No Such Thing as a Free Lunch: Principles of Economics (Part 37)

Rock 'n' roll accepted me and paid me, even though I loved the big bands... I went that way because I wanted a home of my own. I had a family. I had to raise them. Let's don't leave out the economics. No way.

Chuck Berry

Short-Run Cost and Output Decisions

(Part D)

by

Charles Lamson

Output Decisions: Revenues, Costs, and Profit Maximization

To calculate potential profits, firms must combine their cost analyses with information on potential revenues from sales. After all, if a firm cannot sell its product for more than the cost of production, it will not be in business long. In contrast, if the market gives the firm a price that is significantly greater than the cost it incurs to produce a unit of its output, the firm may have an incentive to expand output. Large profits might also attract new competitors to the market.

Let us now examine in detail how a firm goes about determining how much output to produce. For the sake of simplicity, we will continue to examine the decisions of a perfectly competitive firm. A perfectly competitive industry has many firms that are small relative to the size of the market, and the output of one firm is identical to the output of its competitors. In such an environment, product price is determined by the interaction of many suppliers and many demanders.

Figure 9 shows a typical firm in a perfectly competitive industry. Price is determined in the market at P* = $5. The individual firm can charge any price that it wants for its product, but if it charges above $5, the quantity demanded falls to zero, and the firm will not sell anything. The firm could also sell its product for less than $5, but there is no reason to do so.

In the short run, a competitive firm faces a demand curve that is simply a horizontal line at the market equilibrium price. In other words, competitive firms face perfectly elastic demand (When the demand for a good is perfectly elastic, any increase in the price will cause the demand to drop to zero.) in the short run.

In Figure 9, market equilibrium price is P* = $5 and the firm's perfectly elastic demand curve is labeled d.

Total Revenue (TR) and Marginal Revenue (MR)

Profit is the difference between total revenue and total cost. Total revenue is the total amount that a firm takes in from the sale of its product. A perfectly competitive firm sells each unit of product for the same price, regardless of the output level it has chosen. Therefore, total revenue is simply the price per unit times the quantity of output that the firm decides to produce:

total revenue = price * quantity

TR = P * q

Marginal revenue (MR) is the added revenue that a firm takes in when it increases output by one additional unit. If a firm producing 10,521 units of output per month increases that output to 10,522 units per month, it will take in an additional amount of revenue each month. The revenue associated with the 10,522nd unit is simply the amount that the firm sells that one unit for. Thus, for a competitive firm, marginal revenue is simply equal to the current market price of each additional unit sold. In Figure 9, for example, the market price is $5. Thus, if the representative firm raises its output from 10,521 units to 10,522 units, its revenue will increase by $5.

A firm's marginal revenue curve shows how much revenue the firm will gain by raising output by one unit at every level of output. The marginal revenue curve and the demand curve facing a competitive firm are identical. The horizontal line in figure 9(b) can be thought of as both the demand curve facing the firm and its marginal revenue curve:

P* = d = MR

Comparing Costs and Revenues to Maximize Profit

The discussion in the next few paragraphs conveys one of the most important concepts in all of microeconomics. As we pursue our analysis, remember that we are working under two assumptions: (1) that the industry we are examining is perfectly competitive and (2) that firms choose the level of output that yields the maximum total profit. 

The Profit-Maximizing Level of Output Look carefully at the diagram in Figure 10. Once again we have the whole market, or industry, on the left and a single, typical small firm on the right. And again the current market price is P*.

First, the firm observes market price [see Figure 7(a)] and knows that it can sell all that it wants for P* = $5 per unit. Next, it must decide how much to produce. It might seem reasonable to pick the output level where marginal cost is at its minimum point---in this case, at an output of 100 units. Here the difference between marginal revenue, $5, and marginal cost, $2.50 is the greatest.

Remember that a firm wants to maximize the difference between total revenue and total cost, not the difference between marginal revenue and marginal cost. The fact that marginal revenue is greater than marginal cost actually indicates that profit is not being maximized. Think about the 101st unit. Adding that single unit to production each period adds $5 to revenues but adds only about $2.50 to cost. Profit each period would be higher by about $2.50. Thus, the optimal (profit-maximizing) level of output is clearly higher than 100 units.

Now look at an output level of 250 units. Here, once again, raising output increases profit. The revenue gained from producing the 251st unit (marginal revenue) is still $5, and the cost of the 251st unit (marginal cost) is only about $4.

As long as marginal revenue is greater than marginal cost, even though the difference between the two is getting smaller, added output means added profit. Whenever marginal revenue exceeds marginal cost, the revenue gained by increasing output by one unit per period exceeds the cost incurred by doing so.

This logic leads us to 300 units of output. At 300 units, marginal cost has risen to $5. At 300 units of output, P* = MR = MC = $5.

Notice that if the firm were to produce more than 300 units, marginal cost rises above marginal revenue. At 340 units of output, for example, the cost of the 341st unit is about $5.70 while that added unit of output still brings in only $5 in revenue, thus reducing profit. It simply does not pay to increase output above the point where marginal cost rises above marginal revenue because such increases will reduce profit.

The profit-maximizing perfectly competitive firm will produce up to the point where the price of its output is just equal to short run marginal cost---the level of output at which P* = MC.

Thus, in Figure 10, the profit-maximizing level of output, q*, is 300 units.

Keep in mind, though, that all types of firms (not just those in perfectly competitive industries) are profit maximizers. Thus, the profit-maximizing output level for all firms is the output level where MR equals MC.

In perfect competition, however, MR = P, as shown earlier. Hence, for perfectly competitive firms we can rewrite our profit-maximizing condition as P = MC.

Important note: The key idea here is that firms will produce as long as marginal revenue exceeds marginal cost. If marginal cost rises smoothly, as it does in Figure 10, then the profit-maximizing condition is that MR (or P) exactly equals MC. If marginal cost moves up in increments---as it does in the following numerical example---marginal revenue or price may never exactly equal marginal cost. The key idea still holds.

A Numerical Example Table 6 represents some data for another hypothetical firm. Let us assume that the market has set a $15 unit price for the firm's product. Total revenue in column 6 is the simple product of P * q (the numbers in column 1 * $15). The table included revenues, and we can calculate the profit, which is shown in column 8.

Column 8 shows that a profit-maximizing firm would choose to produce 4 units of output. At this level, profits are $20. At all other output levels, they are lower. Now let us see if "marginal" reasoning leads us to the same conclusion.

First, should the firm produce at all? If it produces nothing, it suffers losses equal to $10. If it increases output to one unit, marginal revenue is $15 (remember that it sells each unit for $15), and marginal cost is $10. Thus, it gains $5, reducing its loss from $10 each period to $5.

Should the firm increase output to 2 units? The marginal revenue from the second unit is again $15, but the marginal cost is only $5. Thus, by producing the second unit, The firm gains $10 ($15 - $5) and turns a $5 loss into a $5 profit. The third unit adds $10 to profits. Again, marginal revenue is $15 and marginal cost is $5, an increase in profit of $10, for a total profit of $15.

The Short-Run Supply Curve

Consider how the typical firm shown in Figure 10 would behave in response to an increase in price. In Figure 11(a), assume that something causes demand to increase (shift to the right), driving price from $5 to $6 and finally to $7. When price is $5, a profit-maximizing firm will choose output level 300 in Figure 11(b). To produce any less, or to raise output above that level, would lead to a lower level of profit. At $6, the same firm would increase output to 350, but it would stop there. Similarly, at $7, the firm would raise output to 400 units of output.

*MAIN SOURCE: CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 162-168*

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