Farm-household models, non-separability and basic model assumptions

In the context of peasant economies in developing countries, imperfect market environments are a common phenomenon (Sadoulet & de Janvry 1995, Taylor & Adelman 2003). Generally, farm-households operating in this environment may face imperfect markets for some (though rarely all) of their products or factors of production (Sadoulet & de Janvry 1995, Taylor & Adelman 2003). Common market failures include non-existent land or credit markets, as well as imperfect labour markets (Krusemann 2006, Holden et al. 2005). Under a market failure, the good or the factor that corresponds to that market becomes a non-tradable, the price of which is determined internally within the household, by a so-called shadow price, which serves as the decision price for the household (Sadoulet & de Janvry 1995). Thus the economic decision-making of a household under a market failure is based on shadow prices and not on market prices. When the household’s decision making occurs under a market failure, there is no longer separability between production and consumptions decisions. Both decisions depend upon each other and must be made simultaneously (Sadoulet & de Janvry 1995). This interdependency between consumption and production decisions is called non- separability.

Farming systems and farm-households in lower Okavango River Basin (LORB) are affected by various market imperfections, ranging from lacking finance and insurance markets to high transaction costs, which restrain farm households from market participation. This results in the dominance of subsistence-oriented livelihood strategies, where non-separability can be assumed and where decision-making is more likely to be affected by the levels of shadow prices rather than by levels of market prices. Therefore, a non-separable farm-household model was chosen as the basis for bio-economic modelling in this thesis.

The following paragraphs present a review of (mainly non-separable) farm-household models developed over the last century. This review will afterwards be summarized to present the main assumptions underlying the farm-household model developed within this study:

One of the first attempts of creating a model of non-separable farm-households was made by A.W. Chayanov at the beginning of the 20th century (today only available in English as: Chayanov 1966). He followed basic utility-maximization theory but incorporated two opposing objectives within a farm-households utility function, i.e. income and leisure (Ellis 1988, 106). These goals conflicted as for the generation of income, agricultural work was required which reduced the amount of time available for consuming leisure. To be able to combine both utility maximization from consumer theory and production theory, Chayanov incorporated a production function as a constraint to utility maximization in his model, which depended on varying levels of labour input and market prices of outputs (Hecht 2010). Furthermore, while access to land was assumed to be flexible, labour markets were considered absent, thus leading to a constraint in the time available for production depending on the number of household producers. Chayanov also included a safety-first criterion as an additional constraint, i.e. a minimum level of production which the household had to achieve depending on its size. The incorporation of this variable constraint leads to the phenomenon that in Chayanov’s model, after basic consumption needs have been met, the marginal utility

of additional farm income is relatively low compared to the marginal utility of an additional unit of leisure (Ellis 1988). A last core assumption of Chayanov’s model was that agricultural produce is valued at market prices and either consumed domestically, i.e. within the households, or sold. Chayanov’s model was a powerful tool for analyzing the effect of changes in a farm-households size and composition on a household’s optimal behaviour, also in the African context (Ellis 1988). However, it was weak in predicting a household’s response to changes which affect its production function, e.g. in terms of exogenous variables such as market prices (ibid.). For the sake of this study, the assumption of flexible access to land is unrealistic for the Lower Okavango River Basin. Thus, Chayanov’s basic model may predict the agricultural extensification of farm-households (by relocating farm-household members from tasks such as daily maintenance to farming and by at the same time acquiring new land), but its limited potential to predict changes in cultivation pattern can be seen as an important drawback (see Hecht 2010 for a more detailed review of Chayanov’s model). The next important contribution to farm-household economics was the field of New Home Economics (Becker 196540). Becker (1965) argued that goods themselves are not direct sources of utility. Instead, they are associated with characteristics relevant to a consumer (Ellis 1988). These characteristics cannot be purchased but need to be produced within the household. E.g. via combining the purchased food items with household labour and the energy of an oven to produce a meal, it delivers the desired utility. These products are called Z-Goods. Becker’s (1965) approach was advanced by Barnum & Squire (1979), who developed the full version of the neoclassical farm household model (Sadoulet & de Janvry 1995). This model was then elaborated in a book edited by Singh, Squire, and Strass (1986) (ibid.). In Barnum & Squire’s (1979) basic model, farm-households derive utility from the consumption of four different elements: i) Z-Goods, ii) leisure, iii) own agricultural produce, and iv) market-purchased goods (Barnum & Squire 1979). The strength of New Home Economics is that, by postulating Z-Goods, it allows to apply neoclassical economic theory also on the non-market sector (Low 1986). Also, it is suited to make predictions about household behavior under changing household variables (size or composition) as well as changing market variables (prices, wage rates, technologies) (Ellis 1988). Its weaknesses are neglect of risk and uncertainty (Chen & Dunn 1996) as well as its lower suitability for the analysis of food-deficit households (Low 1986).

In order to make up for the latter (and to be able to analyze rural farm households in Africa) Low (1986) developed an extension of the neoclassical model by combining insights from both New Home Economics and Chayanov (Hecht 2010). He assumed that produced crops can either be considered as consumable Z-Goods or be sold on the market, while farm- households also have the possibility to purchase subsistence goods directly from the market. Another important assumption is that (for food-deficit households) the amount of labour allocated to subsistence production does not depend on farm-gate prices of output but rather on the ratio of wages to the retail price of purchased food (Ellis 1988).

In sum, the early model of Chayanov considered only income and leisure, while Barnum and Squire (1979) extended it to include Z-Goods, leisure and the consumption of both own produced food or market-purchased goods. Low (1986) adapted the latter model to the

40

The important contribution made by Becker (1965) to the analysis of labour within models of farm-households will be presented in more detail in Chapter 2.2.3.

situation of African smallholders (Hecht 2010). In terms of cash income, Chayanov considers only the sale of household production as a potential income source, while Low and New Home Economics also allow for the possibility of engaging in off-farm labour to generate cash (ibid.). All of these models have certain limitations, depending on their basic assumptions. What is shared by all is that utility is aggregated over all household members and the entire agricultural production cycle, thus not taking into account effects such as seasonally limited employment opportunities or different perceptions of utility by different household members (Chen & Dunn 1996). Based on the review of farm household theory, following assumptions will be applied to the farm-household model developed within this study:

1. The utility-function consists of the i) consumption of own agricultural output, ii) the consumption of market-purchased subsistence food and iii) the consumption of leisure. 2. A household has flexible access to land up to a certain point, at which no further land

can be obtained due to a general scarcity of arable land.

3. A market for casual off-farm labour exists; labour can be hired in and hired out. 4. Farm output is either consumed domestically or sold on the local market. 5. Farm-gate prices of food for consumption differ from retail prices.

6. The safety-first criterion is implemented by introducing a minimum food production constraint.

7. The effects of seasonally limited employment opportunities are reflected by dividing each modelled sub-period (year) into two seasons, the dry and the rainy season, for which then different wage rates will be defined as well as a maximum time limit than can be invested in off-farm labour.

8. Due to lack of biophysical data on forest- and rangeland dynamics, livestock keeping and natural resource use are not modelled. Instead, they are included as fixed activities (yielding a fixed annual cash or food income but requiring a fixed annual labour input – see chapter 2.4.2). The model will therefore not simulate the entire household economy, but focus on agricultural production, leisure and casual labour. This simplification is a reason for excluding the Z-Good concept from the utility function. 9. Due to the gradual blurring of division of labour by gender in the research area and the

modelling of casual labour (which, contrary to formal employment, is rarely gender specific in the research area), wage rates do not differ between household members. Instead, household labour is modelled with respect to available producer labour, which is considered to be equal between the genders in terms of productivity and wage. 10. As the focus of this study is on assessing a farm household’s potential to improve its

farming strategy and adopt CA as a new, labour-intensive technology, utility is aggregated over the entire household and intra-household differences are neglected. The innovation of this approach lies in the specific combination of assumptions (e.g. on seasonality and access to land), which follows Börner’s (2006) call for simplification, yet at the same time is expected to allow for assessing optimal farming strategies and technology adoption for non-separable, often food-deficit farm-households in the LORB.