Long-Run Costs and Output Decisions (Part A)
by
Charles Lamson
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Parts 30-38 of this analysis discussed the behavior of profit-maximizing competitive firms in the short run. Recall that all firms must make three fundamental decisions: (1) how much output to produce or supply, (2) how to produce that output, and (3) how much of each input to demand.
Firms use information on input prices, output prices, and technology to make the decisions that will lead to the most profit. Because profits equal revenues minus costs, firms must know how much their products will sell for and how much production will cost, using the most efficient technology. In parts 34-38 of this analysis we saw how cost curves can be derived from production functions and input prices. Once a firm has a clear picture of its short-run costs, the price at which it sells its output determines the quantity of output that will maximize profit. Specifically, a profit-maximizing perfectly competitive firm will supply output up to the point that price (marginal revenue) equals marginal cost. The marginal cost curve of such a firm is thus the same as its supply curve. In the next several posts we turn from the short run to the long run. The condition in which firms find themselves in the short run (Are they making profits? Are they incurring losses?) determines what is likely to happen in the long run. Remember that output (supply) decisions in the long run are less constrained then in the short run, for two reasons. First, in the long run, the firm has no fixed factor of production that confines its production to a given scale. Second, firms are free to enter industries to seek profits and to leave industries to avoid issues.  The long run has important implications for the shape of cost curves. As we saw in the short run, a fixed factor of production eventually causes marginal cost to increase along with output. This is not the case in the long run, however. With no fixed scale, the shapes of cost curves become more complex and less easy to generalize about. The shape of long run cost curves have important implications for the way an industry's structure is likely to evolve over time. We begin our discussion of the long run by looking at firms in three short run circumstances: (1) firms earning economic profits, (2) firms suffering economic losses but continuing to operate to reduce or minimize those losses, and (3) firms that decide to shut down and bear losses just equal to fixed costs. We then examine how these firms will alter their decisions in response to the short-run conditions. Although we continue to focus on perfectly competitive firms, it should be stressed that all firms are subject to the spectrum of short-run profit or loss situations, regardless of market structure. Assuming perfect competition allows us to simplify our analysis and provides us with a strong background for understanding the discussions of imperfectly competitive behavior in later posts. Short-Run Conditions and Long-Run Directions Before beginning our examination of firm behavior, let us review the concept of profit. Recall that a normal rate of return is included in the definition of total cost (see Part 31). A normal rate of return is a rate that is just sufficient to keep current investors interested in the industry. Because we define profit as total revenue minus total cost and because total cost includes a normal rate of return, our concept of profit takes into account the opportunity cost of capital. If a firm is earning an above normal rate of return, it has a positive profit level, but otherwise not. When there are positive profits in an industry, new investors are likely to be attracted to the industry. When we say that a firm is suffering a loss, we mean that it is earning a rate of return that is below normal. Such a firm may be suffering a loss as an accountant would measure it, or it may simply be earning at a very low---that is, below normal---rate. Investors are not going to be attracted to an industry in which there are losses. A firm that is breaking even, or earning a zero level of profit, is one that is earning exactly a normal rate of return. New investors are not attracted, but current ones are not running away, either.  With these distinctions in mind, then, we can say that for any firm one of three conditions holds at any given moment: (1) the firm is making positive profits, (2) the firm is suffering losses, or (3) the firm is just breaking even. Profitable firms will want to maximize their profits in the short run, while firms suffering losses will want to minimize those losses in the short run. Maximizing Profits The best way to understand the behavior of a firm that is currently earning profits is by way of example. Example: The Blue Velvet Car Wash When a firm earns revenues in excess of costs (including a normal rate of return), it is earning positive profits. Let us take as an example the blue velvet car wash. Suppose that investors have put up $500,000 to construct a building and purchase all the equipment required to wash cars. Let us suppose that investors expect to earn a minimum return of 10 percent on their investment. If the money to set up the business had been borrowed from the bank instead, the car wash owners would have paid a 10 percent interest rate. In either case, total cost must include $50,000 per year (10 percent of $500,000). The car wash is open 50 weeks per year and is capable of washing up to 800 cars per week. Whether it is open and operating or not, the car wash has fixed costs. Those costs include $1,000 per week to investors---that is, the $50,000 per year normal return to investors---and $1,000 per week in other fixed costs---a basic maintenance contract on the equipment, insurance, and so forth. When the car wash is operating, there are also variable costs. Workers must be paid, and materials such as soap and wax must be purchased. The wage bill is $1,000 per week. Materials, electricity, and so forth run $600 at full capacity. If the car wash is not in operation, there are no variable costs. Table 1 summarizes the costs of the blue velvet car wash.   This car wash business is quite competitive. There are many car washes of equal quality in the area, and they offer their service at $5. If Blue Velvet wants customers, it cannot charge a price above $5. (Recall the perfectly elastic demand curve facing perfectly competitive firms; review Part 37 if necessary.) If we assume that blue velvet washes 800 cars each week, it takes in revenues of $4,000 from operating (800 cars * $5). Is this total revenue enough to make a positive profit? The answer is yes. Revenues of $4,000 are sufficient to cover both fixed costs of $2,000 and variable costs of $1,600, leaving a positive profit of $400 per week. Graphic Presentation Figure 1 graphs the performance of a firm that is earning positive profits in the short run. Figure 1(a) illustrates the industry, or the market, and Figure 1(b) illustrates a representative firm. At present, the market is clearing at a price of $5. Thus, we assume that the individual firm can sell all it wants at a price of P* = $5, but that it is constrained by its capacity. Its marginal cost curve rises in the short run because of a fixed factor. If you've been reading along, you already know that a perfectly competitive profit-maximizing firm produces up to the point where price equals marginal cost. As long as price (marginal revenue) exceeds marginal cost, firms can push up profits by increasing short-run output. The firm in the diagram, then, will supply q* = 300 units of output (point A, where P = MC).  Both revenues and costs are shown graphically. Total revenue (TR) is simply the product of price and quantity: P* * q* = $5 * 300 = $1,500. On the diagram, total revenue is equal to the area of the rectangle P* Aq*0. (The area of a rectangle is equal to its length times its width.) At output q*, average total cost is $4.20 (point B). Numerically, it is equal to the line segment q* B. Because average total cost is derived by dividing total cost by q, we can get back to total cost by multiplying average total cost by q. That is: ATC = AFC + AVC and TC = ATC * q Total cost (TC), then, is $4.20 * 300 = $1,260, area pink in the diagram. Profit is simply the difference between total revenue (TR) and total cost (TC), or $240. This is the area that is shaded green in the diagram. This firm is earning positive profits.  A firm that is earning positive profits in the short run and expects to continue doing so has an incentive to expand its scale of operation in the long run. Those profits also give new firms an incentive to enter and compete in the market. *CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 173-176* end |
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