Consider the relationship between monopoly pricing and price elasticity of demand.
a. Explain why a monopolist will never produce a quantity at which the demand curve is inelastic. (Hint: If demand is inelastic and the firm raises its price, what happens to total revenue and total costs?)
b. Draw a diagram for a monopolist, precisely labeling the portion of the demand curve that is inelastic. (Hint: The answer is related to the marginal-revenue curve.)
c. On your diagram, show the quantity and price that maximize total revenue.
The correct answer and explanation is :
a. Why a monopolist will never produce a quantity at which the demand curve is inelastic:
A monopolist maximizes profit by producing the quantity where marginal revenue (MR) equals marginal cost (MC). When the demand curve is inelastic, an increase in price leads to a proportionally smaller decrease in quantity demanded, resulting in total revenue (TR) falling.
If a monopolist were to operate in the inelastic portion of the demand curve, any price increase would reduce the total quantity sold by a relatively small amount, but total revenue would decrease because the loss in quantity sold outweighs the higher price. This would reduce the monopolist’s profits, making it irrational for the monopolist to produce in this range. Essentially, the monopolist can increase its profits by moving to the elastic portion of the demand curve where price increases lead to higher total revenue and better profit margins.
Therefore, a monopolist avoids the inelastic region because raising the price further would decrease total revenue and profits, which is undesirable.
b. Diagram for a monopolist with inelastic portion of the demand curve:
To visualize this, consider the following elements:
- Demand curve (D): The downward-sloping curve showing the relationship between price and quantity.
- Marginal revenue curve (MR): A curve that lies below the demand curve. It also slopes downward, but it falls faster than the demand curve.
- Marginal cost curve (MC): The curve that shows the cost of producing one additional unit. It typically slopes upward as production increases.
The inelastic portion of the demand curve is the part where the absolute value of the price elasticity of demand (PED) is less than 1. This occurs to the right of the point where the marginal revenue curve intersects the demand curve.
c. Quantity and price that maximize total revenue:
Total revenue is maximized when the price elasticity of demand is exactly 1 (unit elastic). This corresponds to the point where the marginal revenue curve intersects the demand curve.
On the diagram:
- The monopolist maximizes total revenue at the point where the MR curve intersects the demand curve. This is the unit elastic point.
- Beyond this point, the demand curve becomes inelastic, and total revenue decreases as price increases.
Summary Explanation:
A monopolist will never produce where the demand curve is inelastic because increasing prices in this region would reduce total revenue. The monopolist maximizes profit at the point where marginal revenue equals marginal cost, which occurs in the elastic portion of the demand curve. The quantity and price that maximize total revenue are determined by the point where marginal revenue intersects the demand curve.