The implications of market imperfections on productivity have been studied in different parts of the world (de Janvry et al., 1991; Barrett, 1996; Udry, 1996; Heltberg, 1998; Holden et al., 2001). Holden et al., (2001), in their study carried out in villages of the Ethiopian highlands, found that land and labour market imperfections affected productivity. However, they did not find a significant inverse farm size-productivity relationship, and they attributed this to the small variation in farm sizes in the study area. Such variation is likely to be smaller in areas
where land redistributions have been used more recently to balance the relation between farm sizes and household sizes. In their study area such redistribution had taken place very recently. In our study area, the last redistribution was before 1979. Since then, only new households were receiving land from PA’s common land and mainly from their parents through inheritance.
In many developing countries, markets for land may be thin or non-existent. For example, land in Ethiopia is state property and cannot be sold. This may contribute to the failure of farm households to adjust their own holdings to their family labour (Heltberg, 1998).
Alternatively, farm households may engage into land renting. However, land rental markets are also subject to imperfections due to sharecropping arrangements or interlinked markets (Kassie and Holden, 2007) and tenure insecurity (Alemu, 1999). Land rental markets that operate through share tenancy do not clear like ordinary markets, as the price mechanism does not function like in ordinary markets. Several studies have revealed high transaction costs in land rental markets in Ethiopia (Ghebru and Holden in press; Deininger et al., in press).
Labour market imperfections are due to either imperfect information in labour search that may lead to misallocation of labour, moral hazard related to hired labour (labour activities are complex and difficult to monitor), seasonality in demand for labour in rain-fed agriculture or limited off-farm employment opportunities (Binswanger and Rosenzweig, 1986). While small farmers rely mainly on family labour, relatively larger farmers may depend on hired labour that may face moral hazard problems. Whenever there is no off-farm employment opportunity and an alternative source of income for the family members to meet subsistence needs, smallholders have no choice but use the entire workforce in operating their farm, regardless of efficiency.
Consider a simple household model where the household has the following utility function:
(
, eU U Y L=
)
(4)where, refers to income from crop production after variable costs, it is restricted form of profit; is leisure.
Y Le
The production function from where Yis derived is simply an extension of the yield function in equation (2):
(
, , x, pi, npi, z, k)
Q Q A L O O O= H H (5)
Subject to cash constraint for purchased inputs: Opi =Opi
(
FI NFI Cr, ,)
where Q is quantity produced, A is fixed land, Lis labour input, is oxen (traction power), is other purchased farm inputs and is a function of credit (Cr), farm (FI) and non-farm (NFI) income. is other non-purchased farm inputs, refer to fixed household and farm characteristics, respectively.
Ox
Opi
Onpi Hz Hk
We assume a well behaved production function: i Q 0, 0
Q Q
i ii
=∂ > <
∂ . We assume imperfect substitutability between the inputs and diminishing returns to variable input. Assuming missing land and labour markets and credit market imperfections, Ydepends on land, labour input (L), output prices (pq), and prices of purchased inputs ( px):
(
q, , , x)
Y Y p A L p= (6)
Subject to labour constraint:
L L+ e=T
Now, the household’s utility maximization problem can be expressed as:
( )
By solving the first-order conditions (FOCs) from the utility maximization, we find the point where the marginal value product of labour equals the shadow wage rate (ω∗)2.q
How is the shadow wage affected by the endowments of land and family time? Consider two households with the same family labour endowment but different farm sizes. Large farms have a lower marginal utility of income or a higher marginal utility of leisure for the same amount of family labour endowment while small farms have the opposite. Figure 2 indicates that the household with a smaller farm reaches the point where marginal value product of labour equals the shadow wage rate (ω∗) at a lower level of shadow wage/marginal value product. This implies that households with small farms allocate more family labour on farm and thus have higher output per unit of land. There is a positive marginal return to labour as long as they work more per unit of land and provided that land quality is the same.
The use of purchased inputs is also credit constrained. The FOC for the purchased inputs is:
2 Marginal utility of leisure divided by the marginal utility of income gives a shadow wage rate.
(
, ,)
0Equation (9) indicates that the household will intensify using purchased inputs when the marginal value product of the input is equal to its marginal cost (unit price). The left side of the last term shows, however, the use of purchased input is dependent on credit availability or liquidity constraints.