Question

A monopolist is facing a downward sloping linear market demand. His variable cost of production is zero. The profit maximizing price will

• A. lie in the strictly inelastic region of the demand curve
• B. lie in the strictly elastic region of the demand curve
• C. be at the unitary elastic point of the demand curve
• D. be equal to the marginal cost of production

Hint:

A monopolist always operates on the elastic part of the demand curve because total revenue and profit fall in the inelastic region.

Answer 1

The Correct Option is B

Step 1: Recall monopoly pricing condition.
The monopolist maximizes profit where $MR = MC$. Given $MC = 0$, the monopolist produces where $MR = 0$.
Step 2: Relationship between elasticity and marginal revenue.
\[ MR = P \left(1 - \frac{1}{|E|}\right). \] Setting $MR = 0$ gives $|E| = 1$, i.e., the unitary elasticity point divides elastic and inelastic regions.
Step 3: Check profit behavior.
In the inelastic region ($|E|<1$), $MR<0$ — producing more reduces total revenue. Hence, a profit-maximizing monopolist never operates there. Thus, equilibrium must lie in the **elastic region** ($|E|>1$), where $MR>0$.
Step 4: Conclusion.
The profit-maximizing price lies in the strictly elastic region of the demand curve.