Suppose an unregulated electric company is a monopolist and faces demand of Q = 50 – 10P.

If this company has zero marginal costs, its profit-maximizing price is

Question

Suppose an unregulated electric company is a monopolist and faces demand of Q = 50 – 10P.

If this company has zero marginal costs, its profit-maximizing price is

BlackTom AI · Accepted Answer

A monopolist sets output where marginal revenue (MR) equals marginal cost (MC). With zero marginal cost, the profit-maximizing output is where MR = 0.

1) Relevant concepts:
- Convert demand to inverse demand (P as a function of Q).
- Total revenue R = P·Q. Marginal revenue is dR/dQ.
- Profit maximization for a monopolist: choose Q such that MR = MC.

2) Reasoning and 3) calculations step-by-step:
Start from the demand function Q = 50 − 10P. Solve for P:
P = (50 − Q)/10 = 5 − 0.1Q.  
Total revenue R(Q) = P·Q = (5 − 0.1Q)Q = 5Q − 0.1Q^2.  
Marginal revenue MR = dR/dQ = 5 − 0.2Q.  
Set MR equal to MC (MC = 0): 5 − 0.2Q = 0.  
Solve for Q: 0.2Q = 5 → Q = 25.  
Find the corresponding price using inverse demand: P = 5 − 0.1·25 = 5 − 2.5 = 2.5.

(For completeness, profit = R − cost = P·Q − 0 = 2.5·25 = 62.5.)

4) Why this is correct:
MR falls twice as fast as the demand slope; equating MR to MC = 0 yields the output that maximizes profit given zero additional cost. The corresponding price from the demand curve is the monopoly price that buyers will pay for that quantity.

5) Why the other options are incorrect:
- $0. would yield zero revenue and is not profit-maximizing when positive profit is possible.  
- $1. corresponds to a much larger Q (Q = 40) and MR at that Q would be positive, so the monopolist could increase profit by producing more until MR falls to zero.  
- $5. is the choke price (P when Q = 0); it yields zero sales, so it is not profit-maximizing because selling some positive quantity at a lower price yields positive profit.

6) Conclusion:
The profit-maximizing price is $2.50, which matches the provided answer.

Suppose an unregulated electric company is a monopolist and faces demand of Q = 50 – 10P. If this company has zero marginal costs, its profit-maximizing price is单项选择题

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