**_EpPqq_** _+_ **_IpJqjP =Z_** _p qS +_ **_Ipqff_** _f_ **_i_** _f_

# 5. Cash constraint

Say that a household maximizes their utility (given here by a simple Cobb-Douglas function of the goods which they consume) subject to a set of constraints. The first constraint is the production technology which they have (given above by a simple CobbDouglas function of the primary factors); the next two constraints are simple commodity balances - the quantity of any commodity produced plus the amount purchased must equal the amount consumed plus the amount used as inputs and that sold - similarly the total endowment of a factor which the household may have plus that which is purchased (e.g. labour hired in) must be equal to that used in production and that sold; finally, the household is subject to a cash constraint so that its total purchases of commodities and factors cannot exceed the value of its sales of commodities and factors.<sup>20</sup> Given a set of exogenous purchase and sales prices for commodities and factors (if necessary unit prices from the household survey may be used), households will choose how to allocate their factors between different activities in order to maximize their incomes, consumption and utility. The model requires a small set of parameters (the ai, _ai,_ and i, for each commodity i and factorj) which can either be taken from existing studies or estimated from the data. It is therefore possible in principle to construct a "household level" SAM for each household in the dataset and to estimate the impact of a price shock on household behaviour for each household separately.

Table 6 gives an example of a simple stylized household SAM. This household undertakes two activities -subsistence crop production and cash crop production. These activities use labour, land and capital as well as fertliser. These activities "sell" their output to the commodity accounts (SUB-C and CASH-C) respectively. In addition the commodity accounts "import" some of the subsistence crop from the "Rest of the World" (recall that this is a Household level SAM so that the Rest of the World (ROW) here simply means all other households; "imports" in this context are simply purchases from outside the household) as well as fertliser and non-food commodity. The household also sells their output of the cash crop to the ROW - their cash constraint means that the value of their imports (subsistence crop, fertiliser and non-food) must match the value of their exports (cash crop). The household's endowment of labour, capital and land "pays" the household account which then spends its income on food and non-food.

In a practical example the household may have many more activities and there will be many more commodities. In addition, if the data allows, factors of production can be broken down (e.g. by gender, age, experience, education etc). The model may also allow some factors to be tradable (e.g. labour) whilst others may not be (e.g. land). More significantly, the determination of whether a commodity or factor is tradeable can be endogenous. Our model allowed the possibility of differences in the purchase and selling

> 20 For simplicity we have set up the commodity and factor balance constraints and the cash constraints as equalities - it is possible to specify them as inequalities so that not all factors or commodities have to be used.

20