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

where U_t (∙) is the von-Neumann Morgenstern utility function indexed by time t ; E_t is the
expectation operator at current period t; the “~” above U indicates the stochastic property of
utility. β(0 < β< 1) is the discount factor per period and implicitly defines the decision maker’s
time preference. By consuming att + 1, he/she only consumes a fraction (β) of the utility that
would have been consumed att. α(0 ≠ α< 1 ) denotes the risk aversion parameter, and is equal
to one minus the Arrow-Pratt constant relative risk aversion (CRRA) coefficient. A smallerα
indicates greater risk aversion. ρ(0 ≠ ρ< 1 ) denotes the intertemporal substitutability, equal
to(1 -σ)^-1 withσdenoting the elasticity of substitution. Early (late) resolution of risk would be
preferred ifα< (>)ρ . C_t denotes the current consumption which is a function of the risky
variables and the risk management choice variables. The decision maker’s objective function is
to maximize current utility, which comprehensively incorporates all of the lifetime expected
future utilities.

The recursive GEU specification enables a separation of risk aversion from
intertemporal substitution and the non-additive intertemporal preference relations. This feature is
not usually shared by the EU specification. However, the GEU form nests the EU form as a
special case. The recursive CES EU (CES-EU) preferences, widely used in finance,
macroeconomics and intertemporal consumption analysis, are obtained when we impose the
parametric restrictionα= ρ .

1

(2)                         Max U   {( 1-β)Cα + β[E, (¾ )]}^α       (CES-EU)

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