Part 4, 2006 Thomson Learning/South-Western,Production, Costs, and Supply,Chapter 7, 2006 Thomson Learning/South-Western,Production,3,Production Functions,The purpose of a firm is to turn inputs into outputs. An abstract model of production is the production function, a mathematical relationship between inputs and outputs.,4,Production Functions,Letting q represent the output of a particular good during a period, K represent capital use, L represent labor input, and M represent raw materials, the following equation represents a production function.,5,Two-Input Production Function,An important question is how firms choose their levels of output and inputs. While the choices of inputs will obviously vary with the type of firm, a simplifying assumption is often made that the firm uses two inputs, labor and capital.,6,Marginal Product,Marginal physical productivity, or the marginal product of an input: the additional output that can be produced by adding one more unit of a particular input while holding all other inputs constant. Marginal product of labor (MPL): the extra output obtained by employing one more unit of labor while holding the level of capital equipment constant. Marginal product of capital (MPK): the extra output obtained by using one more machine while holding the number of workers constant.,7,Diminishing Marginal Product,It is expected that the marginal product of an input will depend upon the level of the input used. Since, holding capital constant, production of more output is likely to eventually decline with adding more labor, it is expected that marginal product will eventually diminish as shown in Figure 7-1.,8,Output,per week,Labor input per week,Total,Output,L*,(a) Total output,MP,L,L*,(b) Marginal product,FIGURE 7-1: Relationship between Output and Labor Input Holding Other Inputs Constant,Labor input per week,9,Diminishing Marginal Product,The top panel of Figure 7-1 shows the relationship between output per week and labor input during the week as capital is held fixed. Initially, output increases rapidly as new workers are added, but eventually it diminishes as the fixed capital becomes overutilized.,10,Marginal Product Curve,The marginal product curve is simply the slope of the total product curve. The declining slope, as shown in panel b, shows diminishing marginal productivity.,11,Isoquant Maps,An isoquant is a curve that shows the various combinations of inputs that will produce the same (a particular) amount of output. An isoquant map is a contour map of a firms production function. All of the isoquants from a production function are part of this isoquant map.,12,Isoquant Map,In Figure 7-2, the firm is assumed to use the production function, q = f(K,L) to produce a single good. The curve labeled q = 10 is an isoquant that shows various combinations of labor and capital, such as points A and B, that produce exactly 10 units of output per period.,13,Capital per week,KA,A,B,q = 10,KB,Labor per week,LB,LA,0,FIGURE 7-2: Isoquant Map,14,Isoquant Map,The isoquants labeled q = 20 and q = 30 represent two more of the infinite curves that represent different levels of output. Isoquants record successively higher levels of output the farther away from the origin they are in a northeasterly direction.,15,Capital per week,KA,A,B,q = 10,KB,Labor per week,LB,LA,0,FIGURE 7-2: Isoquant Map,q = 20,q = 30,16,Rate of Technical Substitution,Marginal rate of technical substitution (RTS): the amount by which one input can be reduced when one more unit of another input is added while holding output constant (i.e. negative of the slope of an isoquant). It is the rate that capital can be reduced, holding output constant, while using one more unit of labor.,17,Rate of Technical Substitution,18,Rate of Technical Substitution,The particular value of this trade-off depends upon the level of output and the quantities of capital and labor being used. At A in Figure 7-2, relatively large amounts of capital can be given up if one more unit of labor is added (large RTS), but at B only a little capital can be sacrificed when adding one more unit of labor (small RTS).,19,The RTS and Marginal Products,It is likely that the RTS is positive (the isoquant has a negative slope) because the firm can decrease its use of capital if one more unit of labor is employed. If increasing labor meant the having to hire more capital the marginal product of labor or capital would be negative and the firm would be unwilling to hire more of either.,20,The RTS and Marginal Products,Note that the RTS is precisely equal to the ratio of the marginal product of labor to the marginal product of capital.,21,Diminishing RTS,Along any isoquant the (negative) slope become flatter and the RTS diminishes. When a relatively large amount of capital is used (as at A in Figure 7-2) a large amount can be replaced by a unit of labor, but when only a small amount of capital is used (as at point B), one more unit of labor replace