12. A monopolist faces a constant marginal cost of $1 per unit. If at the price he is charging, the price elasticity of demand for the monopolist’s output is –0.5, then
To determine what happens when the monopolist faces a price elasticity of demand of -0.5, we need to understand the concept of price elasticity and its implications for monopolists.
Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. A negative elasticity value signifies an inverse relationship between price and quantity demanded. In this case, the price elasticity of demand for the monopolist’s output being -0.5 implies that demand is relatively inelastic, meaning that a change in price will result in a proportionately smaller change in quantity demanded.
Given that the monopolist faces a constant marginal cost of $1 per unit, we can analyze the implications of this situation:
1. Increasing Prices: Since demand is inelastic (-0.5), the monopolist can increase the price and still generate revenue. The decrease in quantity demanded resulting from the price increase will be proportionately smaller than the increase in price. However, it is important to note that the monopolist's goal is to maximize profit, not just revenue.
2. Maximizing Profit: To determine the optimal price and quantity to maximize profit, the monopolist needs to consider the relationship between marginal cost and marginal revenue. Marginal revenue represents the change in total revenue resulting from a one-unit increase in quantity sold. The profit-maximizing condition for a monopolist is to produce where marginal revenue equals marginal cost.
Since marginal cost is constant at $1 per unit, the monopolist should set the marginal revenue equal to $1 to ensure profit maximization. However, we need more information to determine the specific quantity and price that would achieve this condition.
In summary, the fact that the monopolist faces a constant marginal cost of $1 per unit and a price elasticity of demand of -0.5 indicates that the demand for the product is inelastic. This means that the monopolist can increase the price and still generate revenue, but further analysis is required to determine the optimal price and quantity that will maximize profit.