262 PART • Producers, Consumers, and Competitive Markets Hours of labor per machine lot F IGURE 7.12 THE LEARNING CURVE A firm’s production cost may fall over time as managers and workers become more experienced and more effective at using the available plant and equipment The learning curve shows the extent to which hours of labor needed per unit of output fall as the cumulative output increases 10 20 30 40 50 Cumulative number of machine lots produced where N is the cumulative units of output produced and L the labor input per unit of output A, B, and b are constants, with A and B positive, and b between and When N is equal to 1, L is equal to A ϩ B, so that A ϩ B measures the labor input required to produce the first unit of output When b equals 0, labor input per unit of output remains the same as the cumulative level of output increases; there is no learning When b is positive and N gets larger and larger, L becomes arbitrarily close to A A, therefore, represents the minimum labor input per unit of output after all learning has taken place The larger b is, the more important the learning effect With b equal to 0.5, for example, the labor input per unit of output falls proportionately to the square root of the cumulative output This degree of learning can substantially reduce production costs as a firm becomes more experienced In this machine tool example, the value of b is 0.31 For this particular learning curve, every doubling in cumulative output causes the input requirement (less the minimum attainable input requirement) to fall by about 20 percent.12 As Figure 7.12 shows, the learning curve drops sharply as the cumulative number of lots increases to about 20 Beyond an output of 20 lots, the cost savings are relatively small Learning versus Economies of Scale Once the firm has produced 20 or more machine lots, the entire effect of the learning curve would be complete, and we could use the usual analysis of cost If, however, the production process were relatively new, relatively high cost at low levels of output (and relatively low cost at higher levels) would indicate learning effects, not economies of scale With learning, the cost of production for a mature firm is relatively low regardless of the scale of the firm’s operation If a firm that produces machine tools in lots knows that it enjoys economies of scale, it should produce its machines in very large lots to take advantage of the lower cost associated with size If there is a learning curve, Because (L − A) ϭ BN−.31, we can check that 0.8(L − A) is approximately equal to B(2N)−.31 12