Peanut research and poverty reduction: impacts of variety improvement to control peanut viruses in Uganda.

Changes in economic surplus can be calculated under various market situations. For example, in a small open economy, the primary beneficiaries from adopting a cost-reducing technology are the peanut producers, either through sales or home consumption (figure 1). The initial equilibrium is defined by consumption [C.sub.0], and production [Q.sub.0], at the world market price [P.sub.w], with export quantity [QT.sub.0] equal to the difference between consumption and production. Research lowers the unit cost of production, causing supply to shift from [S.sub.0] to [S.sub.1] and production to increase to [Q.sub.1], with exports increasing to [QT.sub.1]. Economic surplus change is equivalent to producer surplus change and is equal to area [I.sub.0][abI.sub.1]. If prices in all other markets (for example, labor markets) are unaffected by the supply shift, then the surplus change captures the entire short-run benefits of adoption. In cases where other prices change, additional analysis is needed; a multi-market model is one example of such an analysis (Karanja, Renkow, and Crawford 2003; Renkow 1993). If the price of the product in question changes, due to a less than infinitely elastic demand, then changes in consumer surplus must be computed as well (figure 2).

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Poverty Changes: Allocating Surplus to Households

Analyses of predicted changes in poverty resulting from adoption of a new technology involve three main steps: (a) computing the household-level value of the welfare measure (income or consumption per capita) and comparing it to the poverty line; (b) determining which households are most likely to adopt the technology and estimating how household welfare will change following adoption; and (c) adding up the change in the number of poor people or households resulting from adoption. The household analysis of ex ante income changes among adopting households can be used to create an estimate of market-level surplus changes (corresponding to the total change in income for all participants in the market) and of changes in poverty in the population.

The FGT indices are a commonly used means to add up poverty in a population and are useful because they are additively decomposable with population share weights (Ravallion 1992). Additive decomposability allows evaluation of impacts of agricultural and other policies on subgroups (such as peanut producers). The FGT class of poverty measures is defined as [[P.sub.[[alpha] = 1/n [summation.sup.q.sub.i=1] [[z - [y.sub.i]/z].sup.[alpha], where n is the total number of people, q is the number of poor people, [y.sub.i] is income or expenditure of the ith poor household, z is the poverty line, measured in the same units as y, and [alpha] is a parameter of inequality aversion (3).

Survey data on household production and income allow estimation of poverty rates, and our study examines how adoption of a new technology changes those rates. The correspondence between the economic surplus approach and the household approach comes from the change in marginal (unit) cost of production caused by adoption of the technology. Farm profits for the ith household are given by:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [tau] is a technology shifter, [PX.sub.i] represents revenues and the right-hand integral is the variable costs of production (C'(X, [tau]) is the marginal cost function). Adoption of the technology causes profits to shift by

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where Leibnitz' rule is used to compute the derivative in (2). In an open economy case, the first term on the right-hand side of equation (2) is zero, and the change in profits is equivalent to the surplus ([I.sub.0][abI.sub.1]) in figure 1 in a single-producer economy. To see this, note that the second term on the right-hand side of (2) is equal to [abQ.sub.1][Q.sub.0] in figure 1. The third term is [acI.sub.1][I.sub.0], and the fourth term approximates [cbQ.sub.1][Q.sub.0] for small changes. Summing over the total number of producers in the region leads to equivalence between the measure of change in individual farmers' profits in equation (2) and the area of surplus change in figure 1.

The change in peanut production and household income as a result of agricultural research is related to the value of agricultural production before adoption of the new technology, and the per unit cost reduction that results from adoption. The same k-shift as used in the surplus analysis can also be used at the household level to approximate d[[pi].sub.i]([tau]). For the ith household, in the small open economy case, the change in surplus (income) is

(3) d[tau].sub.i]([tau]) [approximately equal to] [K.sub.i][P.sub.i][Q.sub.i](1 + 0.5 [K.sub.i][epsilon]) = [I.sub.0][abI.sub.1],

where [P.sub.i] is the pre-research price, [Q.sub.i] is the pre-research quantity, e is the elasticity of supply, and [K.sub.i] is the proportionate shift downward in the marginal cost curve due to research. Adopters of the technology receive this income benefit; the market K-shift shown in figure 1 incorporates assumptions about rates of technology adoption.

In a closed economy, or in cases where regional prices respond to changes in market conditions, prices are expected to decline in response to a research-induced outward shift in supply (figure 2). In this case, there are three distinct components of surplus: a loss in producer surplus for all producers due to the price decline (represented by the first component of equation (2), and [P.sub.0][acP.sub.1] in figure 2), an increase in producer surplus among adopting farmers due to the lower cost of production (the second-fourth components of equation (2), and [P.sub.1][bI.sub.1] less [P.sub.0][aI.sub.0] in figure 2), and a gain to consumers due to the price decrease ([P.sub.0][abP.sub.1]). These three components of surplus must be allocated to specific households according to whether they produce peanuts, whether they are likely to adopt the new technology, and whether they consume peanuts.

To assign producer surplus change to each of the households, total peanut production was computed and producer surplus change was assigned according to a household's production share and its probability of technology adoption. Consumer surplus was allocated in a similar manner: assign total surplus to households based on how much an individual household consumed, including home consumption.

The model is general enough to measure changes associated with product and input price changes. In each case, the relevant participants in the markets must be identified and the corresponding surplus allocated to individual households. In our empirical example, we first focus on allocating producer surplus in a small open economy, then on the change in consumer and producer surplus in a closed economy.

Household-Level Adoption

Since we desire ex ante predictions of poverty change, it is necessary to identify farmers who are likely to adopt hybrid or improved varieties in order to implement equation (3) (and a corresponding equation for the closed economy case). A model of adoption probabilities can be estimated to identify households most likely to adopt the new technology. One means of modeling adoption is to assume that farm decision makers face two alternatives--adopt or not, with the decision based on expected profits associated with each alternative, perceptions about risks, availability of information, and household-specific constraints) The adoption probability for each household can be predicted given observations on the adoption of similar technologies and variables affecting the probability of adoption. Households can then be ranked in order of decreasing probability of adoption and "adopting households" can be identified as those whose predicted probability of adoption exceeds a threshold prediction probability. If it is assumed, for example, that 30% of households adopt, those households are selected whose predicted probability of adoption exceeds that of the household at the 70th percentile of our ranking. This approach is similar to propensity score matching techniques (e.g., Godtland et al. 2004).

In an ex ante setting, no information is available from households on adoption of the specific technology of interest. The adoption probability index can be estimated using observations on adoption of an observed alternate technology, such as hybrid seed or fertilizer. Adoption profiles for hybrid seeds are likely to be different from those of new peanuts due to differences in capital requirements, seeding rates, etc. However, the assumption we make is that past adoption propensities of any new technology are good indicators of those households most likely to adopt in the future.

Data and Results