GLOBAL EDITION. Introduction to Agricultural Economics SIXTH EDITION. John B. Penson, Jr. Oral Capps, Jr. C. Parr Rosson III Richard T.

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1 GLOL EDITION Penson, Jr. Capps, Jr. Rosson III Woodward Introduction to gricultural Economics SIXTH EDITION John. Penson, Jr. Oral Capps, Jr. C. Parr Rosson III Richard T. Woodward

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3 economics of input and product substitution chapter seven Isoquants for and D Higher output Figure 7 1 The slope of an isoquant for a particular level of output typically changes over the full range of the curve. 8 G 7 Range Δ capital 6 4 Isoquant for output = Range Δ capital 3 2 Isoquant for output = F Range C Δ capital H Range Δ labor Range Δ labor Range C Δ labor The expression in Equation 7.1 indicates that changes in labor must be compensated by changes in capital, if the level of output is to remain unchanged. 2 For example, if output is to remain unchanged and the marginal rate of technical substitution of capital for labor is equal to three, capital use must be reduced by 3 hours if labor is increased by 1 hour. 3 These observations illustrate that when labor is substituted for capital along an isoquant (output remaining unchanged), the marginal rate of technical substitution of capital for labor falls. declining marginal rate of technical substitution is a consequence of the law of diminishing returns (discussed in Chapter 6). When labor increases, its marginal physical product falls. Reductions in capital imply an increase in its marginal physical product. How do the isoquants in Figure 7 1 relate to the stages of production discussed in Chapter 6? Focusing on the isoquant for units of output, the marginal physical product of capital is negative above point G and to the right of point H. You will recall that the marginal physical product was negative in stage III. ecause stage III is not of economic interest, the economic region of production is bounded by points G and H for the isoquant corresponding to an output of units, and by points D and F for the isoquant associated with an output of units. Thus, only certain regions of input output relationships are of interest to businesses seeking to maximize their profit. Increases in output are reflected in Figure 7 1 by isoquants that lie farther away from the origin. In this figure, the isoquant for an output of units lies farther from the origin than the isoquant associated with an output of units. 2 If output is to remain unchanged (i.e., remain on the same isoquant), the loss in output from the decrease in labor must equal the gain in output from the increase in capital: - labor * MPP labor = + capital * MPP capital. Equation 7.1 simply represents a rearrangement of this statement. 3 ecause the marginal rate of technical substitution is negative in all rational areas of production (i.e., stage II), most economists do not bother to include the minus sign. Choice of isoquant Higher isoquants represent higher levels of output. Does this mean that the firm can or desires to be on a higher isoquant? the answer so far is that we cannot tell with the information we have.

4 130 chapter seven economics of input and product substitution Figure 7 2 graphical illustration of extreme perfect substitutes and complements. Perfect Substitutes Perfect Complements Finally, isoquants at the extreme can be either perfect substitutes or perfect complements. Each case is illustrated in Figure 7 2. set of isoquants for perfect substitutes is a straight line, which implies a constant marginal rate of technical substitution. This differs from the imperfect substitution implied by the isoquants in Figure 7 1, which have a decreasing marginal rate of technical substitution as one moves down the isoquants. set of isoquants for perfect complements forms 90-degree angles, indicating that both capital and labor are required to produce a specific level of output. That is, it takes a certain proportion of labor and capital to produce a product. the Iso-cost line Input costs ll inputs to production (land, labor, capital, and management) have a cost. the cost of two inputs can be captured in something called an iso-cost line. ssume that a business uses two inputs (labor and capital) to produce a particular product. The total cost of production in this case would be equal to the wage rate times the hours of labor used plus the cost of capital times the amount of capital used. The concept of wage rates paid to labor is familiar, but the cost of capital will require further explanation. We have learned that capital includes both variable and fixed inputs. We cited fuel as an example of a variable input and land as an example of a fixed input. The cost of capital therefore equals the price of fuel and other variable inputs purchased times the amount purchased and the rental rate of capital for using fixed inputs such as tractors and other machinery, buildings, and land. In the short run, the business can rent an additional tractor or land. The annual rental payment for leased fixed inputs is a variable cost of production. Owned capital has its costs, too. The owner of a building, for example, has the option of leasing or selling the building to someone else and using those monies in his or her next best alternative. The revenue forgone from not selling or leasing the building is a cost. Economists call this an implicit or opportunity cost. Thus, our cost of capital is a composite variable that reflects in the short run the cost of both variable inputs: labor and rented capital. The prices for these two inputs, or the wage rate for labor and the rental rate for capital, are treated as fixed in the short run; they will not vary with the level of input use by a single firm. Suppose Frank Farmer has $1,000 available daily to finance a business s production costs. The wage rate for labor is $ per hour, and the rental rate for capital is $0 per day. The business s daily budget constraint therefore is (+ * use of labor) + (+0 * use of capital) = +1,000 (7.2) Frank s choice of how much capital and labor to employ must be no more than $1,000. The combination of labor and capital Frank can afford for a given level of total cost is illustrated by line in Figure 7 3. This relationship is referred to as an iso-cost line.

5 economics of input and product substitution chapter seven 131 C 1 1 Original iso-cost line Changes in wage rate Doubling D 1 1 Changes in budget E Doubling Halving C D F Changes in rental rate E Halving Figure 7 3 The iso-cost line plays a key role in determining the least-cost combination of input use. () The slope of curve is given by the ratio of the wage rate for labor to the rental rate for capital. () doubling of the production budget changes both intercepts but not the slope of the iso-cost line. (C) doubling of the wage rate (holding the rental rate constant) would make the iso-cost line steeper as shown by line D. (D) doubling of the rental rate (holding the wage rate constant) would make the iso-cost line flatter as shown by line C. Declines in these input prices would have the opposite effect. Halving C Doubling D F The slope of the iso-cost line is equal to the negative ratio of the wage rate to the rental rate of capital, 4 or slope of iso@cost line = wage rate rental rate (7.3) If these two input prices change by a constant proportion, the total cost will change, but the slope of the iso-cost line will remain constant. To illustrate the nature of the iso-cost line, suppose the budget the firm allocated to these two inputs was doubled. Total costs may double, but the iso-cost line EF would still have the same slope as line (Figure 7 3). Only changes in the relative price of inputs (or input price ratio) will alter the slope of the iso-cost line. For a given total cost, a rise (fall) in the price of capital relative to that of labor will cause the iso-cost line to become flatter (steeper) (Figure 7 3D). If labor s wage rises (falls), the iso-cost line would become steeper (flatter) (Figure 7 3C). Suppose that the wage rate was $ an hour instead of $. The new iso-cost line D would be steeper than line (Figure 7 3C). The new iso-cost line would still intersect the capital axis at point, because a maximum of units of capital can be purchased, if the producer s total budget is limited to $1,000. If the capital price rose to $0 per unit, the iso-cost line C would be flatter than the original iso-cost line (Figure 7 3D). The slope of an iso-cost line is represented by the ratio of two inputs. this line allows us to use economics to determine the least-cost combination of two inputs. 4 Equation 7.3 can be rearranged algebraically to give the iso-cost line and its slope as follows: hours of capital = $1,000 wage rate - * hours of labor rental rate rental rate

6 132 chapter seven economics of input and product substitution The use of herbicides and other chemicals has replaced hand weeding and use of harrows to control weeds as well as insects and diseases in crops today. This illustrates the substitution relationship between a number of inputs to produce a raw agricultural product. Credit: SP Inc/Fotolia. lest-cost use of InPuts For given output There are essentially two input decisions a business faces in the short run that pertain to input use. One concerns the least-cost combination of inputs to produce a given level of output. Here, the level of production is not constrained by the business s budget. The other is the least-cost combination of inputs and output constrained by a given budget. This section focuses on the first of these two concerns. Least-cost criteria the point of tangency of an isoquant and an iso-cost line, and not where they might cross, represents the least-cost combination of two inputs to produce a particular level of output. Short-Run Least-Cost Input Use The first of these two perspectives on the least-cost use of inputs requires that we find the lowest possible cost of producing a given level of output with a business s existing plant and equipment. Technology and input prices are assumed to be known and constant. We know from Figure 7 1 that the alternative combinations of capital and labor produce a given level of output that forms an isoquant and that the relative prices of inputs help shape the iso-cost line in Figure 7 3. We need to find the least-cost combination of inputs that will allow the business to produce a given level of output in the current period. ny additional capital is rented (variable cost) through a short-term leasing arrangement rather than owned (fixed cost), or represents nonlabor variable inputs (e.g., fuel and chemicals). Graphically, the least-cost combination of inputs is found by shifting the iso-cost line in a parallel fashion until it is tangent to (i.e., just touches) the desired isoquant. This point of tangency represents the least-cost capital/labor combination of producing a given level of output and the total cost of production. Figure 7 4 can be used to determine the least-cost combination of labor and capital to produce 0 units of output using the business s current productive capacity. ssume that iso-cost line reflects the existing input prices for labor and capital and current total costs of production. The least-cost combination of labor and capital to produce 0 units of output is found graphically by shifting line out in a parallel fashion to the point where it is just tangent to the desired isoquant.

7 economics of input and product substitution chapter seven 133 C 1 * Least-Cost Input Choice for Given Output Figure 7 4 The least-cost choice of input use is given by the point where the iso-cost curve is tangent to the isoquant for the desired level of output. If the iso-cost line is line, the least-cost combination would occur at point G (where 0 units of G output are produced). 0 units of output 0 * L 1 Figure 7 4 shows that line ** is tangent to the isoquant associated with 0 units of output at point G. The new total cost at point G in Figure 7 4 can be determined by multiplying the quantity of labor (L 1 ) times the wage rate and adding that to the product of the quantity of capital (C 1 ) times the rental rate for capital. fundamental interpretation to the conditions underlying the least-cost combination of input use is illustrated in Figure 7 4. The slope of the isoquant is equal to the slope of the iso-cost line at point G. t this point, the marginal rate of technical substitution of capital (fertilizer, fuel, feed, rental payments, etc.) for labor, or the negative of the slope of the isoquant, is equal to the input price ratio, or the negative of the slope of the iso-cost line. Thus, the least-cost combination of inputs requires that the market rate of exchange of capital for labor (i.e., the ratio of input prices) equal their rate of exchange in production (i.e., their marginal rate of technical substitution). We can express the foregoing conditions for the least-cost combination of labor and capital in mathematical terms as We can rearrange Equation 7.4 as MPP labor MPP capital = wage rate rental rate MPP labor wage rate = MPP capital rental rate (7.4) (7.) Equation 7. suggests that the marginal physical product per dollar spent on labor must equal the marginal physical product per dollar spent on capital. This is analogous to the condition for consumer equilibrium described in Equation 4.2, and it represents a recurring theme in economics. In the present context, a firm should allocate its expenditures on inputs so the marginal benefits per dollar are spent on competing equally. nother way to think of this equilibrium is that marginal benefit equals marginal cost. Suppose that the marginal value product of labor usage (marginal physical product times the price of output) is $ and the corresponding marginal benefit is $7 for capital. The opportunity cost of expending a dollar on increased labor usage is the $7 gain if this expenditure were instead used to purchase another unit of capital services. Therefore, the marginal benefit ($) is less than marginal cost ($7), and labor usage should be reduced. If output is to remain constant when labor is reduced, capital must be expanded until marginal benefit equals marginal cost.