such that s = {s<sup>f</sup> , s<sup>m</sup> }. From this starting point, it is possible to incorporate the role played by agents in establishing the decision making environment by writing s<sup>m</sup> as a function of agent activity and an additional set of exogenous factors τ. In particular, consider s0 ∈s<sup>m</sup> ∈s<sup>i</sup> , where s0 = γi0 (am, τ). Note that differences in either τ or agent activity are sufficient to generate differences in technology choices, since, in general, {a<sup>0</sup> , τ<sup>0</sup> } ≠{a<sup>1</sup> , τ<sup>1</sup> } → s<sup>0</sup> ≠s<sup>1</sup> → f<sup>0</sup> ≠f<sup>1</sup> .

Due to the topology we have constructed, elements of τ must either affect the decision environment directly or affect the decision environment indirectly via agent behavior. Therefore, it is possible to express the relationships more concisely since each element of τ is either tied to a household or farm (and therefore an element of s<sup>f</sup> ), or is a factor that conditions agent activity (and is therefore contained in μ). Consequently, it is possible to express a reduced form of the conditioning state variables in a way that identifies those that rely proximately on agent activity and ultimately on the business environment. With this in mind consider the state variable s0 ∈s<sup>f</sup> ∈s<sup>i</sup> , which can be written as s0 = γi0 (am, τ) = γi0 [am(μ), μ, sf] = γi0 (μ, sf).

At the same time, incomplete markets need not preclude all farmers participating in that marketplace from adopting technologies that depend on inputs that the market fails to provide or provides at high cost. In particular, some farmers may be able to rely on their own resources to make up for market shortfalls. In this case, the conditions that permit households to compensate for weak markets can be written as s1 = i f i f m f i γ�1 (s , τ) = γ�1 �s , μ �, where s1 ∈s ∈s .

# <u>Summary and an example</u>

To summarize, the conceptual model states that implemented technologies and the associated set of chosen inputs by households are conditioned by a set of potentially heterogeneous decision environments, which are determined partly by farm and household characteristics and partly by agent activities. Agent activity, in turn, depends on the business environment, which is homogeneous within a given decision environment. This means that the set of locally available technologies can be expressed equivalently as: where the market-independent characteristics of the decision environment, s<sup>f</sup> ε s<sup>i</sup> , are present in conjunction with the business environment μ<sup>m</sup> that conditions agent activity.

To provide an example of how agent activity might influence a decision environment, consider farmgate i i i i prices ρh ≡[p , w ] ∈s where household h participates in marketplace m. Now write the farmgate prices as a function of agent activity and an additional set of exogenous factors, τh, specific to the farm so that ρmh = ρm[am, τmh ]. This relationship need not be complex. For example, it could be that merchants are willing to sell inputs and purchase output at prices ρih based on border prices, ρb ∈μm, plus mark-ups λm(th), based on the cost of transport from the market border to the farm, th ∈τh. For example, in the case where the transport and transaction costs associated with providing fertilizer at the farmgate is a linear function of the distance, d, from the border to a farm in market m, then whm(am, sf) = ρb + λm0 (am)dh, where λm0 is a constant 9