available technologies to implement.<sup>8</sup> As mentioned, farmers face a variety of circumstances, which, taken together, shape their respective livelihood strategies. Because their individual decisions about how to farm are based on what technology best suits their individual needs and capacities, they collectively implement a heterogeneous set of applied technologies. Differences in farms and farmers generate some differences in the set of decision environments; however, differences in agent activity matter as well. This is because agent activity affects the set of goods and services available as inputs and, consequently, the set of locally feasible technologies from which farmers must choose. Agent activity influences input prices as well, and thereby also influences the choice of applied technology from any given set of available technologies.<sup>9</sup> More formally, let Φ(s) = maxx pf(x, s) −wx characterize the full set of optimization problems faced by a given population of farmers conditional on a set of locally available convex technologies, F(x, s) ⊂F(x, Ω), where F(x, Ω) is the set of all invented technologies, where the set Ω contains all possible combinations of (non-choice) state factors, and where s ∈Ω, is the vector of local state variables that conditions farmers’ choices about which applied technology, f(x, s) ∈F(x, s) ∈F(x, Ω) to employ. Relevant local state variables include input prices and output prices, w, p ∈s. Standard input demand curves and the supply curve can be recovered from the solution via the envelope theorem, such that ∂Φ⁄∂w = −x<sup>∗</sup> (y, s), and ∂Φ⁄∂p = f(x<sup>∗</sup> , s) = y<sup>∗</sup> , where y<sup>∗</sup> ≥0, and x<sup>∗</sup> ≥0 are the solutions to the conditional profit maximization problem.

If, in an applied setting, the decision environment is homogeneous for a given study population, then the expected set of input and output levels {y<sup>∗</sup> , x<sup>∗</sup> } and the chosen applied technology, f(x<sup>∗</sup> ) are the same for all farms, since all farmers face the same optimization problem and arrive at the same optimal solution. Otherwise, the state-variables of the general function Φ(s<sup>i</sup> ) should be scripted to denote the different states, or decision environments, relevant to a particular choice; the same is true for outcomes resulting from that choice, {y<sup>∗</sup> (s<sup>i</sup> ), x<sup>∗</sup> (y<sup>∗</sup> , s<sup>i</sup> )} ≡{y<sup>i</sup> , x<sup>i</sup> }.<sup>10</sup>

- <u>Agent activity, household self sufficiency and heterogeneity in the decision environment</u>

Except in trivial cases, agents in a given market are expected to offer goods and services across multiple decision environments. This is because some elements of s<sup>i</sup> , for example farm soil quality, do not depend on current agent activity. Consequently, heterogeneity in farm and household characteristics will generate heterogeneity in the decision environment within a homogeneous business environment. In contrast, households that participate in different markets and are therefore presented with a different set of options for input goods and services automatically face a different set of state variables.

With this in mind, partition the relevant state variables into those that are independent of currentperiod agent activity, s<sup>f</sup> , and those that depend on current-period agent activity in a given marketplace, s<sup>m</sup> ,

> 8 Mundlak, Butzer and Larson (2012) discuss the implications for panel data.

> 9 For example, Melitz and Ottaviano (2008) discuss how changes in trade policy can induce firm productivity gains through competition.

> 10 This applies to both primal and dual representations. Consequently, it is not a trivial matter to move from one representation to the other in an applied setting when some state variables can go unobserved (Mundlak 1996).

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