5.8 Welfare Calculations
5.8.1 Welfare Changes at Farm Level
If only a single price change of one input or output is considered, the change in producer surplus measured as the definite integral of the supply function from p0 to p1 is the correct measurement for the change in producer welfare (JUST et al.
1982, pp. 55 ff.). For the evaluation of welfare changes in TURKSIM, however, multiple simultaneous price changes must be taken into account. Consider, for example, the case of two substitutes whose prices change simultaneously as presented in Graph 5.3:
Graph 5.3: Welfare Changes with Simultaneous Price Changes
If the price for wheat (left hand panel) rises from Pw0 to Pw1 and wheat supply rises, the supply curve for barley (Sb), a close substitute, shifts left as more area is allocated to wheat and the barley price increases due to lower barley supply.
The increasing barley price, in turn, results in the wheat supply curve shifting left. For a correct determination of the resulting welfare change, price changes must be evaluated stepwise. First, the change in producer surplus for one product must be evaluated under the original supply curve (e.g. the grey shaded area in the left hand panel), and second, the price change for the next product is evaluated under the new supply curve for the product concerned (e.g. the grey shaded area in the right hand panel). This sequential approach can be extended to input prices and the results are not dependent on the path of integration if cross effects are symmetrical.47 As a result, welfare changes at the producer side are determined:
(5.46)
where Pi is the price of product i, SUPi is the supply function of product i, Wj is the price for input j, and FDj is the factor demand function for input j.
47 For an algebraic deduction see JUST et al. (1982, pp. 338 ff).
Pw1 Pw0
Wheat quantity
Sw1 Sw0
Pb1
Pb0
Barley quantity
Sb1
Sb0
i j
i j
1 1
n m
i j
i=1 0 j=1 0
P W
• dP - ,FD • dW
SUPi j
P W
∑ ∫ ∑ ∫
In TURKSIM, supply functions for plant products include product prices as independent variables only. Therefore equation (5.46), with abbreviations as used in TURKSIM, reduces to:
(5.47) .
In TURKSIM, changes in producer surplus are calculated according to (5.47) with prices changed sequentially. The respective definite integrals are multiplied by 1-(seedpl_nq/yieldpl_nq). This is because seed production is assumed to stay at the farm. Therefore welfare changes should not be calculated for this part of production, as the farmer is also the consumer.
Initially, price changes are introduced and definite integrals are calculated for all nonquota products. As a final step, welfare changes for quota products are calculated (only sugar in the current TURKSIM version). Starting from a situation in which the quota is binding (scenario s_quo), i.e. the shadow price is below the effective farmgate price for sugar, there are different possibilities for the resulting welfare effects. Should the quota system be abolished, the calculation of the welfare effects depends on whether the new price is below or above the shadow price of the reference scenario (see Graph 5.4).
Graph 5.4: Welfare Changes Resulting from an Abolition of a Quota System
The left hand panel of Graph 5.4 shows a situation where the new price is above the shadow price of the reference situation. The resulting welfare effects are composed of a loss in quota rent (area "-") and a gain in producer surplus due to
P0
the expansion of production (area "+"). Area "+" is determined in TURKSIM by taking the definite integral of S between P1 and P_SH0 and subtracting area "a".
The right hand panel of Graph 5.4 shows a situation in which the new price is below the shadow price of the reference situation. In such a case the welfare effect is composed of the loss in quota rent resulting from the market price decreasing until it reaches the level of the shadow price (upper rectangle "-"), and the loss in producer surplus resulting from a further decreasing market price (lower area "-"), that is, the definite integral of S between P_SH0 and P1.
In the case of a binding quota in the new situation, possible effects are also manifold. Graph 5.5, as an example, shows a situation where a welfare loss due to a decreased market price (area "-") is combined with a welfare gain due to an expanded quota quantity (area "+").48
Graph 5.5: Welfare Changes Resulting from a Change in the Quota System
Welfare changes which result from production on newly irrigated areas (see Section 5.3.1.1) are linearly approximated by multiplying the price change by the average supply quantity on the newly irrigated area:
(5.48) (P_EFpl, sc_wf - P_EFpl, s_quo) • (ad_ha •SHAREpl, s_quo • YIELDpl, s_quo / 1000 + ad_ha •SHAREpl, sc_wf • YIELDpl, sc_wf / 1000)/2.
48 The automatic calculation of welfare effects in a scenario with a binding quota for all possible combinations of price and quota changes is not yet programmed in TURKSIM.
The CU scenario is the only scenario for which the change in producer surplus is calculated with the quota system maintained, and the respective calculation is included in the code.
P0 P1
Supply S
P_SH0
-Price
+
Q0 Q1
Welfare changes for animal producers are also calculated by introducing changes in product prices sequentially and summing up the definite integrals below the supply curves. Welfare changes of changing feed prices are taken into account by linear approximation (multiplying the change in FCI by the average feed quantity). This is for computational simplicity as feed demand functions for individual components, following from equations (5.40), (5.41), and (5.42) are rather complex:
(5.49)
The sequential introduction of price changes for the evaluation of welfare effects means that results for individual products cannot be interpreted and compared properly. This is because the size of the welfare change for individual products depends on how many cross prices have already been changed, and thus on the path of integration. Therefore welfare changes in TURKSIM are also calculated as definite integrals under supply and demand curves with only the own price changing. These results cannot be used to evaluate the total welfare change, as cross prices are not considered, but it allows for the comparison of welfare changes for individual products due to own price changes.
If supply and demand functions are derivatives of a profit/indirect utility function, the resulting cross effects are automatically symmetric, as they are second derivatives of the same function. This is not the case for the systems of supply and demand functions applied in TURKSIM, as they are not derivatives of any profit/indirect utility function. For this reason, symmetry can be introduced only locally. Symmetry, however, is required for the path independence of the sequential approach of analysis of the welfare effect in case of multiple price changes applied in TURKSIM (JUST et al., 1982, p. 340). A sensitivity analysis with respect to the path of integration was therefore applied.
Maximal changes in total consumer welfare or producer surplus due to a change in the path of integration were found to be 0.4 percent. This is significantly below the deviation of the results of the nonsequential approach from the sequential approach, which was up to 3 percent of the compensating variation and the change in producer surplus. As a result, the nonsequential approach was found to overestimate the welfare gains from liberalization by about 18 percent whereas the welfare gain under the liberalization scenario according to the
( )
sequential approach differed no more than 2.7 percent with respect to the path of integration. Therefore, the results of the sequential approach are used as the indicator of choice for total welfare effects throughout this study even if they are not completely unequivocal.