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Estimating Input Use o f the Commodity System
The last set of adjustments to private costs and returns involves accounting for the possible response of producers to the social prices of outputs and inputs. Patterns of input use by a profit-maximizing firm are dictated by consideration of marginal cost. The producer compares this value to marginal revenue when increases or decreases in output are contemplated. The general case, in which marginal returns to input use are diminishing, is illustrated in Figure 11.3. Figure 11.3a shows the relationship between the use of fertilizer input and wheat output, given by curve ABCD. Fertilizer is only one of the inputs used in production, and the entire production process can be represented by a family of similar curves, one for each input. Producers using fertilizer will be concerned with the relationship between the marginal change in the total cost of inputs and the incremental gain in output that results from increased input use. The producer will insist that
or
The left-hand side of this inequality is the slope of the input-output productivity curve, ABCD, and the right-hand side is the input-output price ratio. In Figure 11.3a, this relation means that the point of tangency between the price line and the productivity curve (point B) represents the point of maximum profit. Because marginal productivity declines as input use increases, expansion of input use beyond that associated with point B will decrease net profits; the additional cost of fertilizer
is greater than the additional value of wheat produced
. Only if the relative price of wheat increases will fertilizer use increase. In Figure 11.3a, an increase in the wheat price from P1W to P2W causes the price line to become less steeply sloped. Optimum input use increases, indicated in the graph by point C.
An increase in the wheat price will exert similar effects on the use of other inputs in wheat production; the aggregate impact of all these changes on output is summarized in the marginal cost curve of the firm (Figure 11.1b). Because all input productivities are assumed to diminish with increasing amounts of input, the marginal cost curve takes on an increasingly steep slope as price increases and output expands. The proportional impact on output of output price increases becomes smaller, because increases in input use have reduced incremental effects on production.
Both the average cost curve and the marginal cost curve can be used to measure profits. In terms of average cost, total profits in Figure 11.36
Box 11.4. The Social Value of Land
Wheat in Portugal
The only alternatives to dryland wheat production in the Alentejo region of Portugal are oats and barley. Both crops require managerial and cultivation practices similar to those of wheat. The crops do not appear to differ much in terms of profitability risk. The private land rental rate is 600 escudos per hectare. Rent control laws require a lower rental rate, but these laws are not enforced.
In calculations of the social value for land, barley represents the best alternative crop. The social costs and returns to 1 hectare of barley are summarized in the following table.
The social profit of barley production is estimated as 4,972 escudos per hectare. This price is thus used as the social value of land.
Irrigated Land in Sinaloa, Mexico
The social valuation of irrigated land in northwest Mexico provides a sharp contrast to the valuation of dryland areas of Portugal. In northwest Mexico, a wide range of crops is technically feasible, with differences in market destination (export or domestic), managerial requirements, and price variability. In this case, the estimation procedures compare profits before land cost for as many crops as possible (see the following table). Private market land rental rates were 40,000 pesos per hectare for all crops except vegetables, which were 60,000 pesos per hectare.
These results show the enormous increase in net returns for exporters of vegetable crops, but these crops require conditions of financial and production management that are very different from the conditions for other field crops. Because of dissimilar management requirements and riskiness, differences in the costs of land would not be expected to account for all of the extra profits in vegetable and field crop production. For farmers without access to vegetable crop production, four of the crops-beans, soybeans, safflower, and cotton-offer negative returns. Social profits in the remaining crops-corn, wheat, rice and sorghum-range from 22,000 to 66,000 pesos per hectare. Social land values would probably fall somewhere in this range.
are the rectangle P1C1DE; in terms of marginal cost, profits are the area of rectangle P1EQ10 less the area under the marginal cost curve, FGE. Because the average cost curve does not determine producer response to changes in output or input prices, old budgets become inaccurate portraits of producer profitability and input use as prices change. If P1represents the private market price for wheat and P2 represents the social price, Figure 11.3b shows that an increase in wheat price from P1 to P2 induces an increase in wheat output from Q1 to Q2. This output increase in attained by increased use of at least
the productivity of input use is diminishing, average cost per unit of output increases. Social costs per unit of output are thus larger than private costs. The correct social cost corresponding to social output price P2 would be that associated with point H; social profits would be P2 - C2 per unit of output. If budgets associated with point D were used to calculate social profitability, the estimate of profit per unit of output would be P2 - C1, overstating the true measure of social profit.
To this point, input prices have been assumed to remain constant as output prices change. But changes in input prices can also induce changes in input use. The profit-maximizing producer tries to decrease usage of inputs whose prices increase in relative terms and increase usage of inputs whose prices fall. These changes create a new pattern of input-output relations in a manner analogous to the previously described effects of output price changes. In this case, however, changes in input prices cause shifts in the firm's marginal and average cost curves rather than movements along these curves. Each new marginal and average cost curve entails input-output relationships for social cost and return calculations that differ from those used in the private cost calculations.
Figure 11.4 illustrates the impact of input substitution on the firm's cost curves. Figure 11.4a shows the unit production isoquant. The curve AB represents all combinations of inputs (in this case, labor and fertilizer) that can be used to produce one unit of output (wheat). Under constant returns to scale, this unit isoquant is sufficient to describe all
possible input combinations; isoquants representing higher levels of output will be direct replications of the unit isoquant. To minimize production costs, the producer seeks the point of tangency between the unit isoquant and the line having a slope equal to the factor price ratio (by reasoning similar to that used for the input-output productivity curve).
The diagram illustrates the impact of a decrease in fertilizer price (because the private market price of fertilizer exceeds the social price). This price change causes a shift in the optimal input combination to relatively more fertilizer and less labor. The input price change encourages an expansion in firm output as well; these changes are reflected in the input-output productivity curve of Figure 11.3. But now output expansion occurs as a result of declines in input costs rather than an increase in output price; therefore, cost curves must shift rather than remain fixed.
These shifts are described in Figure 11.4b. The cost curves MC, and AC, correspond to the initial input prices of P~ and w;. Private revenues per unit are P', private costs are C', and private profits are P1 - C'. An initial effect of reducing the fertilizer price from PF to Pf is to reduce the cost of every fertilizer-using input combination that produces wheat. This effect is shown in the diagram as direct downward shifts of the marginal and average cost curves, to MC2 and AC2. Estimated social cost, C2, is less than private cost. But two further changes occur if private prices are altered to social prices: new input combinations are used because of the relatively lower price of fertilizer, further shifting the cost curves to MC3 and AC3; and increased amounts of all inputs per unit output are used because of the change in output price.
As in the case described in Figure 11.3, observed input-output relationships provide a misleading estimate of social profits. If the analyst first uses budgets that reflect private market incentives and then changes input prices from private to social values, social costs per unit will be estimated as C2 and social profit per unit will be P2 - C2. But true social costs, measured after all the incentive effects of social prices are incorporated, are C3, and social profit is P2 - C3. In this illustration, true social profit per unit of output is less than that estimated from the initial budgets. However, a larger shift from MC2 to MC3 could create the opposite situation, in which true social profits exceed those estimated from budgets. No predictable direction of bias prevails between true social profit and estimates based on observed input-output relationships.
Empirical estimation of the input and output responses can be made
with econometric models of supply response and input demand for commodity systems; Box 11.5 illustrates the approach. Changes from private to social prices of outputs and inputs yield estimates of the quantities of inputs and outputs that coincide with social price incentives. Social revenues, costs, and profits (the second line of PAM) are then calculated by multiplication of social quantities and social prices. The impacts on the firm of distortions and market failures (the third line of the PAM) then contain both quantity and price effects. However, the construction of econometric models can be very demanding of data and research resources. The estimates from econometric models are also subject to uncertainty, and ignoring quantity effects altogether can be preferable to using the results from a poor econometric model.
The decision to undertake econometric estimation hinges on the capability of fixed coefficient assumptions to yield results that are close to the true measures of social revenues and costs. When input-output relationships are fixed, the use of observed input-output relationships provides exact measures of social revenues, costs, and returns. This circumstance is illustrated in Figure 11.5. The input-output productivity curve is represented by a single linear segment because marginal productivities are a constant (Figure 11.5a). Alternative combinations of inputs are not feasible (Figure 11.56), and the average and marginal cost curve is a straight line (Figure 11.5c). In these circumstances, changes in output prices (increases in the price of wheat) and changes in input prices (reductions in the price of fertilizer) have no impact on the optimal tangency points. Social profit is measured exactly as PW - Cz. This case provides obvious advantages to the policy analyst. One set of observable input-output coefficients fully describes the technology side of the analytical problem, and attention can be focused on the collection of price-related information. The decision to use such an approximation of reality depends, of course, on conditions particular to the commodity of interest.
If necessary, an analytical compromise can be struck between the extreme alternatives of continuously diminishing marginal returns and fixed input-output relationships. If the input-output productivity curve is given in linear segments, marginal input productivities change in discrete steps. Marginal productivities are assumed to be constant over some range of input use but can change from one interval to the next. Figure 11.6 illustrates this procedure for one input (fertilizer) and one output (wheat). In Figure 11.6a the relationship between fertilizer input and wheat output is described by the line ABCDE; this line is made up of four linear segments. At low levels of input use, such as an amount
Box 11.5. The Calculation of Social Input-Output Coefficients
The estimation of likely producer response to changes in output and input prices requires a comprehensive estimation technique, such as the profit function. In most cases, cost and supply functions will not provide sufficient information to estimate all of the relevant interactions between inputs and outputs. The application of profit functions to the estimation of social input-output coefficients is illustrated here for a simple one-output (rice), two-input (labor and fertilizer) model.
Private prices are assumed to be 200 Rp per kg of rice, 200 Rp per kg of fertilizer, and 1500 Rp per day of labor. These prices are associated with yields of 6,000 kgs rice per hectare, fertilizer input use of 450 kgs per hectare, and labor input of 300 days per hectare.
Suppose that social values are determined as 150 Rp per kg of rice, 220 Rp per kg of fertilizer and 1,500 Rp per day of labor. Estimation of social input-output coefficients must consider two categories of responses. First, the decrease in output price encourages a decline in yield, that corresponds with a reduction in demand for fertilizer and labor inputs. These changes are shown as a movement from point A to point B in the inset Figure. Second, the increase in fertilizer price encourages a decrease in fertilizer use and an increase in the use of substitute inputs (labor). Together, these changes in input combinations may imply an additional change in yield. These changes are shown as a movement from point B to point C. In constructing the PAM, private cost and returns are associated with point A, whereas the social values are associated with point C.
All necessary information for estimation of input and output quantities associated with point C can be provided by a profit function. Use of a trans-log profit function is assumed to generate the following elasticity values: output with respect to output price, 0.13; fertilizer demand with respect to output price, 0.12; labor demand with respect to output price, 0.34; fertilizer demand with respect to fertilizer price, - 0.62; labor demand with respect to wage, - 0.44; labor demand with respect to fertilizer price, 0.10; output with respect to fertilizer input, 0.075; output with respect to labor use, 0.375; the first three elasticities are used to estimate the impact of the 25 percent reduction in output price: estimated rice yield is 5,805 kgs per ha (- .25 x.13 x 6,000 + 6,000); estimated fertilizer use is 436 kgs per ha (- .25 x .12 x 450 + 450); estimated labor use is 274 days (- .25 x .34 x 300 + 300).
The next three elasticities are used to calculate the impacts of a 10 percent increase in fertilizer price: fertilizer use declines to 409 kgs per ha (.10x (-.62) x 436 + 436); labor use increases to 277 days (.10 x.10 x 274 + 274). These are the input quantities associated with the social prices. To approximate the impact of fertilizer price response on yield, the last two elasticities from the above list are used: the decrease in fertilizer causes yield to decline by 27 kgs (- .062 x.0748 x 5805); increased labor inputs cause yield to grow by 22 kgs (.01 x.375 x 5805). On balance, yield falls by 5 kgs, to 5,800 kgs per hectare. The PAM becomes the following:
Revenue
Tradable Input
Domestic Factors
Profit
Private
1,200,000
90,000
450,000
660,000
Social
870,000
89,980
415,500
364,520
Distortions and
330,000
20
34,500
295,480
divergences
If the analyst had ignored the producer response to altered prices and estimated social revenues and costs on the basis of observed (private) input-output coefficients, the following PAM would result:
Revenue
Tradable Input
Domestic Factors
Profit
Private
1,200,000
90,000
450,000
660,000
Social
900,000
99,000
450,000
351,000
Distortions and
300,000
-9,000
0
309,000
divergences
In this example, total transfers (L) are over-estimated by only 4.6 percent, reflecting the prominence of inelastic values for the assumed elasticities; the errors in individual categories (I, J, and K) are much larger.
between 0 and QF, marginal response of output to fertilizer input is larger than at higher levels of input use, such as Q~. Segment AB thus has a steeper slope than segments CD and DE. Marginal productivities are constant within each interval but diminish steadily across intervals that correspond to higher levels of input use.
Facing five linear segments, the producer chooses among only five alternative levels of fertilizer use: 0, QF, Qj, Q, and QF. Points in between will never be chosen. The explanation for this choice pattern relates directly to profitability considerations, represented by
OQW > PF AQF - PW
For most price ratios, the tangency of the price line and the productivity curve corresponds to one of the kinks in the productivity curve. For example, all prices between
(Qvv - Qw) (QF - QF) and (Qw - Qw) (QF - QF)
dictate the selection of point C as the maximum profit level of fertilizer use. This result follows directly from the linearity of the productivity curve. Within each interval, subsequent increases in input use contribute equally to profitability.
Figure 11.6b illustrates the firm supply curve under the piecewise
linear productivity curve. As the price of wheat increases (with the price of fertilizer held constant), the producer responds by using larger quantities of fertilizer per hectare. Output per hectare increases in discrete steps. Because marginal productivities decline among successive intervals, the steps of the supply curve become progressively larger.
This method of treating diminishing marginal returns means that knowledge of a discrete number of alternative technologies-often obtained from engineering studies, experiment station results, or experiences of other countries-is sufficient to measure social profit. As output prices change from private to social levels, the socially profitable technology may (or may not) differ from the technology currently used (facing private market prices). By evaluating alternative budgets under social price incentives, the profitability of change can be assessed. Analogous approaches can be used to deal with input substitution; linear approximations to the production isoquant can be made, and minimum-cost technologies associated with social input prices can be identified.
Sensitivity Analysis
Sensitivity analysis provides a way of assessing the impact of changed assumptions and errors in estimating profitability. It can be applied to both private and social estimations. In private estimations, it usually involves partial budgeting. In principle, all social parameters can be subjected to sensitivity analysis. However, the social estimates of long-run world prices for output, the cost of labor, and the cost of capital are usually the most uncertain and hence receive the most attention in sensitivity analysis.
The choice of social prices for outputs and inputs is subject to analytical imprecision in several areas. First, estimates of price-equivalent impacts of factor market divergences might not be much better than educated guesses, especially for rates of return to capital and short-run effects of distorted foreign exchange rates. Second, divergencs additional to factor market divergences may influence domestic factor prices, and their impacts may not be well-understood. For example, widespread protection to outputs that are intensive in a particular factor will probably elevate that factor's price. Third, price response within the commodity system could cause the quantities of inputs employed under social prices to be different from those used in the estimation of private profits.
One approach to sensitivity analysis involves the calculation of breakeven values for social profitability. The breakeven value of a parameter is the value necessary to achieve zero social profit when all other revenues and costs are held at their initial values. A second indicator is the elasticity of social profitability with respect to a particular parameter; it is expressed as the ratio of the percentage change in social profit of the system relative to the percentage change in the parameter. The calculation of these elasticities proceeds by an increase in the parameter of interest by an arbitrary percentage (for example, 10 percent). Social profitability is then recalculated and compared to the initial value to estimate the percentage change in social profit. The ratio of the two percentage changes gives the elasticity estimate. Input costs will have negative elasticity values, whereas output prices will have positive elasticity values. The larger the value of the elasticity, the more sensitive are the results to measurement error or parameter change in the social evaluation exercise.
Interpretation of the results of sensitivity analysis is somewhat arbitrary. Whether elasticity values are large or breakeven values are very different from initial values depends on the quality of the initial estimations and the degree of potential change in the variables. As a rule of thumb, if breakeven values differ by less than 15 percent from their initial values, the analyst should be cautious about associating positive or negative values of social profitability with the commodity system. In these instances, judgments about the desirability of the system in the economy may have to be based more on nonefficiency objectives, such as income distribution, food security, and regional development impacts. The tradeoff between efficiency and nonefficiency goods remains, but more empirical research is needed before quantitative estimates are useful. If, however, results appear robust following sensitivity analysis, efficiency gains or losses should be a significant element in policy decisions concerning the commodity system.
Concluding Comments
All social price calculations rely to some degree on the judgment of the analyst. Principles for the determination of appropriate world and domestic factor prices are relatively easy to establish, but their implementation inevitably is limited by data availability. Some would argue that this problem provides sufficient grounds to avoid social price calculations altogether and to focus economic analyses instead only on
issues that can be directly addressed by available data. Alternatively, the logic underlying social price calculations could be altered by the use of a new definition of optimality that associates optimal conditions with data that are easier to collect. An example is a type of second-best approach that assumes that all divergences external to the commodity system are beyond the influence of policy-makers. Divergences in factor and tradable-input markets are ignored, and social input prices are assumed to be equal to private prices.
But such approaches are not especially helpful in most policy analyses. Economists do not determine the issues of economic policy; policy-makers and societal interest groups do, and policy-oriented empirical analyses are expected to address these issues as comprehensively as possible. Trying to hide difficult-to-measure parameters under the cloak of arbitrary definitions of optimality does little to clarify the economic impacts of governments on agricultural producers. Like economic theorists, empirical analysts desire to minimize the number of assumptions needed to generate results. But information is never perfect, and assumptions form an inevitable element of applied analysis. If analysts provide full descriptions of the procedures and assumptions they have used, subsequent researchers will have ample opportunity to improve upon results.
Bibliographical Note to Chapter 11
Empirical estimations of shadow prices require assumptions and approaches that are different for each investigation, because available data vary widely across countries and commodity systems. Often, the details of such calculations are omitted or treated only summarily when materials reach the publication stage. An early study that gives the flavor of such exercises is M. F. G. Scott, J. D. MacArthur, and D. M. G. Newbery, Project Appraisal in Practice (Lon-don: Heinemann, 1976); this work applies the Little-Mirdees method to analyses of projects in Kenya. Works that describe social pricing exercises in a domestic resource cost methodology include Scott R. Pearson et al., Rice in West Africa: Policy and Economics (Stanford, Calif.: Stanford University Press, 1981); and Walter P. Falcon et a1., eds., The Cassava Economy of Java (Stanford, Calif.: Stanford University Press, 1984). The exposition that is closest to the methodology discussed here is Scott R. Pearson et al., Portuguese Agriculture in Transition (Ithaca: Cornell University Press, 1987).
Social pricing of tradable commodities almost always begins with world prices. Prices for many agricultural commodities are monitored by several international organizations. The World Bank's Commodity Trade and Price Trends (Washington: World Bank) contains prices for commodities and for
several inputs. Other sources of world prices are the International Monetary Fund's International Financial Statistics (Washington: International Monetary Fund), the UN Food and Agricultural Organization's Monthly Bulletin of Food and Agricultural Statistics (Rome: Food and Agricultural Organization), and various publications of the U.S. Department of Agriculture, the U.K. Commonwealth Secretariat, and several international commodity organizations (for coffee, cocoa, sugar, cotton, rubber, wheat, olive oil, and others).
World prices are adjusted to correspond to the particular market characteristics for the commodity system under study. A review and analysis of the role of quality and hedonic pricing techniques is provided in Angus Deaton and John Muellbauer, Economics and Consumer Behavior (New York: Cambridge University Press, 1980), chap. 10. An approach to the evaluation of quality effects on price is provided in Eric Monke and Todd Petzel, "Market Integration: An Application to International Trade in Cotton," American Journal of Agricultural Economics 66 (November 1984): 481-87.
The cif-fob distinction is most relevant for processed commodities or for countries with large transportation costs. Analyses of the importance of this distinction are provided in Eric Monke, S. R. Pearson, and J. P. Silva-Carvalho, "Welfare Effects of a Processing Cartel: Flour Milling in Portugal," Economic Development and Cultural Change 35 (January 1987): 393-407; Eric Monke, "The Economics of Rice in Liberia," in Pearson et al., Rice in West Africa, pp. 141-72; and John McIntyre, "Rice Production in Mali," in Pearson et al., Rice in West Africa, pp. 331-60. The problem of price variability over time may be approached as an insurance problem. This literature is reviewed in Peter Hazell, C. Pomareda, and A. Valdes, Crop Insurance for Agricultural Development (Baltimore: Johns Hopkins University Press, 1986). Also relevant is the futures market literature on options contracts; see Todd Petzel, "Alternatives for Managing Agricultural Price Risk: Futures, Options and Government Programs," American Enterprise Institute Occasional Paper (November 1984). An example of the hazards of forecasting expected prices are apparent from ex post analyses of almost all projection exercises; compare, for example, the rice prices reported in Box 13.1 with those expected by Walter P. Falcon and Eric Monke, "International Rice Trade," Food Research Institute Studies 17 (1979-1980), 279-306.
Chapter 7 of W. M. Corden, Trade Policy and Economic Welfare (Oxford: Clarendon Press, 1974), summarizes the arguments about optimal tariffs. Much of the empirical work on optimal trade taxes in agriculture has been done by Andrew Schmitz and colleagues. Examples of this work are Colin Carter and Andrew Schmitz, "Import Tariffs and Price Formation in the World Wheat Market," American Journal of Agricultural Economics 61 (August 1979): 517-22, and Andrew Schmitz et al., Grain Export Cartels (Cambridge, Mass.: Ballinger, 1981). Another work that discusses (skeptically) empirical possibilities for price controls is Carl van Duyne, "Commodity Cartels and the Theory of Derived Demand," Kyklos 28, no. 3 (1975): 597-612.
Discussions of social prices for domestic factors are contained in the books
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