1d Chapter Six Cost of Production 245 LAC SAC4 ;/ z B / ......r,../a "I, / // sAC / 2/ SACS / / ,,/ ///,// Each point on the long-run average cost curve (LAC) represents a least cost combination of inputs and a point on one shortrun average cost Curve. tionship between short-run average cost curves and the long-run average cost curve. Notice that the long-run average cost curve is an envelope curve for the short-run average cost curves. In other words, it is made up of points that indicate the lowest unit costs obtainable for each level of output. We fur- ther observe that such points are not necessarily the minimum points of the short-run average cost curves. In fact, for outputs smaller than that corre sponding to the minimum point of the long-run average cost curve, the short-run average cost curves are tangent to the long-run curve to the left of their respective minimum points. This occurs because of the existence of economies of scale, which means that smaller unit costs can be obtained by producing with a larger size plant than by producing at the minimum short run average cost corresponding to a smaller plant size. (See point A in Figure 6-13.) The opposite result occurs if diseconomies of scale are present, so that it is cheaper to produce beyond the point of minimum shortrun average cost corresponding to a smaller plant than by producing at the minimum shortrun average cost point corresponding to a larger plant. (See point B in Figure 6-13.) Only at the minimum point of the long-run average cost curve, where constant returns to scale are obtained, can the rm produce a given level of output most cheaply by producing at the minimum point of a short- run average cost curve. (See point C in Figure 6-13.) The regions of economies of scale, diseconomies of scale, and constant returns to scale are summiarized in Figure 6-14. These economies and diseconomies of scale occur because of the nature of the firm's production function and are not caused by changes in external data such as input prices. Thus, they are some- times called internal economies and diseconomies. Chapter Six Cost of Production 247 output change by exactly the same percentage, then constant returns to scale will be present. These relationships are summarized as follows: Ec 1 LTC increases by a larger percentage than diseconomies of of scale the percentage increase in output. Economies of scale, or the absence of them, can play an important role in the structure of firms, industries, and markets. For example, Kraft Gen- eral Foods, Inc., found that its salespeople from Kraft, General Foods, Oscar Mayer Foods, and Maxwell House would frequently all appear at a MANAGERIAL PERSPECTIVE Technological Change and Economies of Scale In 1984, a desktop computer that one would example, in the early 1970s, a 19-inch color tel- classify as nearly useless by today's standards evision cost approximately $400. Now, a tech- cost over $2,000. Such a computer would con- nically superior color television with a 27-inch tain something like two 5 1/4" floppy drives, screen can be purchased for less than $200. no hard drive, and about 64 KB of RAM. A 14- Similar, or even more dramatic, stories could inch monochrome monitor might also be be told with respect to VCRs and camcorders. included. By 1997, a computer with 16 MB of Now, many consumers are eagerly awaiting RAM, a Pentium 120 MHZ processor, a 2 GB the benefits of advancing technological devel- hard drive, a color monitor, and a modem cost opment and mass production that will further less than $1,000. By 2002, models far better reduce the production costs and prices of all equipped than these were selling for under types of electronic products. $400. How could this happen? For one thing, competition in the com- References: Jonathan Sidener, "2002 Likely to Be Big puter industry was a factor in lowering prices. Year for HDTV," The Arizona Republic, January 1, However, technological developments and 2002 (reprinted at www.hd.net /clipping.html); economies of scale in the manufacture of com- David Hendricks, "Inexpensive Electronics Buck Marketplace Trend," San Antonio Express-News, Jan- ponents for computers were also critical ele- uary 30, 1999, pp. 1E, 2E; "Breaking the $1,000 Bar- ments enabling computer manufacturers to rier," Business Week (February 17, 1997), p. 75; and lower prices on their machines. "Now PC Buyers Are Getting More for Even Less," A similar progression has occurred with Wall Street Journal, June 18, 1996, pp. B1, B6. regard to other consumer electronics. ForUse the function below (whose parameters qualify it as a STC function) to answer the questions. See the text p. 244 for a representative figure. STC = 4850 + 40Q - 1.5Q2 + .04Q3 a. Total fixed cost is $ b. Obtain the AFC function from (a) and write it here c. Obtain the AVG function contained in the STC function and write the AVG function here d. Write here the MC function e. Find the value which AFC approaches as Q gets very large. . Also write a sentence or two explaining what this implies for fixed costs per unit (AFC) as production quantities get ever larger. f. Find the value of Q at which AVC is a minimum. 9. Is productive efciency at the value in (f) greatest or least? h. Demonstrate that the value of SMC equals the value of AVG at the value of Q where AVC is a minimum. Hint: The level of Q you found in (f) is where AVC is a minimum. If you plug this level of Q into AVC (see c) and also into MC (see d) the two outcomes should be the same if SMC crosses AVC at this level of Q. i. Why does the derivative of Short Run Total Cost (STC) equal the derivative of Total Variable Cost (TVC)? Stated another way, why does dSTCIdQ = dTVCIdQ? Explain in a couple of sentences (Hint: See Truett page 235 and footnote 16). the value of Q where increasing returns ceases and diminishing returns begins. Diminishing returns begins at the level of Q where MC is a minimum. 246 Part Two Production, Cost, and Profit FIGURE 6-14 LAC Decreasing Long-Run Increasing Returns Returns Average Cost and Returns to Scale Constant Returns When the firm experiences increasing returns to scale, LAC declines. When the firm has con- stant returns to scale, LAC is constant. When the firm has decreasing returns to scale, LAC is increasing. The cost elasticity reflects the presence of either economies or disec- Cost elasticity is onomies of scale. Cost elasticity, Ec, is defined as the percentage change in the percentage long-run total cost from a 1 percent change in output: change in long-run total cost from a 1 percent change in Ec = percentage change in LTC output percentage change in Q It measures the relative responsiveness of long-run total cost to changes in the level of output. The formula for arc cost elasticity is given by19 Ec= ALTC 22+ 21 AQ LTC 2 + LTC , If the cost elasticity is less than one, then a given percentage increase in out- put will result in a smaller percentage increase in long-run total cost, and economies of scale will be present. On the other hand, if the cost elasticity is greater than one, then LTC will increase by a greater percentage than the per- centage change in output, and diseconomies of scale will occur. If LTC and 19 The formula for point cost elasticity is Ec = aLTC Q aQ LTC