Peasant supply response in rationed economies

World Developmenr, Vol. IS, No. 4, pp. 431-439, Printed in Great Britain.

Peasant

1987. 0

Supply Response

in Rationed

0305-7.50x/87 1987 Pergamon

$3.00 + 0.00 Journals Ltd.

Economies

D. L. BEVAN*, A. BIGSTEN, P. COLLIER Institute of Economics and Statistics, Oxford University, U.K. and J. W. GUNNING Free University, Amsterdam

Summary. When peasants do not have reliable access to goods on the black market, government price controls may result in rationing of peasants’ demand for consumer goods. We show that supply response is then perverse and that the economy may collapse, as exports fall and rural shortages intensify. Such a crisis may initially be disguised as peasants sell export goods to build up money stocks. We consider the policy options for governments facing such problems.

1. INTRODUCTION In many developing countries, have engineered a deterioration

governments

in the terms of trade faced by peasant farmers, for example by imposing taxes on export crops. Much theoretical and empirical research has been devoted to analyzing how peasant supply would respond if this deterioration were reversed, and the consensus is that supply would respond positively.’ These analyses usually assume, at least implicitly, that peasants trade on markets which clear. In practice, there are often problems of availability, both of imports and of consumer goods. This paper considers the implications of such problems, and extends the usual analysis to cover them. It shows that supply response may well be perverse in these circumstances, even when it is positively related to price in the case where markets clear. While the sources of market failure in developing countries are manifold, those which stem from policies, and which are in principle reversible, are of particular interest. For example, many governments impose price controls on consumer goods. Usually, these controls cannot be widely enforced so that a black market coexists with the official market. While consumers are unable to purchase all they wish in the official market, on the black market prices rise to their market-clearing level. In these circumstances, it might appear that the only consequence of price controls is to make income transfers to consumers, and that a market-clearing analysis remains adequate. This 431

would only be true, however, if all peasants traded actively on the black market, and that is most unlikely to hold for two reasons. First, the coexistence of official and black markets faces the peasant with a kinked budget line. Individual equilibrium may take place on either facet (or the cusp, of course); there is certainly nothing to guarantee that all peasants will enter the black market. Some will be priced out of the market, given that they can obtain a rationed supply on the official market. They would like to purchase more at official prices, but they do not choose to purchase more at black market prices. We may describe these peasants as fully rationed, in contrast to those partially rationed peasants who are rationed on the official market but make purchases on the black market. Second, in some countries peasants do not have reliable access to goods on the black market. This may arise because the government succeeds in suppressing it or because transport bottlenecks make supplies sporadic. For this reason as well, some peasants will be fully rationed in the goods market. Overall supply response will depend on the supply response of these fully rationed peasants as well as on that of the partially rationed ones. For clarity, and because the market-clearing case is well understood, we consider an economy in which all *All of the authors are affiliated with the Unit for the Study of African Economies at the Institute of Economics and Statistics at Oxford University. The research was supported by World Bank research project RPO 672-65.

432

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DEVELOPMENT

peasants are fully rationed. This may be thought of as a polar case, in contrast with the polar case where no peasant IS rationed. Elsewhere we model the supply response of partially rationed peasants.’ Using a simple model we show, first, that peasant supply response to changes in crop prices will be radically different in such an economy. Second, we show that such an economy is liable to collapse into an implosive crisis of falling export revenue and intensified shortages.’ Third, we show that such a crisis may initially be disguised, as the onset of shortages can cause a honeymoon period during which peasants sell crops in order to build up money stocks. Finally, we outline some of the policy options open to governments faced by such problems. Although in this paper we have deliberately avoided describing any particular country, the issues raised are of current policy concern. Because of the tendency of such economies to implode into crisis, they are prominent among the countries currently involved in IMF stabilization programs. Yet the IMF, in requiring a common set of policy adjustments, is failing to recognize that behavior in non-market-clearing regimes is fundamentally different from that in the neighborhood of a market-clearing equilibrium. Policies which may be appropriate for the latter can be perverse for the former.J Elsewhere (Bevan et ul., l%%), we have applied the analysis specifically to Tanzania. In Section 2 we discuss the impact upon peasants of shortages of consumer goods; in Section 3 we formalize the argument. The macroeconomic consequences are discussed in Section 4, and the policy implications in Section 5. 2. PEASANT CHOICES SHORTAGES

UNDER

For the following analysis we characterize peasants as producing food and cash crops and consuming goods, food and leisure. However, we assume that peasants produce food for own consumption only. In these circumstances nothing is lost by neglecting the choice between leisure and work on food production and focusing only on the choice between time spent on leisure and food combined (which we describe as leisure) and time spent on cash crop production. Consider first, the simple case of a barter economy in which the cash crop is exchanged directly for consumer goods. In the absence of price controls consumer goods will be fully available and peasants will optimize by choosing to work on their cash crop up to the point at

which the disutility of the last hour of work equals the utility derived from the goods purchased with that work. However, once controlinduced shortages are introduced, the peasant cannot purchase all the goods he wishes to buy. He will therefore choose to do only enough work on the cash crop to pay for the goods which he expects to be available since further production would be wasted effort, yielding no additional consumption. In this situation, an increase in the price of the cash crop will reduce cash crop output unless it coincides with an increased availability of consumer goods. With constant availability (and hence expenditure), the peasant will wish to maintain constant his crop income, so an increase in the price of the cash crop will induce a proportionate reduction in supply. Thus, the supply elasticity is minus unity regardless of its value in the absence of shortages. While supply response to price is perverse, an increase in the availability of consumer goods at a given cash crop price will induce a corresponding increase in cash crop production, since peasants wish to buy more goods in exchange for crops than is possible at prevailing prices. This simple analysis of perverse response to price and positive response to increased availability is complicated once we move from a barter economy to one in which goods can only be purchased for money. Peasants no longer face significant opportunities to barter, and given that their transactions are monetary their supply response to changes in both prices and goods availability may be perverse. To simplify, suppose that peasants receive cash from their crop sales at the close of the harvest, consume goods evenly throughout the year, and hold money balances only to finance this consumption. Hence, when goods are fully available, the maximum money stock held by the peasant (which he has upon being paid for his crop) is equal to his planned annual expenditure. When the availability of goods is limited the money stock which the peasant chooses to hold depends critically upon the form of the rationing regime. When there is a known ration, future expenditure is also known so the desired maximum money stock is equal to this (reduced) annual expenditure. However, in many present-day price control systems, the rationing is a matter of chance: although shortage is the norm, a household may sometimes strike lucky, in which event its ability to purchase goods is determined by the money stock held. This has important consequences for the relation between goods availability and the money stock held. If the household knew the

PEASANT

SUPPLY

RESPONSE

amount available for certain this relation would be proportional. Since the household cannot buy as much as it wants it will always want to hold just enough money to buy the maximum amount available, hence money stocks will decline if rationing becomes more severe. If, however, availability is uncertain (and the household has limited access to credit) there is a second effect working in the opposite direction. If the household were to hold a money stock sufficient to buy the mean quantity available it would for lack of money not be able to profit from above average availability. Hence it may want to hold a larger money stock to reduce the probability of being constrained. The strength of this effect depends on the utility of leisure (since money can be accumulated only by working more), on the riskiness of availability and on the household’s aversion to risk. 3. A SIMPLE

u = U(L,, G,) + where

G, = the purchased commodity L, = labor on the cash crop. The allocation of remaining labor between subsistence crop production and leisure is not studied in the model since it has no monetary implications. If the commodity market is unrationed then in equilibrium the household optimizes by choosing G* such that

ii$=

-

G*

=

L

=

L*,

(4)

With prices unchanged, the quantity of the consumer good is now reduced and informally rationed so that the expected level of purchases is less than the desired level: &CR) < G* where

CR

(5) = the quantity of consumer goods purchased under the rationing regime. = the conditional mathematical expectation of the term in brackets.

In any particular period the actual purchases of goods may differ from the long run average E(GR). However, we will assume that the good is storable and that should the household have a run of bad luck such that its stocks fall to zero, it is able to borrow from other households (as long as its consumption does not exceed the sustainable level E(GR)), an amount which it returns once its stocks are positive. With this assum P tion, consumption in each period equals E(G ). This has implications for labor input and the marginal utilities of goods and leisure as depicted in Figure 1. Since the budget constraint will still bind, income will equal expected expenditure, so that: E(GR) = L = LR where LR = optimal labor input under the rationing regime. Hence, the marginal utility of goods is greater, and the marginal disutility of labor is smaller than in the unrationed equilibrium. That is:

au

ait

acR>aC*

(1 + r);

433

(where * denotes unrationed equilibrium values). In (3) and subsequently, time subscripts are omitted since we restrict attention to stationary values. The budget constraint requires that income should equal expenditure, so

E( )

(1)

ECONOMIES

M* = G*.

MODEL OF THE DECISION PROBLEM

In this section we present a simple model of the peasant household which formalizes the discussion of Section 2. To keep the model as simple as possible, the peasant household is assumed to produce the cash crop as a function of labor input subject to constant returns. One unit of the crop is produced by one unit of labor and is paid for, one period in arrears. The price of a unit of the crop is the same as the price of a unit of the purchased commodity. We suppose that utility is intertemporally additive, with instantaneous utility at time t given by:

au

IN RATIONED

-au aP

and -

-au av’

< -

(7)

,

where r is the rate of interest, and enters (2) because of the delay in payment. The demand for money in this unrationed equilibrium will be set equal to expenditure, the simplest possible form:

The net benefit of a permanent one unit increase in the ration, E(GR), is therefore the discounted sum of the extra utility from one more unit of the good per period minus the extra labor needed to pay for it:

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434

DEVELOPMENT

Figure

dW -= acK

au -au +l(l+r)'dr acR aLR ( >

7 t=O

-au au

1 ZYr

(

dGR $2

>

(9)

and G 6 G” (the availability

constraint).

(10)

G” denotes the quantity of goods available. In the barter case considered above, the ration G” was identical to GA, but because of the double constraint it is now possible for CR to be less than GA. Which constraint is encountered depends on the level of the money stock and the distribution of availability F(GA). Since goods consumption is below its desired level it is never rational to choose not to make a purchase of available goods if money is available. Thus, one of the constraints (9) and (10) must always bind, so that either G = GA or

G = M.

(11)

(12)

This creates a critical connection between the money stock held and the average value of goods consumption. E(@)

where W = the discounted sum of utility. The utility of money in such a regime derives from the unpredictable access to goods. The access to goods depends upon the type of rationing regime encountered. When there is no formal rationing system at the household level availability is likely to be uncertain. The household cannot purchase more than is available and cannot purchase more than it can pay for. Purchases are therefore subject to the double constraint: G 9 M (the money stock constraint)

1.

=

7

G‘“.fT(G”)dG‘”

0

+ M.p(G”)dG”

(13)

Equation (13) states that expected purchases are the sum of two terms. The second term is the probability that the individual will be subject to the money stock constraint multiplied by the average purchase when this constraint binds, which is of course the money stock itself. The first term is most easily thought of, analogously, as the probability that the individual will be subject to the availability constraint multiplied by the average purchase when this constraint binds. Since the availability constraint can only bind when purchases are less than the money stock, average purchases must be less in this case. Hence, goods consumption is either equal to the money stock (if the money stock is the constraint) or less than the money stock (if goods availability is the constraint) so that expected goods consumption, E(GR) is less than M. For all types of distribution, F(G”), the first order derivative of E(G’) with respect to the money stock is positive and the second order derivative is negative. Unfortunately, the RHS of (13) includes a censored distribution which is likely to lack analytically tractable properties. Recall that since all prices are normalized, dM/dL = unity and from (6) aLRIdE = unity. The cost of an increment in the money

PEASANT

SUPPLY

RESPONSE

stock is therefore the marginal disutility of labor, and for the money stock to be in a long-run equilibrium, this marginal cost must equal the marginal benefit. The latter is equal to the change in goods purchases times the benefit from an increment in goods purchases. previously derived in (8). Hence, the equilibrium money stock, MR. will satisfy:

pg(.&+g)].

G =;

(14)

MR.

This indicates that (I priori MR upon the utility function, and specify a simple instantaneous additivelv < senarable in L and . third order derivatives are set

au -=

2 M* depending F(G”). We will utility function, G in which both to zero Thus:

aL

(lb)

au ,,=B-YG.

(17)

aL

and

From

(2), in unrationed

equilibrium,

P

M* = G* =

(18)

a+y+ar From

(14) ar

dE( G’) -= dM

PIE(G’)

and from

- y- a

(13)

dE( GR) = dM

7 F( G”)dGA M

so in rationed

-

(20)

equilibrium

ar

fVE(G’)

(19)

y -a

=

7 F(GA)dGA.

M

(21)

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ECONOMIES

Finally. a(aE(GR)l

M)

dM

(22)

= -F(M).

The geometric representation of the solution (19), (20) and (13) is shown in Figure 2. When

Now consider how the optimal money stock changes in the long run if there is a change from a permanently unrationed to a permanently rationed commodity market. From (3). (5) and (13): M’ = G* > E(G”) <

IN RATIONED

E(GR)

= G” = M*. dE(G’)ldM

of

= 1,

and the solution is traced out by the broken line. By contrast, a rationed equilibrium is traced out by the dotted line. Equation (19) defines the curve in the northeast quadrant; inspection of the equation shows that the curve is convex. The southeast quadrant simply contains a 45” line, rotating the E(GR) axis. The curve in the southwest quadrant is defined by equation (13) relating expected purchases in the rationed regime to the money holding: evidently expected purchases in the rationed regime always fall short of G*. Finally, the curve in the northwest quadrant is defined by equation (20), i.e., by the cumulative distribution of purchasing possibilities. As drawn in Figure 2, the rationed money stock is greater than the unrationed money stock, but clearly a different distribution of purchasing possibilities could yield the converse case. Indeed, for a sufficiently severe ration (when schedule (20) is twisted far enough anti-clockwise around the vertical intercept) the money stock will be lower than when goods are unrationed. However, computations using credible values and distributions suggest that the onset of rationing may well be characterized by an increase in the desired money stock. These changes in the money stock matter because they imply changes in cash crop output. If the peasant chooses to increase his money stock then he is choosing to sell more crops than is required to finance his expected expenditure on goods. Conversely, a reduction in money stocks can only be effected by selling fewer crops than would be required to cover expenditure. The effects of a change in goods availability on crop sales must therefore be separated into two time periods: the short-run response during which peasants are adjusting their money stocks to the new desired level, and the long-run response which remains once money holdings are fully adjusted. The short- and long-run responses may either reinforce or offset each other. If availability deteriorates so that in the long run crop sales are reduced, in the short run this is at least partly offset by peasants selling crops in order to accumulate money balances. In the short run, in response to a deterioration in availability,

436

WORLD DEVELOPMENT

Figure

crop sales may therefore not change markedly. However, further deterioration induces a reduction in money stocks so that the short-run reduction in cash crop production is then more pronounced than the long run. Conversely, if starting at restricted availability full availability is restored, peasants find themselves with a windfall of excess money balances to be spent. If they discount future consumption at a high rate this excess money will rapidly be spent, partly by consuming more goods and partly by doing less work on cash crop production. Thus, the short-run effect of an improvement in the availability of goods can be a reduction in cash crop production.

4. MACROECONOMIC RATIONING

EFFECTS

OF

So far we have focused upon the cash crop production of the peasant as determined by some unexplained level of goods availability. We now allow for the fact that. in aggregate, since cash crop production is typically a major component of exports, it determines foreign exchange earnings. Hence, it determines the ability to import both consumer goods and the inputs needed to produce such goods locally. Thus, depending

2

upon the system which allocates consumer goods between peasants and other groups in the economy (typically the urban sector), the availability of consumer goods to peasants is indirectly determined by the level of cash crop production as well as directly determining it as discussed previously. If a reduction in crop sales worsens availability, this will in turn further reduce crop sales. This is illustrated in Figure 3. Cash crops are treated as being synonymous with exports, their volume being measured along the vertical axis, and that of imports along the horizontal axis. The world price of the export crop is given and equal to the slope AHIOA, so that the foreign offer curve is represented by the line through 0 and H. The relation between the amount of the cash crop farmers produce and their consumption of imports in the absence of rationing is the concave function through 0, B and I, the peasants’ offer curve. Along this curve the domestic price of the cash crop varies. If, e.g., the producer price were equal to ABIOA, then peasants would choose point B on the offer curve. They would then produce a quantity OA of the cash crop, which would be exported in exchange for a volume AH of imports, of which peasants would consume AB so that the quantity BH would be available for the urban sector. Note that the domestic price is lower than the world

F

E

0

Consumer goods Figure 3. Rutioning of peasants and its macroeconomic

price, the difference BHIOA representing the rate at which the cash crop is implicitly taxed. The macroeconomic effects of price controls depend upon the government’s export crop taxation policy. We will assume the government to be predatory on the peasant sector, using its revenue from crop taxation to reward client groups such as urban wage earners who receive priority claims on consumer goods at official prices. In Figure 3 this exogenous claim is set equal to DH. Its effect on rural availability may be represented in the diagram by a shift OE to the left in the foreign offer curve. The allocation of imports to urban areas can exceed this minimum level, but a lower allocation is not politically feasible. Now suppose that this urban claim increases from DH to MH, e.g., because the government embarks upon an import-intensive investment program. If the producer price remains unchanged then farmers will initially continue to produce a quantity OA of coffee, but now, after deduction of the urban claim, only AM of imports is available for rural consumption. Hence peasants are rationed: they cannot realize their intended consumption AB. When peasants realize that availability is reduced, they will react by producing less cash crops such that their income is only sufficient to sustain available purchases. This implies a move along the ray OB in the direction of the origin. If, for example, they expected availability to be permanently reduced to M, then they would choose point L. This implies a cumulative contraction. The economy gets caught in a downward spiral: cash crop production decreases, exports fall, less can be imported,

consequences

farmers are more severely rationed, they revise their expectation of GR downwards and produce even less. This process does not converge; it stops once farmers move beyond point J. Cash crop output would then be less than OG and the urban claim can no longer be honored. The government then has to give up its policy, either by changing the producer price or by reducing the urban claim on imports. Once peasants are rationed, normative statements about crop prices to producers cannot be made unambiguously. The price may be too high in the sense that for given rural availability of imported consumer goods, peasants would produce more if the price were lowered. At the same time the producer price may be too low in the sense that it would have to be increased (along with rural availability) if the “optimum” is to be reached. The ambiguity of statements of the appropriateness of the level of the producer price in the case of rationing is illustrated by point J. As long as rural availability does not change, the producer price at J is too high: if the price were lower cash crop production would increase until the farmers’ offer curve would be reached at the unrationed equilibrium point N. On the other hand, reaching the “optimum” I requires a producer price which is higher than at N and, indeed, higher than at J. Therefore, whether the producer price at J can be called too high or too low depends on the extent, if any, to which price changes are accompanied by changes in availability. So far we have discussed the possibility of a cumulative contraction in crop output implicitly in terms of certainty. When rationing is a matter of chance, our earlier discussion on optimum

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DEVELOPMENT

money holdings suggests that this process of implosion can be divided into two phases. In the first phase, as availability deteriorates desired money holdings rise so peasants temporarily sell more crops than when their money stocks are at their chosen levels. Hence, although the rationing point presents an unstable equilibrium the decline in output will initially be damped. However, once availability deteriorates to the point at which peasants choose to reduce their money stocks the long-run tendency to implosive output reductions is accelerated by short-run monetary dishoarding. Hence, once a price controlled economy stumbles into a regime of shortages which peasants expect to be sustained, output is subject to initially creeping but eventually rapid cumulative decline.

5. POLICY

IMPLICATIONS

Since a rationed peasant economy is subject to a cumulative retreat into subsistence production, any policy initiative must re-establish marketclearing conditions. This can be achieved either by increasing the availability of consumer goods to peasants or by reducing the price paid to peasants. However, the latter policy is dangerous because, while it is true that in a rationed peasant economy a small reduction in crop prices will increase output, a larger price decrease can have the opposite effect. For example, if the initial situation was point K in Figure 3 then a reduction in the producer price from ACIOA to ABIOA would raise exports (as the economy moved from K to L) and, after some delay, this would be reflected in a reduction in rural shortages. Further price reductions shift point L upward until it reaches the offer curve. This represents a critical price level, for if the price is reduced even further then the rationing constraint not longer binds. Peasants would be in unrationed equilibrium at a point on their offer curve which slides down as prices are reduced. Hence, beyond the critical price, price reductions lower export volumes. Since this critical price cannot in practice be known, reductions in crop prices are a dangerous way of attempting to escape from rationing. The alternative requires an improvement in goods availability to peasants. Either this is financed externally (through aid) or it requires a redistribution from government expenditure and urban workers. If aid is not available, then the domestic options, in requiring a politically powerful group to suffer losses while a weak group experiences gains, involve policy changes likely to be resisted ri outrance. Further, we have

seen that an improvement in availability to peasants, though a necessary condition for a regime switch, will by itself generally not in the short run induce a corresponding increase in marketed output, and may even reduce output despite a massive increase in imports as peasants run down money balances. The precondition both for a powerfully positive short-run supply response to improved availability and for the avoidance of this foreign exchange burden is that peasant households should wish to increase their cash balances at the same time as they encounter improved availability. Only with this conjunction is the long-run availability effect on supply reinforced by the short-run cash balance effect. This requires that the monetary overhang be tackled or sterilized. There are a number of ways of achieving this, but they can be grouped into devices offering something in exchange for the excess balances and devices that default on them. The difficulties associated with devices in the first category make these impractical. The problem is to find a good or asset with two attributes: peasants must want it, and the economy must be capable of supplying it without using foreign exchange or other scarce inputs. The latter consideration rules out currently produced goods, leaving only financial assets (government bonds) and pre-existing real assets. However, it is not clear that peasants would voluntarily exchange cash for bonds and even if they did, this would merely defer the problem. There appears to be no practical alternative therefore to a device involving some measure of default. Two devices in the latter category are inflation and currency reconstruction. The price level can be increased either by increasing the permitted markup on costs (which in the limit removes price controls), or by increasing costs through devaluation (or indirect taxation). A currency reconstruction might involve the exchange of new currency for old with limits on per capita encashment and has two advantages over an increase in prices. First, it would fall disproportionately upon those with large cash balances, and second, it is perhaps less likely to induce expectations of subsequent defaults than is an increase in prices to induce expectations of subsequent inflation. Thus, the rationale for foreign aid is not to bribe a recalcitrant government into making needed reforms but to avoid the need for policy changes which should be reversed once the economy is in unrationed equilibrium. Crop prices, urban living standards and government expenditure may well be unsustainably high in a rationed environment and yet be potentially sustainable or even too low in unrationed equi-

PEASANT

SUPPLY

RESPONSE

librium. Clearly, if the terms of trade are unchanged from that level at which the economy was driven into rationing then the initial configuration was unsustainable and public expenditure, for example, would need some permanent reduction. However, the permanent reduction required cannot be inferred from that level which would be viable in a rationed environment. In conclusion, the notion that agricultural price reforms alone can readily eliminate macroeconomic crises in shortage-prone economies is probably too simplistic. Even if the original cause

IN RATIONED

ECONOMIES

439

of difficulties is excessive crop taxation, the macroeconomic repercussions of this taxation cannot be undone simply by raising crop prices. A necessary antecedent to agricultural price reform is to eliminate shortages in the peasant economy, and this requires a temporary increase in, or diversion of, foreign exchange. The temporary diversion of foreign exchange to the peasant sector, for example as a result of the elimination of controls on consumer prices, may be both politically difficult and economically disruptive, so that there is a powerful case for program-related aid financing of policy reform.

NOTES 1. For normal

a survey of peasant supply case, see Helleiner (1975).

2. See Bevan et al. (forthcoming) an application to Tanzania. 3. Our analysis

derives

response

in the

for the theory

and for

from the new fix-price

economics (1977).

literature.

See,

for

example,

Malinvaud

4. This point is not taken into account in the large literature critical of IMF recommendations; see, for example. Killick (1984) and Williamson (1983).

macro-

REFERENCES Bevan, D. L., A. B&ten, P. Collier, and J. W. Gunning, East African Lessons on Economic Liberalisation (London: Trade Policy Research Centre, 1986). Bevan, D. L., P. Collier, and J. W. Gunning with A. Biesten and P. Horsnell. The Economic Consequences of Trade Shocks (Oxford: Oxford University Press, forthcoming). Helleiner, G. K., “Smallholder decision making,” in

L. G. Reynolds (Ed.) Agriculture in Development Theory (New Haven: Yale University, 1975). Killick, T. (Ed.), The Quest for Economic Stabilisation (London: Heinemann Educational Books, 1984). Malinvaud, E., The Theory of Unemployment Reconsidered (Oxford: Basil Blackwell, 1977). Williamson, J. (Ed.), IMFConditionality (Washington, DC: Institute of International Economics, 1983).