A natural monopolist has TC = 75Q - 4Q 2 + 0.3Q 3 and faces a market demand P =

Question

A natural monopolist has TC = 75Q - 4Q2 + 0.3Q3 and faces a market demand P = 115 - 7.5Q. Regulators will try to set a price that eliminates as much dead weight loss from monopoly power while still making it worthwhile for the firm to operate. What price will regulators set for the natural monopolist while prohibiting other firms from entering the market? A natural monopolist has TC = 75Q - 4Q2 + 0.3Q3 and faces a market demand P = 115 - 7.5Q. Regulators will try to set a price that eliminates as much dead weight loss from monopoly power while still making it worthwhile for the firm to operate. What price will regulators set for the natural monopolist while prohibiting other firms from entering the market?

Explanation / Answer

The price that eliminates deadweight loss is equal to the perfectl competitive outcome which occurs when price is set to Marginal cost (MC).

MC = dTC/dQ = 75 - 8Q + Q2

Equating with Price,

75 - 8Q + Q2 = 115 - 7.5Q

Q2 - 1.5Q - 40 = 0

Solving this quadratic equation using online solver,

Q = 7.12 or Q = - 5.62 (Since Q is non-negative, this value is inadmissible)

When Q = 7.12,

P = 115 - (7.5 x 7.12) = 115 - 53.4 = 61.6

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