266 PART • Producers, Consumers, and Competitive Markets Variable cost General Motors • F IGURE 7.15 VARIABLE COST CURVE FOR THE AUTOMOBILE INDUSTRY An empirical estimate of the variable cost curve can be obtained by using data for individual firms in an industry The variable cost curve for automobile production is obtained by determining statistically the curve that best fits the points that relate the output of each firm to the firm’s variable cost of production •Toyota Nissan Honda Volvo • • • • Ford • Chrysler Quantity of cars Least-squares regression is explained in the appendix to this book Suppose we wanted to characterize the short-run cost of production in the automobile industry We could obtain data on the number of automobiles Q produced by each car company and relate this information to the company’s variable cost of production VC The use of variable cost, rather than total cost, avoids the problem of trying to allocate the fixed cost of a multiproduct firm’s production process to the particular product being studied.16 Figure 7.15 shows a typical pattern of cost and output data Each point on the graph relates the output of an auto company to that company’s variable cost of production To predict cost accurately, we must determine the underlying relationship between variable cost and output Then, if a company expands its production, we can calculate what the associated cost is likely to be The curve in the figure is drawn with this in mind—it provides a reasonably close fit to the cost data (Typically, least-squares regression analysis would be used to fit the curve to the data.) But what shape is the most appropriate, and how we represent that shape algebraically? Here is one cost function that we might choose: VC = bq (7.9) Although easy to use, this linear relationship between cost and output is applicable only if marginal cost is constant 17 For every unit increase in output, variable cost increases by b; marginal cost is thus constant and equal to b If we wish to allow for a U-shaped average cost curve and a marginal cost that is not constant, we must use a more complex cost function One possibility 16 If an additional piece of equipment is needed as output increases, then the annual rental cost of the equipment should be counted as a variable cost If, however, the same machine can be used at all output levels, its cost is fixed and should not be included 17 In statistical cost analyses, other variables might be added to the cost function to account for differences in input costs, production processes, production mix, etc., among firms