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A THEORETICAL EXPOSITION OF CONSUMERS'RESPONSE TO ALTERNATIVE FOOD POLICIES

WAITE LIBRARY DEPT. OF AG & APPLIED 1994 BUFORD AVE. - 232 COB UNIVERSITY OF MINNESOTA ST. PAUL, MN 55108 U.S.A. DEPARTMENT OF AGRICULTURAL AND RESOURCE ECONOMICS DIVISION OF AGRICULTURE AND NATURAL RESOURCES UNIVERSITY OF CALIFORNIA AT BERKELEY

WORKING PAPER NO.615

A THEORETICAL EXPOSITION OF CONSUMERS'RESPONSE TO ALTERNATIVE FOOD POLICIES

. by

G.Mythili

WAITE MEMO s r-- " DEPT. OF AG.AND Avr, 1994 BUFORD Av. UNIVERSITY OF N. ST. PAUL,MN 5C

This paper was written while the author was a Ford Foundation Post Doctoral Fellow in the Department of Agricultural and Resource Economics, University of California at Berkeley. The author wishes to thank Brian Wright for his helpful comments and suggestions.

California Agricultural Experiment Station Giarmini Foundation ofAgricultural Economics August, 1991 37X -79`i 4L3"/55 (//'--6/5

A THEORETICAL EXPOSITION OF CONSUMERS'RESPONSE TO ALTERNATIVE FOOD POLICIES

1.Introduction

&his study is an attempt to relate alternative food subsidy programs with reference to the implication for consumer theories. The Government's goal is set on raising the nutritional standard of those who are underfed rather than redistributional aspects. The rationale for such goal assumes away consumer sovereignty. This study is focussed only on consumer sector and ignores production sector merely to avoid complexities involved in the theoretical formulation, though it is recognized that in. most of the thirdworld countries where a significant proportion of the population live on farming and consume their own produce, the linkage between production and consumption decisions does influence the behavioral pattern of an individual as a consumer.

Broadly four categories of policies can be identified: 1) general subsidy on food 2) subsidized ration where price of food is subsidized subject to a quantity ceiling 3) free in-kind transfer and 4) cash transfeE]the second scheme is further split into various options with main question being whether to provide freedom of choice to consumers to purchase any variable proportion of ration quantity. It is pertinent to emphasize this question because the in-kind transfer that has been discussed in this study assumes that the recipient is not able to resell the ration good in the open .

2. Theoretical Framework

The introduction of the scheme of types (2) and (3) creates non- linearity in consumers' budget sets and figure 1 illustrates this for different options of scheme (2). If y is ' income and a food Coupon worth x dollars is exchanged for z dollars then the subsidy is x-z.s. If the consumer has an option either to purchase the full quota or to go without it , the budget set

1 expands from ACB to ACDE. If he is allowed to purchase either one-half or full quota of the ration food, the new budget line is AFGIDE. If he is allowed to purchase any variable proportion of the allotted food then the budget line is • AGDE. The first two cases result in non-linear non-convex budget sets and the third one results in non-linear convex budget set. Hausman (1985) has noted such non-linearity in budget set in a different context in his survey article. However its similarity to the present problem is not yet recognized. The equilibrium levels of food consumption for various types of indifference curves are noted in figure 2. From 2a, it is clear, the flexible quota provides more than the one-half scheme which in turn is more preferable than fixed quota . Figures 2b and 2c depict a different type of preferences, viz. (i) consumer is indifferent between variable proportion or the one-half quota (ii) he is indifferent between all the three. In the literature, an interesting distinction is made between inframarginal and marginal subsidy programs. A subsidy scheme is inframarginal if the available ration quantity at subsidized price is less than what a consumer would otherwise consume in the absence of the scheme. Since he supplements the quantity from the open market, the marginal price is the market. price and change in consumption has only an income effect. Whereas if the subsidy scheme is marginal, consumption changes have both income and substitution effects and the marginal price is the ration price. Figures 3a and 3b respectively illustrate the inframarginal and marginal subsidy schemes. These two schedules indicate that even after the introduction of the scheme the food consumption is such that the status of the scheme remains the same. Figure 3c illustrates a different situation in which a marginal subsidy scheme has turned into one where at the equilibrium level he consumes more food than the available ration due to higher income effect. Figure 3d shows that the subsidized inframarginal ration can also make him consume lesser food than the initial consumption. This happens if the ration good is inferior (negative income effect). The above arguments explain that a scheme being marginal or inframarginal is determined both by the subsidized quantity as well as consumer's preference schedule. In a real world situation,since consumers' indifference curves are not observed a thorough understanding and a quantitative knowledge of consumption for food is necessary because policy implication is different according as the change in subsidy is effected via subsidy rate or ration quantity. Schneider (1988) has made a comparative static analysis understand to the impact of halving the total subsidy either by reduction in subsidy rate or by ration quantity. He segments the population into three different categories effecting different income elasticities of demand. - - However he has not recognized the reversal of scheme status (marginal or inframarginal) as the subsidized quantity is halved. We elaborate this in Section 4. Figure 4 demonstrates a particular type of preference schedule. When given an option between fixed quota of rationing or no ration, the consumer would rather prefer no ration. Initially he is at uo. u1 is the preference schedule in a hypothetical situation when he is allowed to buy any proportion of the ration food. u2 is the relevant to the restricted choice. It is seen up is above u2.

Ration, Price subsidy and Cash equivalent: - Starting from the works of Coppock (1945) and Southworth (1945) there followed a series of studies which relied on indifference curve analysis in comparing alternative programs with respect to its effect on food consumption and consumer welfare. We extend this analysis to find leakage from Government's expenditure with leakage being defined as the difference between subsidy cost and Hicksian consumer surplus (equivalent variation in income). It is seen from figure 5 that the equivalent variation of price subsidy scheme is less than total cost of subsidy when the whole market is subsidized and hence equivalent cash transfer gives more utility than price subsidy schemes. The is represented by FH in the figure in terms of nonfood. This qualitative result does not depend upon extent of income or price elasticities of food as long as they have the usual sign and are non-zero. However the equilibrium point shifts such that he consumes less food. This clearly shows if the objective is centered around malnutrition problem then the income transfer may not be an effective policy. A similar comparison is made between subsidized ration and equivalent cash transfer in figure 6. Two different types of indifference schedules are considered. U 1 and U1' refer one type of preference. U1 is relevant when the consumer restricted is in his choice whereas U1' refers to a situation of freedom of choice. The deadweight loss is more for former as shown in the figure that IJ is the 'waste' for variable quota and KL >IJ is waste for fixed quota. It is clear, for a fixed subsidy expenditure, as compared to the price subsidy program, subsidized ration• with fixed quota would stimulate consumption for consumers

3 with indifference curve of the type U1. A different type of preference curve considered in U2 implies there is no leakage from the subsidy program. This shows if the scheme is inframarginal after implementation then there is no leakage from the subsidy as income transfer that would giire him same utility is equivalent to subsidy cost. Two obvious conclusions that emerge from this analysis are that the in-kind transfer can be no more effective for increasing consumption as compared to the income transfer if income elasticity of demand for food is high enough. If it is lower, the relative effectiveness of the in-kind transfer program will in general vary inversely with elasticity. Similar remarks apply to the case between this program and a general price subsidy scheme when price elasticity of demand for food is high. Of the four policy options that are noted earlier, both cash transfer and free in-kind transfer equivalent to the subsidy, will have the same effect as that of an inframarginal subsidy scheme.

3.Review ofPast Studies

Theory of consumer welfare in the event of government intervention in the free market by in-kind transfer has received the attention of researchers mainly in areas such as housing and education . Though problems in both areas are somewhat analogous to the present problem of food subsidy , they differ in that (1) they are more of an indivisible nature (2) consumers may not be able to supplement the ration good by purchasing from the open market. The question of concern in those programs tends rather to be participation or no participation. Olsen (1971) has modified the budget set for fixed quota as is shown in figure 7. He has removed all consumption vectors that fall within the set BCG on the ground that a consumer would not be prepared to lose money by paying for good equivalent to OD and buying less than OD. He analyzed the households' participation in the program in the context of education subsidy. This brings to the fore an interesting case of discontinuity in the budget set. Blinder and Rosen (1985) introduce a new strategy that also creates discontinuity in the budget set which they denote as 'Notch Scheme'. We extend the idea that has been put forth by them in the context of stimulating the charity contribution( by tax deduction) by nonlinear taxing method. If the scheme is such that an individual who consumes threshold level c* is eligible for a lumpsum cash subsidy then the consumer budget set looks like ABCD, shown in figure 8. The idea is not totally new to the schemes that have been considered by us earlier because it is analogous to the fixed quota in-kind transfer scheme. Though the issues like 'leakage from subsidy' do not make sense in this new scheme, it can be justified as long as the objective is to attain a target consumption level. Clarkson(1976) has evaluated the welfare benefits of the Food Stamp program. Under this program eligible consumers are provided food coupons for an amount less than market and the coupon is worth roughly households' monthly expenditure on food. Though dual markets physically do not exist it can be assumed that the consumers perceive a hypothetical subsidized price for food based on which they make their choice. Clarkson estimates consumer benefits by Hicksian equivalent Variation in income considering • Cobb Douglas utility function. The feature of this function is in unitary income and price elasticities of demand. He adopts the analytical solution provided by Murray(1975).

Consider the indirect utility function Um=g(,Y,POn) where Um is the highest U attainable given Y,pf and pn. Let the maximum attainable utility under the program be Us=f7,E) The individual will participate in scheme if Us > g(.Y0,PpPn) where yo is initial income. If we obtain g4 by solving g for y as a function of Um, pf, p n then we can obtain equivalent cash grant (B) (i.e. the amount that would give him same utility) which is equivalent to the difference between g4(U,pfyn) for a specific utility Us fixing and the initial income yo. B=g-1(Us,pf,pn)-yo

If U=Fa E 1-a, then it is derived

B.(pfcif/ a)a {(yo+S-pfcif)/ (1 -a))1-a -yo

Clarkson has proposed following two conditions to estimate the equivalent variation assuming a food worth $x is given for $z and subsidy $S is equal to x - z.

B={x a)a ((y0 - z)/ (1 -a))1-a -yo if x> a(y+S) =s if x<=a(y+S) where a(y+S) is expenditure on food under cash transfer equivalent to S. From figure 9 it can be seen that the situation x=a(y+S) arises when the utility curve touches the budget line at G and also tangent to the budget line corresponds to the cash transfer HGK. Clarkson estimates recipients' benefits and 'waste from subsidy' for different income groups by subtracting B from S whenever S exceeds B. It is interesting to note that the equivalent variation of income depends on the maximum attainable utility Us which in turn depends on the quantity of food allotted under the program with choice constraint. Keeping the total subsidy same, different binding quantity leads to different equivalent variation measure. The more and more the quantity is binding, the less and less would be the equivalent income variation.One assumption which raises concern in this derivation is the assumption of unitary income and price elasticities of demand that is embedded in the Cobb-Douglas function. Murray considered the case of subsidies on housing in which the assumption of unitary price and income elasticities of demand may be acceptable. Based on the • empirical evidence, the unit elasticity assumption is not acceptable for food.

6 Galatin(1973) has considered three different alternatives. (i) food stamp program comprising in-kind transfer of food less than its market value. (ii) free food for the amount equivalent to subsidy (iii) cash transfer equivalent to the subsidy amount If M is money income of the and if foodstamp worth m(l+b) is provided in exchange for m then the subsidy is mb. The three alternatives are illustrated in figure 10 where F is quantity of food and E is expenditure on nonfood. In the figure if the equilibrium point lies between AB then the consumer is indifferent between all the three programs. If it lies between BC then he prefers free foodstamp or cash transfer to foodstamp plan. If he stays on CD then he prefers cash transfer to the other two.

If r is proportion of expenditure on food to total income M+mb then r = pf(F/E)/(1.+PiF/E) ) since FM= r/pf(1.-r)

He stays on AB if the ratio F/E > slope of the line OB. m(l+b)/pf

i.e > P(1-r) M-m r> m(1+b)/(M+mb)

He prefers point on BC if

m(l+b) mb > r > M+mb M+mb He prefers to stay on CD if mb > r M+mb

Utilizing the household sample data Galatin attempts to relate the consumers' preference with household characteristics and noneconomic factor like location. We have discussed earlier that both income transfer and inframarginal in-kind transfer will have the same effect on food consumption. However there are counter arguments which favour in-kind transfer to stimulate consumption -to a greater level even in the face of inframarginality based on empirical evidence (Rogers,1983 Senauer and Young, 1986). These arguments stem from recipient's perception of treating cash and equivalent money derived from inkind transfer differently and hence utility based comparison is challenged by empirical analysis. The administrative feasibility of implementation also supports in-kind transfer on the basis that it involves lower misappropriation risk against cash transfer (Per Pinstrup-Anderson, 1988). The foodstamp system that is practised in United States (food stamp) is slightly different from the one that is prevailing in the developing countries (subsidized ration with dual market) though both take a form of in-kind transfer. Under food stamp program the deficit good is offered along with some other (with substitutability between goods). Raaj K. Sah (1986) has made marked distinction between these two when making evaluation of the programs with respect to its distributional impact between poor and the rich in his theoretical work. He has found that the poor are better-off under mere deficit good allocation system than under the allocation system of deficit good with other goods if the income elasticities of the deficit and the other goods are constant and close to one another and if the secondary is possible in atleast one of the two goods. However the distinction may not be meaningful when the other goods do not form significant portion in the consumption bundle. The distributional impact has also been studied by Bigman(1985). Whereas in Sah's work welfare is assessed by utility Bigman assesses welfare by consumption level. Weitzman (1977) has compared the different schemes on the basis of social loss function. By specifying an ideal of consumption of specified good, the social loss is defined as the square of deviation of actual distribution from the ideal distribution. Rivera-Batiz (1981) extends this analysis by including a cubic term in the social loss function.

8 4. Analytical Derivation

In this section we derive the subsidy cost that is to be incurred by the Government to achieve a target consumption, say, a% more than the present consumption of go, in terms of consumption parameters. The problem is fairly simple for inframarginal scheme. The restriction in choice occurs only for marginal scheme. Before deriving this let us analyze these two situations with the aid of MarshaMan and Hicksian demand curves'.

In figure ha, p* and q* represent subsidized price and ration quantity, whereas po and cio represent equilibrium price and quantity in the absence of the program. It is clear, for marginal scheme the quantity at which p* cuts the ordinary (D) is below q*. If the consumer is given freedom of choice ,consumption would be ql. If he is restricted in choice (forced to buy full ration quantity) then change in( Marshallian) consumers' welfare measure is poAGpi-p*CGpi. The Hicksian consumer welfare (equivalent variation) which is considered to be more appropriate, is given by poKGpi-p*CGpi. In the figure CD curves represent compensated(Hicksian) demand curves. Hence to achieve a targetted consumption of q*, the social planner can save money to the extent of p*CGpi as compared to the price subsidy program for which price needs to be subsidized to the tune of pl.

1 It is to be mentioned here that for non convex budget sets the existence of a unique and continuous demand function is a question (see Hausman, 1985). However if we restrict the opportunity set such that utility under no-ration regime is less than utility under ration regime, then the relevant portion of the budget set is convex and a unique demand is justified.

9 Figure 11.b represents a different situation where, the quantity at which p* cuts the demand schedule is above q*. Since there is only income effect the equilibrium quantity is determined by the shifted demand curve(D') drawn with reference to the new income level. Consumption is given by ql, the quantity at which po cuts the new demand curve. This shows that the consumer is supplementing the ration quantity by purchasing from open market to the extent of qi-q*. In this case Hicksian welfare measure (poCICp*) coincides with total 2 subsidy cost . There is no leakage from the government expenditure as we have already seen this (fig.6) using indifference curves. In this situation any shift in policies that changes p* and q* for a fixed subsidy will not shift equilibrium consumption as long as q* does not exceed ca, whereas in the previous case such changes shift the equilibrium consumption and hence can be checked by restricting consumer's choice for achieving a target consumption. In studies such as Reutlinger and Selowsky (1976) and Bignaan(1985) the distinction between the two cases with respect to its implication for food consumption is not clearly identified when deriving the analytical solution for policy variables. This is crucial, considering the fact that the objective is set at achieving a target consumption. First we take the inframarginal situation to derive the minimum subsidy needed to achieve a target consumption. The Engel curve is specified by the following relation: (q)= ln(y) (14 q=-Tly(1/Y) Ly

Ay is the additional income needed to make them consume q0(1.+a) = q* and hence Ay=subsidy cost S. For a discrete change from qo to qo (1+a), Lq = qoa. Let the initial income be yo.

2 The change in Marshall's consumer welfare measure is not very relevant because of non- linearity in prices.

10 Therefore qoa = llAy (10 (1+a)/ (yo+Ay) cm a(yo+ Ay)= y y cio (1+a) Ay(a - (Tiy (1+a))) = -ayo Ay= S =(ayo) / tny (1+a)- a} The fixation of q* and p* is immaterial in this case because changes will not affect• consumption as long as a)total subsidy cost is same and b)q* does not overtake the quantity that corresponds to the subsidized price in the unconstrained demand.

To derive the subsidy cost that is required to increase consumption by a% in the situation as shown in figure 11a, let us introduce the concept of 'virtual price'(Neary and Roberts,1980) which is defined as the price at which the ration quantity would have been chosen by the consumers under no-ration situation. If the =compensated demand elasticity is specified as id then it follows that

ln(q*) Tid ln(pi) where pi is virtual price at q* = q0(1+a) in.( q0(1+a))=TI ciln(p* - y) where y= p*-pi, p*. ration price

For a discrete change from cm to %(1A-a) Ap = po and iq = qoa Consider change in equation (1) qoa =id q0(1+a)[ (p* -7) po /(p* - y) (1)* - qoa = - scio(l+a)[Po - P* + 7] Total subsidy expenditure S = q0(1+a)(p 0 - p*) (p* - y) qoa = - [S + y q0(1+a)] S =- (((p* - 7)q 0a/ - Itio(l+a)] The difference between the virtual price and ration price y can be characterized by the expenditure function. If there are two goods q and z among which the consumer has to allocate his income then the expenditure function 'e' is specified as e (pi, p2,u0)= Min [p1q+p2z: u(q,z)>. uo] - q,z

This expenditure function is an unconstrained one under general price subsidy scheme. The constrained expenditure function e* is defined as the minimum cost

11 of attaining the same u0 under constrained situation, say, when quantity one is preallocated at q = q* . e* q*,p1,p2.u0)= Min [p1q*+p2z: u(q*, z)>=u 01

If z1 is the quantity chosen of second commodity under constrained situation then

e* (q*,p1,p2,u0)= p1ce+p2z1(q*,p1,p2,u0) By introducing the virtual price pv ,the price which induces an unconstrained consumer to purchase the ration level q*, the above expression becomes = P1q1(Pv,P2,4) P2z1bv,P2,u0) =(131-Pv+Pv)[c11.(Pv,P2,u0) P2z1bv,132,u0A =(P1.-Pv)cl*+ e(Pv,132,u(J) since q* = qi(Pv,P2,u0)

a e*/a =(pi-p v). This can be used to interpret the difference between ration price and virtual price(y). It is marginal change in the minimum cost of remaining on the same indifference curve (the one that corresponds to the general price subsidy) for a unit change in the ration quantity. The minimum cost decreases as the ration quantity declines exhibiting a positive relation between e* and q*. This has been delineated in figure 12. In the figure, point C has the same expenditure as that of A. Hence to remain on u0 a reduction in the expenditure up to the extent of AB in terms of nonfood is realised if the ration quantity decreases from q* to q*' keeping the total subsidy same. The above analysis explains the importance of identifying the crucial factors in the consumers' objective function and incorporating them in policy modelling which facilitates understanding of consequences for changes in policy.

12 5. Effect of Changes in Policy Parameters

Ration quantity versus total consumption: _ In order to study the magnitude of change in total consumption as ration quantity (q*) changes, we fix the subsidy price and assume that changes in q* do not affect market price. In the initial stages for each unit of increase in q* there is only income effect. Let yo be the initial income level of consumers and y be income under the scheme. YO+(P0-13*)q* ay / a q* = pop* a q/ a q* = (q/ y).(a y/a q*)=i yq(po-p*)/ y a 2q/ ce2 = ca( a q/a q*)/ a y]. a y/a q* = [a[iyq(p o-pic)/y) / ay )].(p o p*) =(po-p*) 2 [ty ny(cily)-q1/y2]

=(p 0-p*)2 Tiy erly (q/y2).>=<0 as Tly >=<

Let the consumption in the absence of program be q0. Figure 13 explains the relation between q* and q. The curve reaches its maximum at q = q*. Once q* exceeds the quantity that corresponds to p* in the demand schedule any more increase in q* will not change equilibrium consumption3. Hence the relevant segment of the curve is AB. If the choice is restricted (consumer is forced to buy full ration quantity) then for more increase in q*, q=q*. In this case points move along 45° line AC until a stage is reached after which he opts out of the program because the utility under no ration regime exceeds utility under ration.

3 It is worth mentioning here that the derivatives need not exist at the kink point of the consumers' budget set. In our derivation the differentiation conditions are meaningful only upto the point A. Subsidy rate versus total consumption:

If q* is fixed and p* is allowed to vary (with no change in market price) then the change in equilibrium consumption for changes in p* is illustrated in figure 14. In the initial stages for smaller p* it has only income effect. Once p* crosses the price that corresponds to q* in the demand schedule it has both effects subject to the non-restriction in choice. Otherwise q = q*. If we study the relation by subsidy rate 8=(p 0 - p*)/ po ,then Total subsidy cost S = poeq* Income y = yo+poeq*

Initially for each unit of increase in subsidy rate the locus looks like BC (non restriction in choice) or AC( choice restriction). Once the subsidized price reaches the price that corresponds to q* in the demand schedule, the equilibrium consumption has only income effects , so the curve looks like the ones depicted in the previous case( relation between q and q*) for more changes in O.

6. Trade-off in Government's Objectives

It is evident that less developed economies face acute malnutrition in a considerable portion and considering the facts that the population is high and also price subsidy scheme involves a huge fiscal cost for achieving a nutritionally optimum level of consumption, the relevant strategy for the government would be subsidized ration forcing the quantity q*( It is observed, for developing countries, the situation is similar to the one designated in 11a). Given a knowledge of demand and a fixed budget for the scheme and a predetermined q*, the subsidy price can be immediately determined if the coverage is 100% and there is no price uncertainty at the decision making stage. However if the scheme is to be aimed at a section of the population (equally important issue is to make the program beneficial to low income consumers) then there is a trade off between subsidy rate and coverage of the scheme.

14 If 00.is subsidy rate for total coverage then 0 ought to be adjusted such that

0= 00 + X2 (B-TC). where Xi measures the relative importance of coverage over subsidy rate and w is the factor relating to the deviation of intended coverage from total coverage. For less and less coverage (more deviation from 100%) more and more subsidy rate is expected and hence Xi is positive. The magnitude of Xi is to be determined exogenously by the program criterion. B is budget ceiling and TC is total cost of operating the program of which subsidy cost is a portion. X2 gives the marginal increase in the subsidy rate due to unit increase in the budget allotted to the program holding.all the other factors constant. However it is not a simple decision for the fact that in TC, the variable cost , C(q*) of subsidy cost i.e cost of operating the program, also varies as coverage varies. This happens because quantity handled changes with the coverage. But the change in. subsidy rate will not have any effect on the other variable cost. If we specify the above objective in a more general form of deciding on choice variables 0 and co simultaneously then it is important to find factors dictating the trade-off Xi in planner's objective function. It is an empirical question which needs further study. Another point worth mentioning here is that the past studies find different elasticities of demand for different income groups and in practice it is difficult to implement different policies for different groups; Increasing the average consumption qo by a% • may not satisfy the target consumption q* for certain groups. Very often the within group variation itself may be significant complicating the issue further.

7.Alternative to Targeting Program

The above discussion leads us to some new avenues to explore how the subsidy grant can be successfully diverted to the intended groups. From the experience of some countries the programs aiming at the targeted groups have not been largely successful due to the planner's difficulty in identifying the relevant group of beneficiary and also to incorrectly specified policies. For instance, in foodgrains, it is found in a developing economy like India, fiscal cost on these programs has been alarmingly increasing every year without any adequate increase in the consumption level of the targeted groups. In an attempt to find reasons for this, some empirical studies (for eg. refer Senauer and Young,1986) came to the conclusion that participation in program distorts the consumption parameters in a manner beyond the explanation of simple utility based arguments. This section characterizes one such factor that distorts the behavior of the Consumer. Moffit(1983) proposes 'stigma' (lack of self-respect) as one reason for the distorted behavior of consumers where the income elasticity of demand between welfare income and private income differs. We attempt to incorporate the 'stigma' effect into the model to show how the 'stigma' attached to welfare benefit can be exploited by a social planner to avoid more complexities involved in targeting the program. We hypothesize that the stigma effect distorts the price and income elasticities of food after participation in the program and it affects differentially the various sections of consumers. This influences individual's decision on participation, and the stigma factor may lead to conclusions different from the traditional model where more income means more utility and this leads always to the participation. All these factors explain that under appropriately specified policies, taking into account of these factors, the leakage of subsidy to the unintended group can be minimized. Moffit proposes two types of stigma effects. One is a flat component and another component varies with the size of the benefit. The presence of variable component alters income elasticity of demand between private income and welfare income. Our model which considers transfer in kind treats stigma variable as one entering into the consumer's utility function endogenously and it varies with the subsidy per unit of commodity.

The Model: Let the individual's utility level depend on the income and a variable capturing stigma effect 'arising from participation in the welfare program. The utility is represented, before participation by U(yo)and after participation by W(y, s(.)) W(y,s(.)) = W [yo+(p-p*)q*, s(p-p*)] (1) where 's(.)' is stigma factor, p is market price, p* is subsidized price and q* is subsidized quantity. (p-p*)q* is the total subsidy received by an individual. Both U and W are assumed to be concave functions. The crucial assumption in this

16 model is, the stigma variable 's(.)' is a decreasing function of(p-p*).U' >0 , U" <0 , W1 >0, W11<0 , W2 <0, W22 >0. 's(.)' is assumed to be absent for low income• categories and hence the utility for this section is always higher with participation as compared to 'no participation'. W can be modified to represent a group •of consumers by incorporating a variable z representing individual's characteristics which is assumed to affect 's'. W(y,$)= W Ry0+(p-p*)q*), st(p-p*), z}] (2)

The main aim of the model is to see the impact of changes in p* , the subsidized price, on participation in the program and hence p and q* are fixed initially. It is hypothesized that given p and q* there exists a unique price p * at which U(yo) = W (y,$). i.e. U(yo)= W [(37.0+(p4*)q*), s(p-D*,z)]. For all p* < p *, the individual will choose to participate in the program. For p* P *, the individual will not participate. This model assumes that either the individual buys all the allotted subsidized quantity or they do not participate. This is reasonable because the stigma is assumed to be present only in those categories of consumers (middle or high income) for whom the scheme is inframarginal. Hence they buy all the quantity. If the stigma is present in those consumers for whom the scheme is marginal then the model becomes complex because the welfare income then is endogenous in the variable, consumption of q*. The subsidized quantity allotted q* and the quantity bought (1.1* differ and cll.* is determined by the of welfare income and marginal disutility of 'stigma'. This problem can be avoided by assuming that government enforces fixed quantity of consumption q*. The main emphasis of this model is the sharp discontinuity in the utility function • • that arises due to stigma between welfare income is equal to zero and positive. Let us illustrate the situation with the aid of figure 15. Initially the marginal disutility due to 's' outweighs marginal utility due to welfare income and at the point 'A' , U(Y0)= W(y,$). If the total subsidy is such that the income cuts utility between B and C then the individual with 's' >0 will not participate in the program. If the income cuts the utility above C then the individual will choose to participate.

17 - Alternative Specification:

If the utility function is•respecified as

- V(y,$) = V(Y0+(p-p*)q*) - s((p-p*),z) (3)

then this is a special case of (2) with utility being separable in income'y' and stigma 's' and it is a linear function in stigma variable. It is clear that 'V' is a special case of'W' and that the utility is separable in 'income' and 'stigma' . W2 is constant and equal to -1. This specification assumes absence of substitution between welfare income and stigma. Since the marginal disutility is constant in (3) as compared to the decreasing marginal disutility of the one represented by (2), it requires higher income to equalize U(yo)and V(y,$) in utility type (3). This is illustrated in figure 15. In both specifications, it is clear, both the income elasticity of demand and price elasticity of demand are altered. In Moffit's analysis, the introduction of variable 'stigma' component alters only income elasticity of demand between private income and welfare income. In the present model, even the price elasticity varies between changes in market price and changes in subsidized price. Keeping the ration price fixed, when there is an increase in the market price, it leads to less stigma and more utility. When p* increases for a constant p, it leads to more stigma and less utility. In all respects, a transition occurs when the individual participates in the program and any kind of transition can be modelled in this fashion.

The above analysis shows the knowledge of differences in taste to welfare subsidy between different sections of consumers would help planners choose appropriate policy instruments to avoid benefits going to non-intended groups. It also shows theoretically that the subsidy range within which the policy options are allowed to vary differs significantly among different specifications of utility. For instance, the subsidy amount ranging between yo and D would prevent a whole lot of non-intended consumers whose are characterized by equation(3) from participating in the program. If the utility is characterized by (2) then the subsidy ranging between yo and A would make the same set of consumers opting out of the program. The planner can operate with more degree of freedom if the utility is represented by (3).

18 There is an analogy between this phenomena and a queue system for rationing which has been discussed by Sah(1986). If each individual is forced to stand on queue to obtain his/her quota of subsidized food then it has consequences similar to the stigma role. Queuing creates different opportunity price for ration good for different categories of consumers according to their opportunity costs of waiting time. Since , the higher income groups have greater of waiting time as compared to the lower income groups, opportunity price of food is higher for former. However this is equivalent to the program where any kind of differential is involved in participation. This does not distort the consumption parameters unlike in our model. Weitzman(1991) extends the queueing phenomena to searching, queueing and hoarding phenomena. He discusses a situation under which price distortion creates unproductive search and storage activity due to the 'effort' cost involved in obtaining the commodity each time. This leads to welfare loss of a price subsidy scheme and this loss is linked to the coefficient of price distortion.

8. Conclusion

In,this study we have related modern approaches to commodity subsidization from various fields to the question of nutritionally oriented food subsidization in less developed economies. In this context we have seen that under the non-resale assumption the 'lumpiness' of the ration feasibly enforced with on-site feeding program can be very important in target attainment in some circumstances, wherein in others, a whole range combination of subsidy level and ration quantities gives equivalent results. Welfare evaluation of different alternatives has been illustrated, and shows some subtleties not previously recognized, even in the single consumer model upon which we focus. There is a need for empirical investigation to confirm the distortion of consumption parameters due to participation in the subsidy scheme. Further discussion of handling costs, distributional considerations and uncertainty about prices awaits subsequent analysis. REFERENCES

Bigm.an, David (1985) 'Food-Distribution Policies : Price Subsidies and Income Transfer' in Food Policies and Food Security under Instability, Lexington,Mass: Lexington Books. Blinder, A.S. and Rosen H. S.(1985) 'Notches' American Economic Review , 75, No.4, 736-747. Clarkson, K.W (1976) 'Welfare Benefits of the Food Stamp Program' Southern Economic Journal ,43, 865-78. Coppock , J. D (1945) 'Indifference Curve Analysis Applied to the Food Stamp Plan' American Economic Review , 35, 99 - 110. Deaton, A (1981) 'Theoretical and Empirical Approaches to Consumer Demand under Rationing' in Essays in the Theory and Measurement of Consumer Behavior ,Cambridge, Cambridge University Press. Galatin, M (1973)' Comparison of the Benefits of the Food Stamp Program,Free Food Stamps, and an Equivalent Cash Transfer' Public Policy, Spring, 291-302. Hausman, J.A (1985) 'The of Nonlinear Budget Sets' Econometrica 53, 1255-82. Horan, Patrick and Austin,Patricia (1974) 'The Social Bases of Welfare Stigma' Social Problems, June ,21, 648-657. Moffit, Robert (1983) 'An of Welfare Stigma' American Economic Review, December, 1023-1035. Murray ,M (1975) 'The distribution of Tenant Benefits from Public Housing' Econometrica ,43, 771-88. Neary, J.P. and Roberts, K.W.S. (1980) 'The Theory of Household Behavior under Rationing' European Economic Review, 13, 25-42. Olsen, E.(1971) 'Some Theorems in the Theory of Efficient Transfers' Journal of , Jan/Feb, 166-176. Per Pinstrup-Anderson (1988) 'Food Subsidies in Developing Countries' Ed. Johns Hopkins University Press, Baltimore. Raaj K. Sah (1986) 'Queues, Rations and Market: Comparisons of Outcomes for the Poor and the Rich ' Centre , Yale University , Center Discussion Paper, No.504 . Reutlinger, S. and Selowsky, M.(1976) 'Malnutrition and Poverty: Magnitude and Policy Options' Baltimore, Johns Hopkins University Press, Staff Occasional Paper, 23. Rivera - Patiz , F.(1981) 'The Price System vs. Rationing: An Extension' The Bell Journal ofEconomics, 12, 245 - 248. Rogers , Beatrice (1983) 'The Internal Dynamics of Households : A Critical Factor in Development Policy' Washington D.C., U.S. Agency for International Development. Schneider, Robert, R.(1988) 'A Framework for Analyzing Food Subsidies 'World Development, 16, No.7, 835-845. Senauer, Benjamin and Young, Nathan (1986) 'The Impact of Food Stamps on Food Expenditure : Rejection of the Traditional Model' American Journal of. ' 68, 37 - 43. Southworth, H. M.(1945) 'The Economics of Public Measures to Subsidize Food Consumption 'Journal of Farm Economics , 27, No.1, 38 - 66. Thurow, L.C. (1974) 'Cash versus In-kind Transfer' American Economic Review, 64, 190-95. Weitzman, M.L. (1977) 'Is the Price System or Rationing More Effective in Getting a Commodity to Those Who Need it Most' The Bell Journal of Economics 8,517-524. Weitzman, M.L. (1991) 'Price Distortion and Deformation, or What Happened to the Soap?' American Economic Review, 81,No.3, 401-414

21

Equilibrium Consumption for Different Indifference Map

NF NF

Figure 2a Figure 2b

NF

Figure 2c I nframarginal and Marginal Subsidy Schemes

NF NF

Figure 3a Figure 3b

NF NF

Figure 3c Figure 3d Fixed Quote of Ration versus No Ration Price Subsidy and Equivalent Income Transfer Ration end Equivalent Income Transfer

Figure 6 Modified Budget Set

•e• re ;1,9,;4 Ild C

..,..% e,#/e4.• ;';\ e.1;•doe

Figure 7

Budget Line under 'Notch' Scheme

NF

c*

Figure 8 Comparison of• Three Different Schemes Uncompensated and Compensated demand

Marginal Scheme

Po P*

P1

qo q1- q

Figure 11a.

Inframarginal Scheme

Po A J

1

cd • cd

q'1

Figure llb Reduction in Minimum Cost Due to reduction in Ration Quantity

NF

Figure 12 Ration Quantity versus Total Consumption

= fly 1 fl <1

=q* qq*

Figure 13

Subsidy Rate versus Total Consumption

Figure 14 Utility Comparison for 'Stigma' and 'No Stigma'

utility

U=V=W

AD

Figure 15