What is Short Run Cost? We are ready to assign prices to resources and thus transform production data into cost data. Before we do so it would be well to identify the nature of the cost pattern to be described. The firm under study has already committed itself to a plant of a given size, that is, to a fixed “bundle” of resources in the form of land, buildings, machinery, top management, etc. This bundle represents the fixed input of the firm, in the sense that it will remain unchanged throughout this section of our investigation into costs. The variable input is labor and the added raw materials with which each laborer must be supplied. The question we will be asking is this: “What will it cost this firm to produce various quantities of output when it is free to vary only the amount of labor and raw materials used with its fixed plant?”
The answer to this question will be a schedule of costs that may be identified as the short-run cost schedule of the firm. The short run is defined as a period of time long enough to permit the firm to vary its rate of use of some but not all resources. The long-run is defined as a period of time long enough to permit the firm to vary its rate of use of all resources.
SHORT RUN COST IN THE FIRM
In the short run cost, the firm employs a combination of fixed and variable inputs; corresponding to these types of inputs are two types of costs: overhead or fixed costs and variable costs. Total overhead costs do not vary with output; total variable costs do. Total overhead cost per time period is the sum of the costs of the fixed inputs—the land, buildings, machinery, top management, etc.
Particular attention should be given to the fact that the economist includes a payment to management as part of the overhead cost of the firm. This payment includes more than just the salaries of the top executives. In a modern corporation, it includes a payment to the common stockholders, the basic decision-making group in the corporation, equal to what they could have earned had they put their resources into the best alternative uses. The accountant does not treat payments to common stockholders or returns to partners and proprietors on their equity capital as part of the “costs” of the firm; the economist does. The logic of the economist’s position (in terms of his purposes) will be made clear later on.
Total variable cost is equal to the sum of the expenditures per time period on variable inputs, such as labor and raw materials.
Total cost is the sum of total fixed and total variable costs. Fixed, variable, and total costs may be expressed as totals or as costs per unit of output.
Average fixed cost at a given rate of output is equal to total fixed cost divided by the output.
Average variable cost at a given rate of output is equal to total variable cost at that output divided by output.
Average total cost at a given rate of output is equal to the sum of the average fixed and average variable costs at that output, or it can be found by dividing the total cost by the output. Of particular interest to the economist is the marginal cost.
Marginal cost is the additional cost of producing one more unit of output. The marginal cost between any two outputs can be found by dividing the increase in total cost (or total variable cost, since changes in total cost can come only through changes in total variable cost) by the increase in output. (The mathematical symbol A is used to indicate an increment or addition; thus, ATC should be read as “the increase in total cost/’) Obviously, if the increase in output is one unit, marginal cost can be measured directly by the increase in total cost or total variable cost.
The abbreviations, TVC, TFC, TC, AFC, AVC, ATC, and MC, are frequently used to represent respectively, total variable cost, total fixed cost, total cost, average fixed cost, average variable cost, average total cost, and marginal cost.
Table 10-1 presents the short-run cost pattern of the firm whose production data were given in Table 9-2. Labor and the added raw materials with which each laborer must be supplied are assumed to be the only variable input used and are assigned a price of $10 a day. The total fixed costs are assumed to be $50 a day. All of the other costs can be developed from these figures and from the production data, in the manner indicated in the heading of each column. Thus at a rate of output of 18 units per day, total variable cost is $30 (the daily wage of 3 workers). Total cost at this output is $80 ($30 of variable costs plus $50 of fixed cost). Average variable cost at this output is obtained by dividing total variable cost (30) by the rate of output (18), which yields $1.67. Similarly, the average fixed cost of $2.78 is obtained by dividing total fixed cost ($50) by the output (18). The average total cost of $4.45 is the sum of variable cost ($1.67) and average fixed cost ($2.78). This same figure (give or take a penny, because of rounding errors) can be obtained by dividing total cost ($80) by output (18). Marginal cost at a rate of output of 18 is found by dividing the $10 increase in total cost ($80 — $70) by the increase in output (18 —• 12) of 6. It can be observed that average fixed cost decreases as output is increased; this is the familiar result of “spreading the overhead over more units.”
Average variable cost first decreases and then increases as output is increased. These stages in average variable cost correspond to the stages of first increasing, then decreasing, average product. Average variable cost is at a minimum where an average product is at a maximum. In other words, at that rate of output where the firm is getting the most out of its variable resources, its variable costs are the lowest.
Average total cost also decreases and then increases as output is increased from zero. In the early stages, both average fixed and average variable cost are decreasing. Hence, average total cost must fall. When average variable cost starts increasing as the law of diminishing returns, or variable proportions tells us it must, the resulting upward pull on average total cost is at first more than offset by the continued decrease in average fixed cost. Eventually, however, the upward pull of increasing average variable cost overcomes the downward pull of decreasing average fixed cost and average total cost begins to increase.
Marginal cost can be seen to decrease and then increase as output is increased from zero. It reaches its minimum at that rate of output where marginal product is a maximum. In other words, the greater the addition to total output resulting from the use of one more man, the less the extra or marginal cost of producing an added unit.
Cost data, like demand data, can be presented graphically. Figure 10-1 presents the four short-run cost curves as they would appear if taken from a more complete cost schedule than the one presented in Table 10-1. The curves give a visual picture of the way a firm’s costs per unit of product change with every change in its output. The AFC curve falls throughout. (It has the shape of a rectangular hyperbola.) The AVC curve depicts the effects of variations of output on average variable costs. It shows that this average falls for a time and then begins to rise. The upper curve, marked ATC on the diagram, is the average total unit cost curve. Lv is the low point on the AVC curve; Lt is the corresponding point on the ATC curve. Lt necessarily lies to the right of Lv since average fixed costs are still falling more rapidly than average variable costs are rising in the range of output involved. At output Lt, the downward pull of average fixed costs is exactly offset by the upward pull of rising variable costs. It will be noted that the marginal cost curve cuts both the average variable cost and the average total cost curves at their lowest points. This is not just a coincidence. So long as marginal cost is less than either of these costs, it exerts a downward pull on the average; so long as marginal cost is greater than either of these costs, it exerts an upward pull on the average. Consequently, marginal cost must be equal to average variable cost where average variable cost is at a minimum and must be equal to average total cost where it is at a minimum. We shall find that these relationships are of more than geometric importance. Cost curves plotted from actual operating data (if such were available) would not necessarily display the same eye-pleasing symmetry of the curves in Fig. 10-1. For example, it is entirely possible that the average variable, average total, and marginal cost curves would all be “flat-bottomed” curves, that is, would show little change in the level of cost over a wide range of intermediate outputs. However, the curves would still bear the same relationship to one another as that pictured in Fig. 10-1.