Non-Separable Household Model (Household Production and Consumption Decisions in A Market Failure)

Households in developing countries are systematically exposed to market imperfections and shadow prices play a similar role to market prices in the decision process of the household. When they apply, the shadow prices are equal to marginal utility of the consumption of food and leisure, and marginal productivity of labor. They indicate the price that the household would be willing to pay to have the corresponding constraint relaxed by one unit. Hence, household characteristics in consumption, total time endowment, exogenous cash transfer ( S ), and consumption prices affect production decisions as opposed to the separable household model. Transaction costs should be reduced by the Governmental and non-governmental institutions to narrow the gap between purchasing and selling prices, and increase market participation of households and also increases their gain from changes in price.

as separately or independently maximizing profits as a producer and utility as consumer (Lofgren and Robinson, 1999). Depending on the nature of market imperfections, there may be threshold effect whereby policy changes have no effect on household behavior until the changes is large in some measure. When all markets work, the only linkage between production and consumption is through the level of farm income achieved in production (Sadoulet and Janvry 1995). When not all markets work, there are direct interrelations between production and consumption. In developing and transition economies, the lack of markets, the existence of mixed markets, and the presence of risk are well-accepted problems (Findeiset al., 2003). However, even in developed countries the assumption of separability should be questioned. As an example, labor and hired labor may be far from perfect, and risk exists.

Review on non-separable household models 2.1. Definition of non-separable household models
Household is defined as a person or group of related and unrelated persons who live together in the same dwelling unit or in a connected promises, who acknowledge one adult member as a head of the household, and who have common arrangements for cooking and eating their food (Anonymous, n.d).A household model is said to be nonseparable when the household's decision regarding production (use of inputs, choice of activities, desired production level) are affected by its consumer characteristics (consumption preference, demographic composition, etc) (Thorbecke, 1993). Within households, the non-separability and interdependence between production and consumption decisions is likely to be important. Household makes production, consumption and labor allocation decision that may be interdependent up on one another (Taylor and Adelman, 2002).Household production and consumption decisions are non-separable whenever the shadow prices of at least one production or consumption good is not given exogenously by the market but instead is determined endogenously by the interaction between household demand and supply (Lofgren and Robinson, 1999).

Sources and Uses of Non-Separable Household Model
It is well recognized that, in developing countries context, rural households are systematically exposed to market imperfections (Muller, 2014). Non-separability originates in market failures and in a binding credit constraint, both of which transform the products and factors affected in to non-tradables (Janvryet al., n.d). Farm households are located in an environment characterized by a number of market failures for some of its products (some of food, particularly the most perishable or bulky, or those with high price risk) and for some of its factors (low access to labor market or facing discrimination). Market fails when the cost of a transaction through market exchange creates disutility greater than the utility gain that it produces, with the result that the market is not used for transaction. Non-existence of market is the extreme case of market failures. In more general market may exist but, the gains for a particular household may be below or above the cost, with the result that some household will use while some others are not. PBUY and PSELL are the boundaries of the households' price band.If the household's MC Market may fail for a particular household when it faces wide price margins between the low price at which it could sell a commodity or factor and the high price at which it could buy that product or factor (Sadoulet and Janvry, 1995). Faced with thus price band, the household may be better off choosing self-sufficiency in that good or factors if it is subjective price (defined as the price which equates its demand to supply) falls inside the band (Janvryet al., 1991). If the shadow price is above price band, the household should buy the commodity until the shadow price that equates supply and residual. (supply curve) crosses its demand curve within the price band, the household doesn't participate in the market. Because, it is more advantageous to the household to neither buy nor sell commodities. If the household's MC (supply curve) crosses its demand curve above the price band, the household is a net purchaser until the shadow price that equates supply and residual demand for home production fails to purchase price. If the household's MC (supply curve) crosses its demand curve below the price band, the household should sell the commodity until the shadow price that equates residual supply after sell of a marketed surplus, and demand rises to the sale price. According to (Sadoulet and Janvry, 1995), the magnitude of price band may be increased by; High transaction costs, Shallow local market(in a good season household could have a marketed surplus and when there is a drought household's supply fails) and price risk and risk aversion (the greater the level of price risk and the greater aversion to risk, the wider the effective price band and market failure).

Model specification
According to Sadoulet, (2006) the model can specified as; Consider a household producing two crops, a cash crop ( !" ) and a food crop ( #" ) with two inputs, labor ( $" ) and other inputs such as fertilizers ( %" ). The production technology is represented by &[ #, !, %, $; ' ( ] where outputs ( !, and #, > 0) and inputs ( %, and $, > 0), ' ( is fixed factors in production and producer characteristics. On the consumption side, household consumes food () #, ), a manufactured good () *" ), leisure () $ ) which is the complement in total time of its labor supply. It may also has total time endowment (+) and exogenous cash transfer (-). There is farm get sale price of cash crops (. ! ) and farm gate purchase prices of other inputs (. %, and. * ) which are provided by the market. The household is assumed to maximize a utility function subject to a cash income constraint for the commodities tradable on the market, a technology constraint and equilibrium conditions for tradables and non-tradables.
considered). The model questions how household respond to 10% increase in price of cash crops, manufactured goods and productivity of food crops (technological change) respectively and the result is depicted on the table (1). When there are no market failures at all, the household increases factor use and shifts its resources from food, with a 5.4% decline in production, to cash crops which increases by 9.9% (Sadoulet and Janvry, 1999). As real income increases, more food, manufactured goods, and leisure are consumed. Since both home time and labor used in the production rise, the hiring of outside labor increases by 6.1% to fill the deficit. And since less food is produced while more is consumed, demand for food on the market increases by 7.9%. When both the markets fail, by contrast, the elasticity of supply response of cash crops drops from 0.99 to 0.18, showing very little response (Janvryet al., 1991). This is due an inability to reduce food production by any significant amount, since the family needs to feed itself while income rises, with only some substitution in consumption between food and the manufactured good, and an inability to use more labor in production since the consumption of leisure rises slightly as income improves. Output response mainly comes from increased use of fertilizer. On the consumption side, the reward to household is increased consumption of manufactured goods. When the labor market fails but the food market is used, the shock can be exported on the food market. The household responds by shifting out of food production and buying food instead, as demonstrated by an elasticity of cash crop production of 0.93. This allows an increase in food consumption, but without corresponding increase in leisure, since the family needs to produce a labor effort. When it is only the food market fails, response in cash crops is enhanced as revealed by an elasticity of 0.55, by hiring labor from outside. This allows an increase of consumption of leisure, but not that of food, which declines slightly as resources are shifted to cash crops. Note: the sign (-) indicates that no changes relative to base value Source; Janvry, Fafchamps and Sadoulet, 1999

CONCLUSION
Under perfect market conditions all products and factors are tradable and opportunity cost of any product or factor held by household is its market price. Under this condition, separability holds, and the producer side of the model can be solved prior to consumer (worker) side, with farm profits serving as the hinge between the two problems.
Ownership of the variable factors is irrelevant for production decisions and affects consumption decisions only through income level, which is its self determined by ownership. This separation, however, is often less clear-cut for agricultural households in lower income countries. The household may be the locus for both consumption and production. Farm household cannot be viewed as separately or independently maximizing profits as a producer and utility as consumer. Households in developing countries are systematically exposed to market imperfections and shadow prices play a similar role to market prices in the decision process of the household. When they apply, the shadow prices are equal to marginal utility of the consumption of food and leisure, and marginal productivity of labor. They indicate the price that the household would be willing to pay to have the corresponding constraint relaxed by one unit. Hence, household characteristics in consumption, total time endowment, exogenous cash transfer ( ), and consumption prices affect production decisions as opposed to the separable household model.

RECOMMENDATION
Depending on the review undertaken the following recommendation has been given; ü Transaction costs should be reduced to narrow the gap between purchasing and selling prices, and increase market participation of households. ü Enhancing infrastructural and institutional facilities such as market information and road are necessary to reduce market failures and increase farmers gain from their product. ü Enhancing of multi-purpose agricultural cooperatives to reduce the number of middle men involved in the market and increase farmers gain from the market.