Famine: a simple general equilibrium model.

1. Introduction

Famine, according to Thomas Malthus (1798), 'seems to be the last, the most dreadful resource of nature', that restores demographic equilibrium after the arithmetic advance of the means of subsistence is overwhelmed by the geometric explosion of population. Such a perspective enervates relief policy, a point illustrated by the essentially negative approach to relief of the British administrators of India in the nineteenth century, well versed as they were in Malthusian theory (Ambirajan, 1976). Given that population expansion is held to be responsible for the decline in per capita food supply, the provision of relief can almost be viewed as prolonging the misery.(1)

The relationship between distress and decline in per capita food supply, referred to as the Food Availability Decline (FAD) doctrine, is far from being the sole preserve of Malthusians. The power of the approach is founded on intuition, even if the economic mechanism is not elaborated. FAD was dramatically challenged by Sen's (1981) seminal work; famines have occurred without a significant fall in the local supplies of food. The distinctive characteristic of famines has been that they represented a collapse of the entitlements, the command over food, of major sections of the population due to adverse price movements as well as endowment losses. Each agent has a bundle of endowments - seed, labour, and livestock, for instance, that by market exchange and production can be converted into a bundle of food. When this leaves the agent with insufficient food to survive he or she falls into the starvation set.

Does the adoption of the entitlement approach change the evaluation of policies to counter famine? The typical implementation of entitlement analysis divides the population into groups defined by particular endowments and then relates aggregate outcomes to average group endowments and the food price ratios that pertain. So if we are dealing with fishermen, we take the average fish output and multiply it by the fish-food price ratio. If this falls short of the subsistence level then the group is clearly at risk (see Locke and Ahmadi-Esfahani, 1993, for example). What policy recommendations flow from such an analysis?

Before attempting to answer this, several points are worth noting. The approach outlined ignores Sen's (1981) own warning that 'this drastically simple modelling of reality makes sense only in helping us to focus on some important parameters of famine analysis; it does not compete with the more general structure' we have briefly outlined above. In particular, what determines the price ratios that play such a crucial role? Secondly, 'Strategies of Entitlement Protection', the title of a chapter in the major (1989) book by Dreze and Sen, covers the principal policy instruments available together with issues relating to their implementation. However, the discussion of the issues would elicit no objection from a FAD adherent. This fits in with Osmani's (1995) position that entitlement analysis constitutes an approach, rather than an hypothesis, and so encompasses the FAD doctrine as a special case. But surely one would anticipate that an analytic advance would have more definite consequences for policy evaluation?

This paper investigates whether the entitlement approach can support a relatively general ranking of policies, in particular relief works and food distribution, to protect entitlements. In order to compare their economic impact, a general rather than a partial equilibrium approach has to be adopted. What then are the markets that are essential to include to make the model insightful while avoiding the technical distraction of generality (a rigorous general equilibrium approach to famine is developed by Coles and Hammond, 1995)?(2) At the very least the food and labour markets demand inclusion; the central price ratio is the food wage, that is, the quantity of food that the wage will purchase. If this affords subsistence, then how is there distress? If it does not, then who accepts it?

The peasant, the most common victim of famine, combines the role of producer and consumer and so we have to move beyond exchange.(3) Now the time dimension of production is fundamental since current endowments will frequently be the result of past production decisions; to allow for this we assume that the agent's decisions are influenced not only by current consumption but also the anticipated level of endowment in the next period, which is taken as a proxy for future consumption.

This does not have the sophistication of Glomm and Palumbo's (1993) study of how the threat of starvation can influence the optimal pattern of intertemporal consumption. However the relationship between time and consumption we seek to explain is a simple though vital one and is captured by the following account of the famine in Darfur: 'In Furawiya, one woman described how she had harvested just enough millet to provide seed for the next year. She had buried it, mixed with sand and gravel to prevent her children digging it up and eating it, and then gone south for the dry season. In June she returned, dug it up and planted it' (de Waal, 1989, p.149). Clearly the level of future endowment was a crucial consideration for this woman and its inclusion into the utility function employed in the model below seems entirely reasonable.

The final market we include is the one for land services. While it does not play the central role of the other two markets, any change in the food wage will have major repercussions for the optimal technique of production, which in turn will affect the demand for labour and consequently the level of distress. Land is assumed to be owned by a class of landlords who sell its services in a competitive market. The three markets examined in this paper operate within the framework of a poor and predominantly agrarian economy. It is poor in several senses: firstly, securing subsistence is a major challenge for a large proportion of the population; secondly; the lack of a capital market constrains an agent to use his own resources at each time period - he cannot borrow today and pay back tomorrow. The agrarian character justifies the two period framework adopted in this paper, reflecting the agricultural cycle.

The basic story behind our model can be briefly outlined; the cycle begins with agents endowed with the output from the previous period; this can be consumed or used to produce the next period's endowment by paying rent for land and, if the agent is wealthy, hiring labour from poorer agents; such wages provide their recipients with the income to purchase food in the current period. The model is spelt out in the following section.

The most direct trigger of famine in this simple model is loss of endowment. The crucial market is that for labour where the loss results in a wage rate below that which can support subsistence. To survive, those who supply labour must supplement earnings from their endowments; those with insufficient assets starve. The process is examined in Section 3.

Given that the famine wage rate is below subsistence, one avenue for policy is to intervene in the labour market to raise the wage and for public works to soak up the excess supply. Alternatively endowments may be increased (even across the board) so that the resulting wage rate may ensure that no one starves. These policies are analysed and contrasted in Section 4 which is followed by our conclusions.

2. The model

In this section the basic model is outlined and the 'normal' case, that is when there is no acute distress, is discussed. This provides the background against which the consequences of a shock to the system can be clearly delineated.

Given the importance of subsistence in a poor economy, we assume that the only commodity produced is rice. In period 0 each agent, i, possesses an endowment of rice, [Mathematical Expression Omitted]. To be physically capable of supplying a unit of labour, at least [c.sup.*] amount of rice must be consumed.(4) The market wage w is a piece rate and so amounts to the return for completing a series of specified tasks such as cultivating a particular acreage of rice. The precise mechanism that secures this need not concern us - the point is that efficiency wage issues are not relevant.

The alternative to participating in the labour market is to work [l.sub.i]([less than or equal to] 1) on the domestic holding and thereby secure an endowment of rice in the next period. Labour, [l.sub.i], together with [k.sub.i] acres of land produces [Mathematical Expression Omitted] rice in the next period via a simple Cobb-Douglas production function

[Mathematical Expression Omitted] (1) …