Chapter 10: Monopoly: Decision-Making Without Rivals As is the case for any firm, a monopolist determines profit per unit by subtracting average total cost from price. In Figure 10-3, profit per unit is represented by the double-headed arrow labeled π/q. Total profit is determined by multiplying profit per unit by the number of units sold, q0.
Maximizing profit with calculus Figure 10-3 indicates that profit is maximized at the quantity of output where marginal revenue equals marginal cost. Marginal revenue represents the change in total revenue associated with an additional unit of output, and marginal cost is the change in total cost for an additional unit of output. Therefore, both marginal revenue and marginal cost represent derivatives of the total revenue and total cost functions, respectively. You can use calculus to determine marginal revenue and marginal cost; setting them equal to one another maximizes total profit. Earlier in this chapter, in the section “Deriving maximum profit with derivatives,” I noted that the monopolist’s demand curve
generated the total revenue equation.
Also assume your total cost equation is
Given these equations, the profit-maximizing quantity of output is determined through the following steps:
1. Determine marginal revenue by taking the derivative of total revenue with respect to quantity.
2. Determine marginal cost by taking the derivative of total cost with respect to quantity.
3. Set marginal revenue equal to marginal cost and solve for q.
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