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Determining third-degree price discrimination with calculus (if you’re interested
Relying on calculus in monopolistic competition
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Profit is always maximized at the quantity where marginal revenue equals marginal cost. To determine marginal revenue, you take the derivative of total revenue with respect to quantity. To determine marginal cost, you take the derivative of total cost with respect to quantity.
Assume your monopolistically competitive firm’s demand curve is
where P is the good’s price in dollars and q is the quantity produced by the monopolistically competitive firm.
Also assume your total cost equation is
where TC is total cost in dollars and q is the quantity of the good produced.
Given these equations, the profit-maximizing quantity of output, price, and profit are determined through the following steps:
1. Determine total revenue.
Total revenue equals price multiplied by quantity.
2. Determine marginal revenue.
Marginal revenue is the derivative of total revenue taken with respect to quantity.
3. Determine marginal cost by taking the derivative of total cost with respect to quantity.
Chapter 13: Monopolistic Competition: Competitors, Competitors Everywhere
4. Set marginal revenue equal to marginal cost and solve for q.
5. Substitute 15,000 for q in the demand equation to determine price.
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Thus, the profit maximizing quantity is 15,000 units and the price is $32.50 per unit.
The following steps enable you to determine the firm’s economic profit per unit and total profit.
6. Determine the average total cost equation.
Average total cost equals total cost divided by the quantity of output q.
7. Substitute q equals 15,000 in order to determine average total cost at the profit-maximizing quantity of output.
Thus, average total cost is $28.70 at the profit-maximizing quantity of 15,000 units.
8. Calculate profit per unit.
Profit per unit equals $3.80.
9. Determine total profit.
Total profit equals profit per unit multiplied by the profit-maximizing quantity of output.
Total profit equals $57,000.
Adjusting to the Long-Run Tendency of Profit Elimination
Easy entry and exit indicate that firms have little or no difficulty in moving into and out of a monopolistically competitive market. If firms perceive an opportunity to earn economic profit in this market, they enter the market. The entry of new firms results in demand decreasing for other firms in the market as some customers switch to the new firm. Entry continues until the typical firm’s demand decreases to the point where the firm earns zero economic profit. At that point, new firms no longer have incentive to enter.
Similarly, if initial economic losses (negative economic profit) exist, firms leave the market. This loss of firms results in an increase in demand for firms remaining in the market until zero economic profit is reached. Demand increases for remaining firms as customers for the firms that left switch to surviving firms.
The long-run equilibrium in monopolistically competitive markets is associated with firms receiving a normal rate of return. A firm receives a normal rate of return when its price equals average total cost.
Figure 13-2 illustrates the movement to the long-run equilibrium from an initial situation with positive economic profit. Initially, the firm’s demand and marginal revenue curves correspond to d* and MR*. Given these curves and the illustrated cost curves, the profit-maximizing quantity and price are q * and p *. The firm is earning positive profit because price is greater than average total cost at q * .
Figure 13-2:
Long-run equilibrium in monopolistic competition.
