Question

When a monopolist identifies its profit-maximizing quantity of output, how does it decide what price to charge?

Short answer

A monopolist identifies its profit-maximizing quantity of output by equating its marginal revenue (MR) with its marginal cost (MC). Once the optimal output level is determined, the monopolist finds the price to charge by plugging the profit-maximizing quantity into the demand curve equation (P(Q)). In this way, the price is set based on the demand curve at the profit-maximizing output.

Step-by-step solution

Understanding the Concepts

A monopolist is a single firm that controls the entire market for a product. It will try to maximize profit by producing a quantity that balances its marginal revenue (the additional revenue generated from selling one more unit) with its marginal cost (the additional cost incurred for producing one more unit). The monopolist identifies the profit-maximizing output by finding the point where marginal revenue equals marginal cost (MR = MC). Once the output level has been determined, the price at which it will sell those goods is obtained from the demand curve.

Determine the Marginal Revenue Curve

To find the marginal revenue curve, we need to understand the monopolist's demand curve, which is usually a downward-sloping curve. As the monopolist increases the quantity of output it sells, the price it can charge decreases. The price (P) at each quantity (Q) can be expressed as a function of demand, P(Q). The revenue earned by the monopolist is the product of price and quantity (P x Q). The marginal revenue (MR) curve shows the increase in total revenue resulting from selling one more unit of output, so we differentiate the total revenue with respect to quantity (Q) to find the marginal revenue curve.

Determine the Marginal Cost Curve

A firm has different costs, including fixed costs (which do not vary with output) and variable costs (which vary with output). The total cost (C) is the sum of fixed and variable costs, C(Q). To find the marginal cost (MC), we need to approximate the increase in total cost caused by a one-unit increase in output. To derive the marginal cost curve, differentiate the total cost function with respect to quantity (Q).

Find the Profit-Maximizing Output

Once we have both the marginal revenue curve (MR) and the marginal cost curve (MC), we can find the profit-maximizing output. Set MR equal to MC and solve for the quantity that equates the two (MR = MC). This point is where the monopolist identifies its optimal quantity of output.

Determine the Price to Charge at the Profit-Maximizing Output

After identifying the profit-maximizing output, the monopolist needs to set the price to charge for that quantity. To find the price, we obtain the corresponding point on the demand curve. Plug the profit-maximizing quantity (Q) into the demand curve equation (P(Q)) to calculate the price that the monopolist will charge. In conclusion, a monopolist identifies its profit-maximizing quantity of output by equating its marginal revenue with its marginal cost (MR = MC). Once the optimal level of output is determined, the monopolist will set the price based on the demand curve.