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Weekly UpdatesRecent large increases in cereal and other food prices have led many governments to adopt policies intended to mitigate the adverse impact on households, especially on low-income households that allocate a substantial proportion of their total budget to food. From 2000 to mid 2008, the nominal price of wheat increased about threefold, and the prices of corn and rice doubled. Many countries responded with policies aimed at reducing domestic food prices (International Monetary Fund 2008). Exporting countries increased food export taxes or imposed export quotas. Importing countries reduced import tariffs and other taxes or introduced price controls.
Madagascar was faced with such a hike in rice prices in 2004. (1) The world price of rice increased substantially with a 43% increase in the Bangkok dollar price of rice and the Malagasy franc (FMG) experienced rapid depreciation of 58% relative to the dollar. The import parity price of rice thus increased by 113% between January and August 2004. Because rice is an important staple in Madagascar, such price increases can be expected to have a substantial welfare impact on households. These events led to an active policy debate regarding the appropriate policy instrument to use to mitigate their poverty impact, in particular whether the government should decrease the import tariff on rice to bring about a decrease in the domestic price of rice or instead rely on direct transfers to poor households. At the time, rice imports were subject both to an import tariff of 20% and an ad valorem tax of 21% (levied on the import tariff-inclusive price), which together yielded a net tax rate of 45%.
In this article, we set out a simple partial equilibrium framework that captures the efficiency, equity, and revenue implications of such tariff and transfer policy responses. This model is then used to evaluate these two alternative policy responses in the context of Madagascar.
Partial Equilibrium Model
In this section, we present a partial equilibrium model that provides a useful framework to guide our evaluation of the relative welfare effects of tariff reductions and transfers. Although the model has a clear general equilibrium counterpart, the assumptions we make transform it into a partial equilibrium model. (2)
The Model
The model has two agents: households and the government. Rural agricultural households are incorporated into the household sector so that formally there is no need to distinguish between agricultural producers and nonproducers. All other producers in the economy are implicitly assumed to produce using constant returns to scale technology, with producer and factor prices being fixed.
Household welfare is captured by a standard indirect utility function V(p, y), where p is a vector of prices facing the household sector (factor prices are included as negative entries) and y is lump-sum income--later, superscript h will be added to denote specific households. (3) Household lump-sum income is given by
(1) y = [pi](p, c, A) + m
where m is lump-sum transfers to or from the government, and [tau](p, c, A) is a (restricted) profit function given by the solution to
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
subject to a fixed land endowment, A, where q is a vector of agricultural output, c is a vector of input prices, and f is vector of input quantities. Households without land finance consumption out of (fixed) factor incomes.
The government derives revenue from both rice import tariffs and lump-sum taxation of households so that revenue R is given by
(3) R = [t.sub.i][S.sub.i] + T = [t.sub.i]([x.sub.i]-[q.sub.i]) - [summation over (h)]
where subscript i denotes rice and superscript h denotes households, [x.sub.i] = [[summation].sub.h] [h.sup.h.sub.i] is aggregate household demand for rice, [q.sub.i] = [summation.sub.h][q.sup.h.sub.i] is aggregate household production of rice, [s.sub.i] = [x.sub.i] - [q.sub.i] is imports of rice calculated as the difference between aggregate consumption and production of rice in the economy, and [m.sup.h] is the lump-sum transfer to each household (if positive) or lump-sum tax from each household (if negative) so that T = - [[summation].sub.h] [m.sup.h] is net lump-sum taxes and transfers between the government and households. The import tariff per unit of rice is denoted by [t.sub.i] = [p.sub.i] - [p.sup.*.sub.i], where the asterisk denotes border import prices. (4) Note that, with this specification, a unit increase in the rice tariff leads to a unit increase in the domestic price under the assumption that domestic demand and supply decisions do not influence world prices.
Social welfare in the economy is defined, over H households, by a standard Bergson-Samuelson social welfare function:
(4) W = w[[V.sup.1](p, [y.sup.1]), ..., [V.sp.h](p, [y.sup.h]) ..., [V.sup.H] (p, [y.sup.H])].
The effect on social welfare of a (marginal) "reform" of each policy instrument (i.e., tariff [t.sub.i] or transfers [m.sup.h]) is derived by differentiating the social welfare function with respect to that instrument. Each of these reforms will also have revenue implications that need to be incorporated into the overall welfare analysis. In order to avoid having to explicitly identify the social cost of raising an extra unit of government revenue to finance the resulting expenditures, the approach taken here is to focus on "equal-revenue" expenditure reforms. Specifically, we will identify the welfare effect of a tariff reduction that results in a unit decrease in government revenue and compare it with the welfare effect of allocating an extra unit of revenue to a transfer program that delivers transfers to households identified as poor. Under such revenue-neutral comparisons, the social cost of raising an extra unit of revenue to finance these unit expenditures can be assumed common across the alternative policy instruments and thus cancels out in any comparison across reforms. (5)
Rice Tariff Reform
Differentiating the above social welfare function with respect to [t.sub.i], and applying Roy's identity to the indirect utility function and Shepard's lemma to the profit function, gives the effect on social welfare of a marginal change, [dt.sub.i], in the rice tariff as (6)
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[beta].sup.h] is the social valuation of an extra unit of income to household h, typically referred to as the "welfare weight," and [S.sup.h.sub.i] = [x.sup.h.sub.i] - [q.sup.h.sub.i]. The revenue effect of this reform is given by differentiating the revenue in equation (3) with respect to [t.sub.i], which gives
(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[tau].sub.i] is the tariff rate (i.e., the share of the tariff in the market price); [[eta].sup.x.sub.i], [[eta].sup.q.sub.i], and [[eta].sup.s.sub.i] are the price elasticities of aggregate rice demand, aggregate rice production, and rice imports, respectively; and [x.sub.i]/[.sub.i] and [q.sub.i]/[s.sub.i] are the ratios of aggregate demand and production to imports. The term [[tau].sub.i][[eta].sup.s.sub.i] can be interpreted as the marginal deadweight loss associated with a unit increase in the tariff level: the effect on social welfare (ignoring equity concerns so that welfare weights are implicitly unity) is--[s.sub.i], the effect on revenue is [s.sub.i](1 + [[tau].sub.i][[eta].sup.s.sub.i]) SO that the net effect on the economy is [s.sub.i] [[tau].sub.i][[eta].sup.s.sub.i] < 0 because [s.sub.i] > 0, [[eta].sup.s.sub.i] < 0, and [[tau].sub.i] > 0.
Dividing the social welfare effect by the revenue effect gives the social welfare cost of an increase in the tariff sufficient to increase revenue by one unit. This can be derived as
(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[theta].sup.h] = [[summation].sub.h][[beta].sup.h][s.sup.h.sub.i]/[s.sub.i] is the share of the burden borne by household h, and [[eta].sub.R] = (1 + [[tau].sub.i][[eta].sup.s.sub.i]) is the elasticity of revenue with respect to the tariff so that its inverse is the price (or tariff) increase required to increase revenue by one unit. If demand and production do not respond to prices, then [[eta].sup.sub.i] = 0 and the welfare effect arises solely from a redistributional effect. Every unit increase in revenue results in a unit decrease in aggregate household income, and the numerator captures how this burden is distributed across households. The greater the positive correlation between the burden share and household income (or, equivalently between [[beta].sup.h] and [[theta].sup.h]), the higher the share of the burden borne by low-income households, and the greater the decrease in social welfare.
With [[eta].sup.s.sub.i] = 0, the revenue elasticity is unity, implying that a 10% increase in the tax will result in a 10% increase in revenue. However, if [[eta].sup.s.sub.i] < 0, then the revenue elasticity is less than unity and the tax needs to increase by more than 10% to raise an extra 10% in revenue. Therefore, the welfare effect of raising a unit of revenue is greater when [[eta].sup.s.sub.i] < 0, that is, when the revenue base is elastic. This, of course, is the source of the marginal deadweight loss associated with tariff increases; by fixing the revenue requirement, we are simply returning this extra deadweight loss to households via higher tariffs.
Targeted Transfers
The social welfare impact of a transfer program is derived by differentiating the social welfare function with respect to lump-sum transfers from the government, that is, [m.sup.h]:
(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where dm [equivalent to] {[dm.sup.1], ..., [dm.sup.h], ..., [dm.sup.H]} is a vector of the lump-sum transfers to the households, and different transfer programs can be thought of as different vectors of such transfers. The revenue effect of transfers is made up of the sum of transfers plus an adjustment for the additional revenue effects from the resulting increase in rice consumption due to higher household income:
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