A Dynamic Regional Model of Irrigated Perennial Production
Perennial crop production is inherently dynamic due to several salient physical characteristics including an establishment period of several years with low or no yields, long lives in commercial production (40 years or more), and path-dependence of yields on input use and other exogenous factors, such as weather. While perennial crop production is properly regarded as a dynamic investment, the literature on regional agricultural production is typically static or uses simplified two-stage dynamics, and rarely if ever are the dynamic biophysical elements of perennial crops represented. This paper seeks to address some of the shortcomings of the literature by developing a dynamic regional model of irrigated agriculture with representative perennial and annual crops. The model explicitly accounts for the age composition of perennial stocks including crop establishment period and age-dependent yields and input use. The age composition of perennial stocks provides a parallel to forestry economics and allows us to derive a Faustmann rule for perennial crops. The model is applied to wine grape production in the Riverland region of the Murray-Darling Basin (MDB) in Australia. Over two-thirds of irrigated land in the region is typically planted in perennial crops. During the recent severe drought experienced in the MDB, water allocations to farmers in the Riverland were cut drastically leading to a variety of adaptations by perennial crop producers including changes in irrigation at the intensive and extensive margins. The Australian government has responded to the drought by creating a plan to buy water rights which would then be allocated to an environmental water holder with the express purpose of ensuring the long-term sustainability of river-dependent ecosystems and the economic activity which depends upon them. The fact that the plan calls for the purchase of up to 35% of existing water rights in the Riverland underscores the need for a more robust model of perennial production in order to inform policymakers of the potential effects on the agricultural sector. Given the vast majority of agricultural enterprises in Australia are family-owned, we analyze joint consumption and investment decisions of a utility-maximizing representative agricultural household. Borrowing is allowed but the household faces an interest rate schedule that is increasing in the amount of debt held. We explore the dynamic properties of the model including the existence and uniqueness of a steady state and the conditions required for convergence to the steady state or other periodic solutions. The effects of liquidity constraints and annual crop cultivation on the dynamics of the model are explored as well. Because the state-space required for an age-explicit regional model is too large for conventional dynamic programming methods (i.e., the curse of dimensionality), a running horizon algorithm is used to approximate an infinite horizon dynamic programming solution. We investigate the effects of the age structure of initial perennial plantings. Preliminary findings from the deterministic model suggest that maximizing the net present value of profits from agricultural production with an initial age distribution of grapevine stocks different from those at the steady state levels leads to cycles in area planted by vintage and hence quantity supplied of wine grapes. However, given a CRRA utility function, over very long time horizons the cycles in area planted are shown to be dampened oscillations which eventually converge to a steady state with an equal age distribution analogous to a normal forest in the theoretical forestry literature. Since time to convergence increases with age heterogeneity of the initial land distribution and perennial stocks are path-dependent on irrigation history, stochastic water supplies may imply that convergence will rarely occur in practice. Nevertheless, a steady state perennial age distribution may be useful for the analysis of changes in water policy. The impacts from changes in economic and biophysical characteristics are estimated under both deterministic and stochastic frameworks, the latter of which is based on historical water allocations within the region. Finally, the long-run water demand for perennial crops is identified by systematically running simulations over varying water allocation levels and capturing the farmer’s marginal willingness to pay for more water.
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