TR-TC = (1150Q-Q^2)- (8000+50Q+3Q^2)= $66104

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