Question

Maximizing Profits A manufacturer of tennis rackets finds that

the total cost C(x) (in dollars) of manufacturing x rackets/day is
given by C(x) = 200 + 7x + 0.0003x2. Each racket can be sold at a
pric

Answer 1

In a perfectly competitive market, firms maximize profits by producing at an output level where the price, marginal revenue, and marginal cost are equal. Total revenue minus total cost equals profit, and the profit-maximizing quantity is where this difference is greatest.

Step-by-step explanation:

To maximize profits in a perfectly competitive market, firms determine the optimal level of output where the price equals marginal revenue (MR) and marginal cost (MC). Total Revenue (TR), Total Cost (TC), and profits are critical factors in this calculation. Profits are maximized when the quantity of output is at a level where total revenue exceeds total cost by the greatest amount.

For example, a raspberry farm selling packs at $5 each may find that producing 85 packs (point E') maximizes profits, with total revenues shown as a rectangle up to E' and the price level, and total costs as the area of a rectangle up to point C. The difference is the profit area, or the blue shaded rectangle on top. Similarly, using data from Table 8.1, a firm's total profits are found by identifying the output level with the largest vertical gap between the TR and TC curves.