Economics: Proving the Profit-Maximizing Rule

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We just developed the firm's rule for profit maximization. The rule is produce where price is equal to marginal cost and make sure that marginal cost is increasing. What I want to do in this his short segment is apply that rule to the numbers that we were looking at a moment ago and make sure that it jives with our calculations of profits in a real example. Then I want to prepare you for the next step in analyzing a firm's profit maximization decision.
So let's look at our real numbers. In our real numbers from a moment ago, we saw that profits were maximized when the firm was producing 48 television sets. Not surprisingly, notice that if you calculate the marginal cost of production, that when you're producing 48 television sets, the marginal cost of production is $333. That's just under $500, which is the price of a television set. If you go beyond to produce the 49^th television set, the marginal cost of the television set has risen to $1,000. Marginal cost is now greater than price, and the firm can improve its position by cutting back on its output. Anytime marginal cost is greater than price, you can reduce your marginal cost by reducing output and getting back in the direction of profit maximization.
Notice here, that the firm is maximizing profit, profit continues to increase, as long as marginal cost is less than price. But after marginal cost exceeds price, profit begins to decline again. One more thing to notice about these numbers is this. Marginal cost is equal to price when we're producing two television sets. Marginal cost is $500 per television set. But notice, however, at that point, marginal cost is declining. It's going from something to $500 to $125 down to $50. Marginal cost is decreasing at that point. And as we talked about a moment ago, if you produce where price equals marginal cost and marginal cost is decreasing, then you're going to be minimizing profit, and that's exactly what we wind up with. Price equals marginal cost gives us the smallest profit number or the biggest loss that we earn in this whole table. So our two rules then to repeat are--price equals marginal cost and make sure marginal cost is increasing to make sure you're at a profit maximum instead of a profit minimum.
Now all this talk about price and marginal cost and marginal cost increasing--this is the rule for a firm to do the best it can with what it has. This is the way a firm maximizes its profit. However, just because a firm is maximizing its profit, doesn't mean that the profit is positive. Maximizing a profit and minimizing a loss amount to the same thing. How do we make sure that when a firm is maximizing its profit, when it's doing the best that it can, that it's actually making a positive profit instead of a loss, a negative profit? Well, this is where those average cost curves come back in. The average cost curve doesn't tell us about what's happening at the margin. It looks at the whole picture. It summarizes everything going on in the firm to tell us the cost, on average, of producing a television set. The average cost tells us the per unit cost of producing a television set. As long as the price is above the per unit cost, the firm is maximizing its profit and making a positive profit. If the price is below the per unit cost, the firm is making a loss.
So when you find that point of price equals marginal cost, and the marginal cost curve is increasing, once you've found the best the firm can do, then compare the price at that point with the average total cost. And that lets you know whether the firm is making a positive profit or if price is less than cost, making a loss. We'll do that next when we look at the curves.
Perfect Competition
Calculating Profit and Loss
Proving to Profit-Maximizing Rule Page [1 of 1]