How does a monopoly firm determine its price?

Question

BlackTom AI · Accepted Answer

A monopoly chooses output where marginal revenue equals marginal cost (MR = MC), and then reads the price consumers will pay for that output from the market (demand) curve.

1) Relevant knowledge points and concepts
- Profit maximisation for any firm occurs where MR = MC.  
- For a monopolist the demand curve is the market demand; price depends on the quantity sold.  
- Marginal revenue (MR) for a downward‑sloping linear demand is less than price and falls faster than the demand curve.  
- The monopolist cannot set price independently of quantity — the demand curve constrains the price it can obtain for any output.

2) Step‑by‑step reasoning
- Write demand as P(Q). Total revenue TR = P(Q)·Q.  
- Compute MR = dTR/dQ.  
- Set MR = MC and solve for the profit‑maximising output Q*.  
- Take Q* and substitute into the demand function P(Q*) to get the monopoly price.

3) Example calculation (linear demand)
- Suppose P = a − bQ, so TR = aQ − bQ^2.  
- MR = dTR/dQ = a − 2bQ.  
- With constant MC = c, set MR = MC: a − 2bQ* = c.  
- Solve: Q* = (a − c) / (2b).  
- Price: P* = a − bQ* = a − b[(a − c)/(2b)] = a − (a − c)/2 = (a + c)/2.  
This shows P* is read off the demand curve at Q* and lies above MC.

4) Why the correct answer is correct
- Option (a) states the firm chooses Q* (via MR = MC) and uses the demand curve to determine the price that will sell that output. That is exactly the standard monopoly pricing rule.

5) Why the other options are incorrect
- (b) A monopolist cannot pick any price unconstrained; demand determines how much will be bought at a given price.  
- (c) Elasticity alone does not determine the profit‑maximising price; the correct rule is MR = MC, which implicitly incorporates elasticity.  
- (d) The average cost minimum is an efficiency concept, not the monopoly profit‑maximising price; monopolists typically set P > MC and do not generally price at average cost minimum.

Conclusion: The correct choice is (a), which matches the provided answer.

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