Intertemporal Risk Management Decisions of Farmers under Preference, Market, and Policy Dynamics

Moreover, the standard multi-period recursive EU (MR-EU) preference is obtained
when we further imposeα=ρ=1. As indicated in equation (3), when the utility function is
defined as a linear combination of current and future consumption levels, the optimization of
MR-EU becomes a decision maker maximizing the summarized discounted expected
consumption over a lifetime (finite or infinite time periods).

Here C_t+i denotes consumption for thei^thperiod in the future. With risk preferenceα= 1 , the
decision maker is risk neutral. The additive specification due to ρ= 1 implicitly assumes
preferences are homogeneous (perfectly substitutable) over time; each one of them carries the
same weight when discounted to the current period. Such additivity is now well known to be too
restrictive (Weil, 1990). Decision makers may have a clear preference for early resolution of risk
compared to late resolution of risk (Kreps and Porteus, 1978).

Application of GEU to Farmers’ Intertemporal Decisions in the PNW

When applying the GEU framework to our optimization problem, current consumption
is further defined as net income from the farmer’s wheat production and risk management. The
farmer uses futures contract, yield insurance, and government programs to construct risk
management portfolios. Hedge ratios and insurance coverage ratios are endogenous choice
variables to be determined at the optimum, based on information available at t-1:
(4)         Ct = NCt + CIt + FIt + GIt

where NC_t = P_tY_t PCt,

FIt = Xt-ι[Ft — Et-ι(Ft)]-TCt,

CIt = Pb max[0, zt-1 E t-1 (Yt) - Yt] - Pret

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