to differentiate in a cross-year setting. They may be competing against or reconciling with each
other, which, neither of which is observable.
The CES-EU results are comparable to the MA-EU results in that they both share the
same risk aversion. Interestingly, these two models yield nearly the same optimal hedge ratios.
We have further checked with other risk aversion values including α= -2 and α= 0.5, and get
similar results. The comparison gives the impression that these two models work very similarly
in modeling the optimization behavior for the decision maker’s risk management. This result
indicates that although the GEU does not include the popular additive EU models for risk
averters, its CES-EU component is equivalent. So, GEU is perhaps more general than it appears.
As a very special case of the GEU model, the MR-EU model applies to a farmer who is
risk neutral and has perfect intertemporal substitutability in consumption. Consistent with these
preferences, the optimal hedging ratio is zero for each year, reinforcing that the decision maker
does not care about risks and has no specific concerns regarding consumption across years.
Optimal choices for the representative farmer in Grant County are very similar to
Whitman County. The farmer prefers slightly less hedging than the Whitman farmer but still
buys the same coverage of crop insurance. Although the production is riskier in Grant County
because yield is a bit more stochastic, there is no huge gap between the yield levels as shown in
the historical data (Figure 2.1). Also we assume farmers in both counties face the same prices, so
they are exposed to the same price risks. The hedge ratios are very close to those in Whitman
County under the same preference set.
In summary, the comparisons between the four models for Whitman County and Grant
County in Washington State show that the GEU model is feasible by yielding reasonable results
on optimal risk management portfolios. For a farm planning on multi-period management, GEU
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