Food Subsidies: A Multiple Price Model

IN MANY COUNTRIES, food subsidies are the most politically and emotionally charged of all government expenditures. To some observers, the fundamental measure of a successful government is its commitment to, and effectiveness in, providing its population with adequate nutrition. To others, food subsidies are a token, temporary treatment masking serious structural illnesses, ranging from chronic unemployment due to the failure of economic policy to hopelessly skewed access to economic opportunity. Whatever the short-run economic, political, or moral justification for food subsidies, however, experience has shown that the long-run consequences are often different from the short-run objectives.


IN MANY COUNTRIES, food subsidies are the most politically and emotionally charged of all government expenditures. To some observers, the fundamental measure of a successful government is its commitment to, and effectiveness in, providing its population with adequate nutrition. To others, food subsidies are a token, temporary treatment masking serious structural illnesses, ranging from chronic unemployment due to the failure of economic policy to hopelessly skewed access to economic opportunity. Whatever the short-run economic, political, or moral justification for food subsidies, however, experience has shown that the long-run consequences are often different from the short-run objectives.

IN MANY COUNTRIES, food subsidies are the most politically and emotionally charged of all government expenditures. To some observers, the fundamental measure of a successful government is its commitment to, and effectiveness in, providing its population with adequate nutrition. To others, food subsidies are a token, temporary treatment masking serious structural illnesses, ranging from chronic unemployment due to the failure of economic policy to hopelessly skewed access to economic opportunity. Whatever the short-run economic, political, or moral justification for food subsidies, however, experience has shown that the long-run consequences are often different from the short-run objectives.

These consequences relate to unforeseen effects on the domestic agricultural sector, the budget, and the balance of payments, as well as on the distribution of income—effets that are often both disappointing and poorly understood. The purpose of this paper is to develop a simple, calculable, partial equilibrium model that explicitly incorporates the too-often-neglected links among food subsidies, food imports, domestic producer incomes, and the budget. Much of this analysis could be carried out through graphical supply and demand analysis with the same qualitative results.1 The mathematical treatment, however, can also provide a quantitative measure of the relevant policy trade-offs and several interesting results which cannot be obtained through graphical techniques. For policy analysis in many developing countries, it may constitute an acceptable compromise between the qualitative results of graphical analysis and a fully articulated general equilibrium model—with all its trappings of econometric sophistication and data development and management.

I. The Model

In its most general form, the model includes a government that transfers financial resources, two consuming sectors (an administered and a free market), and two sources of food supply (imports and domestic production). Access to the administered market is assumed to be limited by government policy to households in a specific income range. (The authorities typically achieve this through the location of government “fair-price shops,” the self-selection of consumers on the basis of the perceived quality of the food in these shops, or through regulation.) The analysis assumes that prevailing prices clear in both markets, given their level of provisioning and the number and demand characteristics of consumers with access to them. In practice, these market-clearing assumptions exclude arbitrage between the two markets. While they include the case where a poor man queues at a fair-price shop to purchase goods for resale (at a profit) to another poor man, they do not allow the poor man to resell to a rich man. Such arbitrage is handled in the context of this model by a special case where the two markets are merged. In a strict sense, the model does not reflect rationing under a system of disequilibrium between supply and demand. Rather, the model reflects a form of market segmentation, with differential prices prevailing in two markets, each with different demand characteristics.

Equation (1) expresses the fact that the sum of the value of goods in each market must equal the value of goods produced and imported, plus a government subsidy:


(PF is the free market price; CF is free market consumption; PA is the administered market price; CA is administered market consumption; Pw is the world market price; I is imports; Ps is the domestic supply price; S is domestic production (supply); and G is the government subsidy.) With no government intervention in the market, the price in all markets is equal to the world market price:2


Consumption is equal to imports plus domestic production:


so the budgetary cost (G) is zero. From equations (1), (la), and (lb):


For any change in any of the terms in equation (1), the following condition must continue to hold true:3


From the definition of the price elasticities of demand and supply, the price-quantity combination that would clear each market can be determined:

Domestic supply elasticity:εs=ΔSΔPsPsS.(2a)
Price elasticity of demand in the free market:εF=ΔCFΔPFPFCF.(2b)
Price elasticity of demand in the administered market:εA=ΔCAΔPAPACA.(2c)

The financial implications of any policy involving change in the quantity of food distributed in the two markets can be derived by solving for ∆Ps, ∆PF, and ∆PA, respectively, in equations (2a), (2b), and (2c), and substituting into equation (1c). This will express the financial balance with market clearing in terms of quantity changes:


Alternatively one can solve for ∆S, ∆CF and ∆CA to express the financial balance equation with market clearing in terms of price changes in the various markets:


II. Policy Analysis: Alternative Policies

The model can be used to compare the relative success of six alternative policies in achieving a goal of a 20 percent decrease in consumer prices for the poorest 40 percent of the population. Assuming a price elasticity of demand of ‒1.1 for the poor, this is equivalent to aiming to increase their food consumption by 22 percent. (This, as mentioned above, assumes that the market is effectively segmented and adequately provisioned so that it clears at the fixed price.)

The major elements of five of the policies are shown in Table 1, and the initial conditions of the hypothetical country in Table 2. The sixth policy channels food between the free and the administered markets. Under Policy I, the government provisions the entire rice market at a price 20 percent below that of the world market. Policy II is a modification that targets the subsidy on the poor, separating the administered from the free market by a mechanism such as food stamps or fair-price shops. Policy III attempts to decrease dependency on food imports by encouraging domestic production through an increase in official producer prices. Policy IV attempts to subsidize domestic producers and consumers and simultaneously achieve self-sufficiency in food. This Policy also illustrates several interesting points concerning the relationship between market segmentation, subsidies, and producer prices. Policy V is the same as Policy IV, except that consumer subsidies are restricted to the poor. Finally, Policy VI allows the transfer of food between the free market and the administered market, and vice versa.

Table 1.

Effects of Alternative Policies

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Table 2.

Assumed Parameters for Policy Scenarios: Initial Conditions

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Note: The price elasticities of demand for the rich and the poor are derived from Timmer (1981) for rice in Indonesia (rounded for simplicity). The short-run supply elasticity is derived in a study of Indonesian data by Mubyarto and Fletcher (1966), and reviewed in a study of supply response by Askari and Cummings (1976). The long-run supply elasticity is assumed to be one (approximately that observed for West Malaysia and Thailand). See, also, an excellent summary of the literature on price elasticities of supply and demand in Scandizzo and Bruce (1980), from which several summary tables of observed agricultural supply and demand elasticities are reproduced in the Appendix.

As suggested by the model developed in Section II, the policies to decrease prices (or raise consumption) also affect the cost of food imports, expenditures on food consumption, the price of food for the rich, agricultural receipts, and the budgetary costs to the government. These effects are compared for each policy.

Policy I: Subsidize Imports

In terms of the model above, this policy can be defined by the following conditions:

No price discrimination:ΔPF=ΔPAΔPC.I1
Initial prices are equal:Ps=Pc=PAP.I2
Supply equals demand:ΔI=ΔCΔS.I3

For convenience, an aggregate price elasticity of demand is expressed as a weighted average of the two group elasticities as follows:


Solving for ∆C from I4 and for ∆S in the definition of supply elasticity (2a), and substituting both in the market-clearing equation I3, yields:


and the change in the price in the domestic market that would result from a change in the level of imports:


Note that for a given elasticity of demand, the larger is the elasticity of domestic supply, the less is the effect on domestic prices of an increase in imports. In effect, equation I6 says that, to the extent that domestic production is price-sensitive, increases in imports will result in a substitution of imports for local production. Given the domestic market-clearing price from I6, the changes in domestic supply and domestic demand (in each income class) can be calculated from the elasticity definitions. Finally, all derived values can be substituted into any of the original equations (la, 3a, or 3b) to determine the cost of the program to the government.

Table 3 shows the effect of government Policy I, based on the data for initial conditions in Table 2. At this reduced price, the poor increase their food consumption by 22 percent and the rich by 14 percent. Because the consumption of the poor increases by a higher percentage, their reduction in total food expenditure is considerably lower. (In terms of its effects on the demand for other goods in the economy, a lower total expenditure on food has the same effect as a higher disposable real income.) Imports, which would have to be increased by 141 percent to lower consumer prices by the planned 20 percent in the short run, would, in the long run—after farmers have had time to adjust production patterns to reflect the lower producer prices—have to be increased by another 33 percent (to 220 percent of their initial level) to compensate for the loss of domestic supply. Receipts from domestic food production would fall by 25 percent as a short-run result of subsidizing imports, and by 36 percent over the long run. The budgetary cost of this policy would be 6.2 percent of the economic value (calculated using the border price) of the food consumed in the short run and 8.3 percent in the long run.

Table 3.

Policy I: Subsidize Imports

(Producer prices depressed)

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Source: Table 2.

Initial budgetary cost is 0.

The value of food is calculated using the border price of food imports.

To offset the depressive effect on domestic production of lower producer prices, the government may combine a general subsidy on imported food with interventions to maintain domestic producer prices, either through a marketing authority (that would offer an above-market price to producers), or through a system of deficiency payments (made to farmers by the government when actual market prices are below an officially guaranteed price). In developing countries, such policies are usually an attempt to maintain producer incentives in the face of an import-sustained and urban-oriented “cheap food” policy, while in industrial countries they are more typically used to subsidize producer prices that are already above the world market level. This difference is clearest when the subsidy on imported food in a developing country is thought of as a negative tariff providing negative protection to the domestic food industry. Industrial countries, on the other hand, often give positive tariff protection to domestic food industries and, in addition, provide direct subsidies to producers. Food subsidies in developing countries may take many forms. Besides direct, explicit budgetary subsidies, there are often cross-subsidies through “stabilization” funds (especially prevalent in francophone countries) and implicit subsidies through food imports made at a grossly overvalued exchange rate.

Under a policy of maintaining domestic producer prices, the only change from the initial conditions (in Table 2) is that imports must be increased sufficiently to depress consumer prices to the 20 percent desired by the authorities. This, as calculated above, would require that total food availability be 116 units, which, with no change in domestic production, means that imports must be more than doubled to 31 units. As shown in Table 4, the subsidy must now be paid on both imported and domestically produced food and, consequently, the budgetary cost of the program increases to 20 percent of the value of the food (evaluated at world market price), compared to 6-8 percent when domestic producer prices are allowed to decrease. Domestic agricultural incomes are now protected, however, with important implications for the structure of development and for the balance of payments over the long run. Whereas food imports increase from an initial 15 percent of food availability to over 40 percent under Policy I, they now grow to less than 30 percent of the total.

Table 4.

Policy la: Subsidize Imports

(Producer prices constant)

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Source: Table 2.

Initial budgetary cost is 0.

Policy II: Subsidize Imports for the Poor

The experience with Policy I shows that the failure to target subsidized imports has a severe effect on either the budget or the incomes of domestic producers as well as having substantial negative implications for the balance of payments. Policy II aims to achieve the same increase in consumption and reduction in expenditure for the poor, while reducing the undesirable effects on rural incomes and the balance of payments through restricting the number of recipients of the subsidy. Such a policy requires some form of a means test to determine eligibility and an administrative mechanism such as food stamps or fair-price shops to allocate the subsidized good.4 The desired relationship between the increase in consumption and the decrease in price for the poor can be determined from their price elasticity of demand in equation (2c):


This increase in consumption is supplied by an increase in imports:


and there is no change in the high-income group’s market:


Combining these results into the form of the financial balance equation expressed in terms of price changes (3b) yields:


The results are shown in Table 5.

Table 5.

Policy II: Subsidize Imports for the Poor

(Producer prices constant)

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Source: Table 2.

Initial budgetary cost is 0.

The results of Policy II clearly indicate the advantage, to both producers and the budget, of restricting food subsidies to the poor only. Farmers, who suffer a 20 percent reduction in long-run producer prices and a 36.0 percent long-run loss in receipts from food products under Policy I, suffer no loss under Policy II. (Note that this result assumes a two-price system.) As a result, unlike the previous policy, this policy causes no deterioration in domestic food production. In addition, the budgetary cost is reduced by 74 percent relative to Policy la where all consumers are subsidized.5

Policy III: Increase Producer Prices

An alternative to lowering domestic market prices by increasing official imports is to stimulate domestic production by increasing official producer prices—either through the deficiency payments mentioned earlier or through actual government participation in the market, as in Policy la. If domestic consumer prices are to be maintained below world market prices, however, either existing imports must be subsidized as well as domestic production, or producer prices must be raised sufficiently to achieve food self-sufficiency at the desired consumer price. Policy III assumes that food imports continue at the initial level and that the government covers the resulting loss on import payments. The case of food self-sufficiency will be treated in Policy IV. Policy III can be defined as follows:

No market discrimination:ΔPF=ΔPAΔPc.III1
Initial prices are equal:Ps=Pc=PAP.III2
All consumption increases to be met through changes in domestic supply:ΔI=0,ΔC=ΔS.III3

The quantity required to reduce the price to the desired level can be calculated from the aggregate price elasticity (equation I4) as:




Similarly, the price required to induce farmers to produce the additional quantity can be calculated from the supply elasticity (equation 2a):


Finally, substituting the desired price changes, the budgetary cost is calculated from the financial balance expressed in terms of price changes in the form of equation (3b):


Note that the terms on the right-hand side of equation (III6) reflect the change in expenditure of the high-income class, the change of expenditure of the low-income class, and the change in farm receipts, respectively. The results are shown in Table 6.

Table 6.

Policy III: Increase Producer Prices

(Imports constant)

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Source: Table 2.

Initial budgetary cost is 0.

The major results of Policy III can be best seen by comparison with the two previous policies. Compared with a policy of subsidizing imports (Policy I, Table 3), the budgetary cost of stimulating local production to meet demand (at the same subsidized price) is over 12 times as high in the short run and just under 4.4 times as high over the long run. While food imports are not changed (by assumption) in Policy III, under Policy I imports more than double over the long run as declining farm receipts (which fall by 36 percent in the long run) lead to a withdrawal of resources from agricultural production. Under Policy III, however, long-run domestic farm receipts are increased by over 40 percent, stimulating an increase in production of nearly 19 percent. In order to encourage the desired level of domestic production, producer prices must be held at double the consumer price in the short run, and at nearly 50 percent more over the long run.

Policy IV: Subsidize Domestic Food Production and Consumption

Policy IV combines farmer incentives adequate to achieve food self-sufficiency with a policy of general consumer subsidies. The increase in consumption induced by the desired price change (for an undifferentiated market) was given in equation III4 above as:


Under the policy of self-sufficiency, domestic production must be adequate both to meet the induced increase in consumption and to replace the supply previously provided by imports:


As before, the price change necessary to induce the required increase in domestic production is calculated from the supply elasticity (equation 2a):


Finally, the budgetary effects and the changes in consumer expenditure, agricultural receipts, and the import bill can be most directly calculated from the financial balance equation expressed in quantity form (equation 3a).


The results of Policy IV, shown in Table 7, highlight the costs of food self-sufficiency. The short-run budgetary cost of replacing the assumed 15 percent of imports (valued at 15 currency units (CUs) at imported prices) is 78 CUs, the difference between the short-run budgetary cost under Policy III (Table 6) and that of Policy IV. Over the long run, this difference is reduced to 23 CUs. Compared to the benchmark free-market alternative, domestic farm receipts would be tripled in the short run and increased by 86 percent over the long run. (Obviously, these costs would be lower with a smaller imported share or a higher elasticity of supply.)

Table 7.

Policy IV: Subsidize Domestic Food Production and Consumption

(No food imports)

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Source: Table 2.

Initial budgetary cost is 0.

Policy V: Subsidize Domestic Production and Consumption of Poor

Policy V is identical to Policy IV except that food subsidies are restricted to the poor with the rich continuing to pay the world market price. The equations describing the policy are identical to that for Policy IV, except that ∆C becomes ∆CA and ∆CF = 0. The results, shown in Table 8, indicate that restricting the food subsidies to the poor reduces the budgetary cost to 91 CUs in the short run and 32 CUs over the long run. This is equivalent to a 45 percent reduction relative to the untargeted case (Policy IV) in the short run and a 52 percent reduction over the long run.

Table 8.

Policy V: Subsidize Domestic Food Production and Consumption of Poor

(No food imports)

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Source: Table 2.

Initial budgetary cost is 0.

Policy VI: Rechannel Food

Policy VI is of particular interest for several reasons. First, it demonstrates that levies on producers to subsidize the poor raise agricultural receipts above the levels that would prevail under a noninterventionist policy. Second, the result demonstrates that when the same levies are used to subsidize higher-income consumers, as they are in many developing countries, producer receipts are reduced. In many developing countries, for instance, consumer subsidies are preferentially allocated to civil servants and the military—two relatively high-income groups. The general conditions for a rechanneling program without government subsidies are as follows:

No change in imports:ΔI=0.VI1
The market is stratified:ΔPFΔPA.VI2
Producer revenue is not decreased (from equations 1a, 3a):ΔPsS+PsΔS+PsS0.VI3
The ratio (R) is a transfer of consumption from the free market to the administered market:ΔCF=ΔCAR.VI4
Government expenditure is to be unaffected by the transfer:ΔG=0.VI5

Substituting equations VI1-VI5 into the financial balance and rearranging yields:


This result states that the subsidy policy can be self-financing as long as the elasticity of demand in the administered market is large relative to that in the free market, and that the ration is not “too” large relative to the initial consumption levels. (Strictly speaking, these results hold only for linear demand curves with elasticity measured at the initial consumption levels. For constant elasticity demand curves, a transfer from the inelastic market to the elastic market will always improve producer revenue.) The result assumes that the government procurement price (for the obligatory levies) is equal to the (subsidized) consumer price in the administered market. Tables 9 and Table 10 demonstrate the results. In Table 9 it is assumed that a 22 percent increase in consumption of the poor takes place at the expense of the consumption of the rich (although the trade-off is far from equal). Table 10 represents the case where the same absolute amount of food is transferred from the administered to the free market. This example illustrates two interesting points. First, as demonstrated theoretically above, producer receipts are improved when food is administratively channeled from the rich to the poor: producer receipts increase, in this case by 1.4 percent. Transferring the same quantity of food administratively from the market for the poor to that for the rich has, as expected, the opposite effect and reduces producer receipts (by 2.3 percent). In addition, the reduction of food availability to the poor increases their prices by one third, while the increase in availability to the rich reduces their prices by 10 percent.

Table 9.

Policy VIa: Rechannel Food—Rich to Poor

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Source: Table 2.
Table 10.

Policy VIb: Rechannel Food—Poor to Rich

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Source: Table 2.

III. Summary and Discussion

This paper has developed a simple calculable partial equilibrium model that explicitly links food subsidies, food imports, domestic producer receipts, and the budget. In addition, the model deals explicitly with the relative effect of different policy changes on two different income classes. Using typical values for the relevant supply and demand elasticities, the model is applied to evaluate six alternative subsidy policies. The coverage of subsidies differs in these policies, as does the extent to which domestic producer prices are protected from the price-depressing effect of a subsidy policy. With the results of this analysis, it is possible to sketch below the evolution of a typical food subsidy crisis (see Table 11). The numerical values reported are based on the policies explored above, the effects of which are derived from the representative initial conditions of Table 2. Obviously, the conditions of particular countries will differ greatly.

Table 11.

Selected Results of Alternative Food Policies

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Note: Data in parentheses are percentage changes from the no-intervention case.Sources: Tables 3-9.

The seeds are sown for future food policy problems when, whether for domestic political reasons or out of genuine humanitarian concern, the authorities move from the free-market situation and adopt Policy I. This policy is intended to reduce the cost of staple foods by 20 percent by increasing official imports that are sold domestically at subsidized prices. If the policy is implemented at a time of relative ease in both the government’s external and internal balances, in the short run, the costs are not exorbitant: although food imports increase substantially (by 141 percent), the budgetary cost is relatively small (6.2 percent of total food value). The effect on domestic production is severe, however. Domestic production falls (by 6 percent) in the short run, and producer receipts are slashed (by 25 percent). As a result of the effect on producer prices, domestic production falls further over the long run (an additional 14 percent), forcing the authorities to make an additional increase in imports (to 220 percent over the original level). The required increase in imports requires additional budgetary outlays, again raising the total subsidy outlay (to over 8 percent of the value of domestic food availability at world market prices).

This policy is sustainable as long as the country’s external position is comfortable. Difficulties arise, however, when the external position deteriorates, whether from adverse developments in export markets, a loss of competitiveness due to the effect of domestic inflation on real exchange rates, or, as happens all too often in countries exporting agricultural goods, the cumulative effect of harmful policies (such as the subsidy and exchange rate policies) on the agricultural sector’s terms of trade (see Schultz (1978)). Typically, the authorities attempt to maintain Policy I for as long as possible, preferring to squeeze other imports rather than face the difficult decision to increase food prices or reduce subsidy coverage.

If the external imbalance worsens, it becomes more difficult to continue to subsidize imports, whether targeted or not. To attempt to relax the foreign exchange constraint by encouraging domestic production through the two-price system of Policy III involves very high budgetary costs. These would be borne precisely when the appropriate budgetary stance should be to reduce domestic absorption. Thus, this policy can only be successful if implemented in tandem with other fiscal measures either to raise the necessary revenue or to reduce other expenditures. To attempt to finance incentives to agricultural producers through increased deficit (bank) financing would, through its inflationary impact, exacerbate the deterioration of the real rate of exchange and lead to a further loss in competitiveness in export industries.

In fact, when faced with severe foreign exchange shortages, governments have often resorted to providing subsidized imported and domestically produced food only to stores open to civil servants and military personnel. The result (Policy VI(b)) is a significant increase (33 percent) in the price of food in the open market and a fall in producer prices (2 percent) below that which would prevail in the absence of government intervention. Such a perverse evolution of subsidy policy, while not inevitable, is all too common. At this stage, the food subsidies can clearly no longer be justified on the basis of their effect on the nutrition of the poor; the program has become an implicit tax on producers and on those unfortunate enough to have to purchase on the free market.

How can the government intervene to make food subsidies a more effective instrument of nutritional policy while reducing their stress on the budget and the balance of payments? Obviously, waiting until the situation has deteriorated to the extent that subsidized food is only available to the rich greatly increases the difficulties of implementing a more humanitarian strategy. Switching early from general subsidies (Policy I) to targeted subsidies (Policy II), on the other hand, would prevent the decline in domestic agricultural production associated with depressed producer prices, and, as a result, greatly reduce the pressures of a food subsidy program on the balance of payments.

One of the most important points demonstrated by this exercise is the extent to which a policy of untargeted subsidized imports (Policy I) is paid for by the agricultural sector rather than the budget. (Budgetary costs increased by 9.6 units over the long run, while domestic farm receipts decreased by 30.6 units.) If subsidized prices are to be maintained, reduced agricultural production due to this loss in incentives forces the authorities to increase food imports much more than originally anticipated. In addition, these higher food imports combine with the government’s commitment to a fixed domestic price of food to create a serious problem of budgetary exposure to vacillations in the price of food imports. Within reasonable budgetary constraints these problems can be avoided only if domestic producers can be insulated from the effect of the food subsidy program. This, in turn, requires that the subsidy be confined to those who would not otherwise purchase; that is, to the poorest classes in the society.


Table 12.

Price Elasticities of Supply in Developing Countries

(By numerical range)

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Sources: Asakari and Cummings (1977); Sobhan (1977). Reproduced from Scandizzo and Bruce (1980).

Long-run elasticity.

Short-run elasticity.

Pre-World War II.

Post-World War II.

Table 13.

Numerical Ranges of Price Elasticities of Food Demand in Developing Countries

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Note: OECD is the Organization for Economic Cooperation and Development; LDC is developing country; DC is developed country; and CPE is centrally planned economy.Source: Reproduced from Scandizzo and Bruce (1980).

Statistically significant at 10 percent level.

Statistically significant at 1 percent level.

Statistically insignificant.

Statistically significant at 30 percent level.


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Robert R. Schneider is an economist in the Government Expenditure Analysis Division of the Fiscal Affairs Department. He holds degrees from the University of Wisconsin, and has taught at Williams College.


See, for example, Schneider (1984), which also deals with ration policy, a topic that cannot be treated in a partial equilibrium framework.


For clarity, this presentation ignores the marketing and processing margin. For actual estimation and calculation, supply and demand prices and elasticities should refer to consumer conditions.


The formulation assumes discrete changes, which account for the third term in each parentheses. In actual calculations derived for policy analysis, changes are likely to be sufficiently large to make the differential form an unacceptable approximation.


These administrative costs are typically small relative to the effective food subsidy. Mateus (1983), for example, reports the administrative costs of Sri Lanka’s (post-1979) food stamp scheme at 1.8 percent of the effective income transfer. The scheme, which eliminated the subsidy to the richest upper half of the population, increased the per capita transfer to the poorest by 30 percent.


Note that the budgetary cost under Policy I is increased with higher price elasticities of supplies and is decreased with lower supply elasticities.