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Complex Commodity Systems
In budget calculations, the relationship between output and the activity numeraire is expressed as the output of a single crop per unit area, such as kilograms of wheat per hectare. In most instances, the crop can be planted every year, using the same or equivalent production technology. The data collection exercise focuses only on the inputs and the yield for a single commodity.
Multiple Commodities
Sometimes the cropping patterns will not be so simple. In intercropping, for example, two or more crops are grown simultaneously on a particular parcel because of some mutually beneficial relationship, such as reduced likelihood of pest problems (vegetables and staple food crops) or more efficient use of space (grass for animal feed intercropped with vineyards). A second type of complexity arises when agronomicconsiderations require crop rotation on a particular parcel of land. Some crops, such as cotton, place substantial demands on soil and usually are rotated with alternative crops to maintain soil fertility.
Models of multiple commodity situations can choose between two alternatives. In the sustainable unit area approach, a representative hectare (or acre, feddan, or other area-based numeraire) includes all agricultural practices required by the representative crop system. For example, if cotton cultivation is limited by agronomic constraints to two of every three years, a representative hectare includes two-thirds of a hectare of cotton and one-third of a hectare of an alternative crop. Intercrop systems will be based on shares of area occupied by the various crops.
The second alternative is the pure-stand-equivalent approach. The commodity system is modeled as if only one commodity were grown on the land. Input and output measures for the pure-stand-equivalent budget are estimated by division of observed data by the decimal share of the commodity in the mixed-crop system. For example, if corn yields in a mixed-crop system are 1 metric ton per hectare and the corn occupies only two-thirds of the hectare (the remainder being devoted to other commodities), the pure-stand-equivalent yield is 1/0.67 = 1.5.
The choice between the two alternatives is dictated by the availability of data and research resources and by the representativeness of the farm system. The sustainable unit area method is more data-intensive, because inputs, outputs, and prices for each crop must be estimated and then summed in proportion to their relative importance in the cropping pattern. But this more complicated approach might be necessary, particularly if the analysis requires estimates of policy effects per unit area or per farm. Only the sustainable unit area approach can reflect the interplay of agronomic constraints and PAM results. Calculations of private profit, social profit, and divergences for a crop rotation, for example, are required, because farmers subject to rotational constraints engage in diversified cropping rather than complete specialization.
If agronomic constraints are not binding, economic analysis of the commodity system can ignore the complications of multicrop systems and utilize the computationally easier pure-stand-equivalent approach. Rotational constraints are irrelevant if land is in excess supply, because the producer can choose to leave it fallow at necessary intervals rather than altering the crop mix. If crop interaction effects have little impact on yields or levels of input use, the phenomenon of multiple crops is again uninteresting from the PAM perspective. In this situation, the choice of the farmer to grow multiple commodities in an intercrop fashion or in pure stands makes no difference to input-output relationships, and the simpler pure-stand approach suffices for the construction of PAM budgets. Other commodities may be ignored; only the share of the targeted commodity per unit area is needed to estimate the budget for the pure-stand equivalent.
Permanent Crops
Permanent crops, such as tree crops or vineyards, present another group of problems for budget estimates. A sustainable unit area model could be built, so that the representative area included different stages of the crop life cycle. Each year of a ten-year crop cycle, for example, is represented in one-tenth of a unit area in the representative crop budget. The inputs and outputs from each portion are then added to give total output and input requirements for the sustainable unit area. The resulting production pattern is sustainable over an infinite time. The problem with the sustainable unit area calculations for permanent crops is the omission of the time-related costs of production. In the example of a ten-year crop cycle, the sustainable level of profits indicated by the budget will not actually be achieved until eleven years after the project's inception. But the sustainable unit area method calculates profits as if they were available every year, from the inception of the activity.
Only a project cycle evaluation approach can provide an exact evaluation of benefits and costs that vary over time. In this procedure, a budget is prepared to represent each year of the crop cycle, with annual equivalent costs for all inputs and outputs. Each year's budget is thus prepared in a manner identical to that used for annual crops. Revenues, costs, and net profits from each year are then discounted to a present value and summed to indicate the expected present value of the use of the land over the cycle. Division of total present values by the number of years in the cycle determines annual average costs and revenues. In most projects, benefits are relatively small in early years and relatively large in later years. Discounting the time path of net benefits reduces future values more than early period values, thus yielding lower totals for the project cycle method than for the sustainable area method. Box 9.2 compares the two approaches to the evaluation of permanent crops.
Many permanent crops have a long production cycle; for example, most tree crops and vineyards have useful lives of 20 to 30 years. In this case, an alternative presentation of results may prove convenient. The budget represents the observed costs and returns of the activity in a year of full production (commonly attained six or seven years after initial
Box 9.2. Calculation of the PAM for Permanent CropsThe nut crop is assumed to have a three-year life cycle. The per hectare quantities and prices for inputs and outputs in each year are described in the following tables.Time path of total costs and revenues is shown here.The last line indicates the numbers for use in the PAM. The actual calculations needed for the PAM would be more complex than what is shown here, because separate entries would be neededfor labor, capital, and tradable inputs and because all inputs would be evaluated in social prices as well as in private prices.The sustainable unit area method would ignore the time path of costs and benefits and would estimate per hectare values as follows.This method overestimates profit, because crop production has more costs relative to revenues in the early periods.
planting). Net profitability from each of the previous years is calculated and then compounded to give a net present value in the year of full production. These present values are summed and treated as an investment cost, where the useful life of the investment is the remaining term of the production cycle. For example, if a coffee production cycle were 30 years, reaching full production in the eighth year, the activity budget could represent the eighth year. The value of net profits in each of the first seven years is compounded to give present value in the eighth year. Profits from the first seven years are then summed and amortized over the remaining 22 years using the capital recovery cost method. This procedure generates an annual equivalent cost of investment that can be added to the representative budget as a part of fixed costs.
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