Daniel l. Rubinfeld

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190 Part 2 Producers, Consumers, and Competitive Markets 6 Production 'd': CI~ ::l 570,000 ~ 40,000 '"' ,q ,::: 30,000 u ;::l u ~ 20,000 L~-LLLil~I-LLL~-LLI~lil}I-LLI~I~I}I-L~~I~'-L1 L'~'~~~'~'~'~' ~'~'~ o 1960 1965 1970 1975 1980 1985 1990 1995 2000 Year During the 1960s and 1970s, productivity growth in the United States ~as lower' than in Germany, France, the United Kingdom, and Japan, although the leve~ of productivity was higher, In the 1980s and 1990s, productivity growth slowed m all of other developed nations, Second, productivity gwwth du~ing 1974-1997 was much lower in all developed countries than it had be~n m the past, Both of these patterns can be seen in the table and in Figure 6.5," 111e figure shovvs productivity, measured in 1997 US dollars per worker, for theynit~d States ~d for four other countries, Observe that in 1960 labor prodUCtiVIty m the Urut:d States was more than three times labor productivity in Japan and about twICe as great as labor productivity in Germany, France, ~nd the United Kingdom. However, by 1997 the differences had narrowed conSIderably., Throuahout most of the 1960-1997 period, Japan had the highest rate of productivit/'arowth followed by Germany and France. U.s. productivity gro~~ was the lo~est, e~en somewhat lower than that of the United Kingdom. TIus:s partly due to differences in rates of investment and ,growth in the stock..of car tal in each country. The greatest capital,grovdh dUl',mg the pos~ar peIl~d V\~ in Japan and France, which were rebUllt substantially after World Wal II: 'II some extent, therefore, the lower rate of growth of productivity in the Uruted States, when compared to that of Japan, France, and Germany, is the result of these countries catching up after the war, Productivity grO'wth is also tied to the natural resource sector of the economY. As oil and other resources began to be depleted, output per worker fell, En~ironmental regulations (e.g., the need to restore land to its original condition after sh'ip-mining for coal) magnified this effect as the public became more concerned with the importance of cleaner air and water. Observe from Table 6.4 that productivity growth in the United States has increased in recent years, Economists have debated whether this is a short-term aberration or the beginning of a long-term trend. Some economists believe that rapid teclmological change duril~g,t~~ 19Os, and in, p,articular the co~put~r revolution, has created ne,v possibilItres tor produCtrVIty growth. If thIS optimistic ,'iew is correct, we 'will see continued high rates of productivity growth , 6 in the commg years. 8.4 Now that vve have seen the relationship between production and productivity, let's hun to production in the long run, where both capital and labor inputs are variable, The firm can novI' produce its output in a variety of ways by combining different amounts of labor and capital. We will use isoquants to analyze and compare these different ways of producing. Recall that an isoquant describes all combinations of inputs that yield the same le,'el of output. The isoquants shown in Figure 6.6 are reproduced from Figure 6.1; they all slope dowmvard because both labor and capital have positive marginal products. More of either input increases output; thus if output is to be kept constant as more of one input is used, less of the other input must be used. Diminishing Marginal Returns Even though both labor and capital are variable in the long run, it is useful for a firm that is choosing the optimal mix of inputs to ask what happens to output as each of the inputs is increased, with the other input held fixed, The outcome of this exercise is described in Figure 6.6, which reflects diminishing marginal returns to both labor and capital. We can see why there is diminishing marginal returns to labor by drawing a horizontal line at a particular level of capitalsay, 3, Reading the levels of output from each isoquant as labor is increased, we note that each additional unit of labor generates less and less additional output. For example, when labor is increased from 1 mut to 2 (from A to B), output increases by 20 (from 55 to 75). Ho'wever, when labor is increased by an additional unit (from B to C), output increases by only 15 (from 75 to 90). Thus there is diminishing marginal rehll'IlS to labor both in the long and short rml. Because adding one factor while holding the other factor constant eventually leads to lower and lower incremental output, the isoquant must become steeper as more capital is added in place of labor and flatter \vhen labor is added in place of capital. 5 Recent O'rowth numbers are based on data from Ilidustrial Policy ill OECD COlilitries. A!'lIual RC"vielV; and hlten~ational Comparisolls ProductiL'ity and LIlllt Labor Cost Trends. US Bureau a Labor Statistics (1998), For more information on labor productivity and standard of living, go to , Under "International Comparisons of Productivity, Unit Labor Costs, and per ~aplta,,, click on: Unpublished Comparati\'e Real Gross Domestic Product per Capita and per mployed Person, Fourteen Countries, 1960-1996
192 Part 2 Producers, Consumers, and Competitive Markets Chapter 6 Production 193 Capital 5 per lvlonth Capital per Month 5 3 2 2 Q, = 75 J.L 1 Q, = 75 2 3 5 Labor per Month o 2 3 Labor per Month When both labor and capital are variable, both factors of p~·od~c~io.n ~an exhibit diminishina marcinal returns. As we move from A to C, there IS dlffilluslung returns to labor and as :e move from 0 to C, there is diminishing returns to capital. , &bk '" Like indifference cmves, isoquants are downward sloping and convex. The slope of the isoquant at any point measmes the marginal rate of technical substitution-the ability of the firm to replace capital with labor while maintaining the same level of On Q2' the Iv1RTS falls from 2 to 1 to 2/3 to 1/3. marginal rate of technical substitution (MRTS) Amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant. In §3.1, we explain that the marginal rate of substitution is the maximum amount of one good that the consumer is willing to give up to obtain one unit of another good. There is also diminishing marginal returns to capital. With labor fixed, the marainal product of capital decreases as capital is increased. For example, when capi~al is increased from 1 to 2 and labor is held constant at 3, the marginal.pro~uct of capital is initially 20 (75-55) but falls to 15 (90-75) when capItal IS increased from 2 to 3. Substitution Among Inputs With two inputs that can be \'aried, a manager will.wa:'t to consider substi~ting one input for another. The slope of each isoquant mdlcates hm: the quar:tlty of one input can be h"aded off against the quantity of the other, whIle OUtpL:t IS held constant VVhen the nega ti\'e sign is removed, we call the. slope the margma~ rate of technical substitution (MRTS). The marginal rate Of teclllllcal substItutIOIl of labor for capital is the am.ount by which the input. of c~pital can be red~lc:d wh: one extra unit of labor IS used, so that output lemams constant. ThIS IS anal gous to the marginal rate of substitution (MRS) in consUl:ner theory. Recall from Section 3.1 that the MRS describes hm\' consumers substlhlte among two goo~s while holdina the level of satisfaction constant. Like the MRS, the MRTS IS 1:> always measured as a positive quantity: MRTS = Change in capital input/ change in labor input - .:iK/.:iL (for a fixed level of Q) In Figure 6.7 the MRTS is equal to 2 when labor increases from 1 Lmit to 2 and output is fixed at 75. However, the MRTS falls to 1 when labor is increased from 2 units to 3, and then declines to 2/3 and to 1/3. Clearly, as more and more labor replaces capital, labor becomes less productive and capital becomes relatively more productive. Therefore we need less capital to keep output constant, and the isoquant becomes flatter. We assume that there is a diminishing MRTS. In other words, the MRTS falls as we move down along an isoquant. The mathematical implication is that isoquants, like indifference curves, are convex, or bowed inward. This is indeed the case for most production teclmologies. The diminishing MRTS tells us that the productivity of anyone input is limited. As more and ~or~ labor is added to the production process in place of capital, the productiv Ity of labor falls. Similarly, when more capital is added in place of labor, the productivity of capital falls. Production needs a balanced mix of both inputs. . As our discussion has just suggested, the MRTS is closely related to the margmal products of labor MP L and capital MP K . To see hm'\', imagine adding some labor and reducing the amount of capital sufficient to keep output constant. The a.dditional output resulting from the increased labor input is equal to the additional output per unit of additional labor (the marginal product of labor) times the number of units of additional labor: In §3.1, we explain that an indifference curve is convex if the marginal rate of substihltion diminishes as we move down along the curve. where .:iK and .:iL are small changes in capital and labor along an isoquant. Additional output from increased use of labor = (MPd(~L)
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Daniel l. Rubinfeld

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