Climate change, mitigation and adaptation: the case of the Murray–Darling Basin in Australia

Mallawaarachchi, and Quiggin (2007). The model simulates the allocation of
land and water to agricultural activities as the result of constrained optimization
by representative farmers in each catchment in the Basin, as well as flows of
water for urban use and residual ‘environmental flows’ in the main stream and a
number of sensitive ‘icon’ sites.

The model captures uncertainty in the availability of water inflow to the system
using the theory of state-contingent production developed by Chambers and
Quiggin (2000). Each activity produces a bundle of state-contingent outputs, one
for each state of nature. An activity may produce net profits in some states of
nature, and net losses in others.¹

The idea that multiple state-contingent activities may be available for the
production of a single commodity is what distinguishes the approach put forward
here from most previous simulation models that incorporate uncertainty. The
standard approach has been to introduce stochastic variation into the outputs of
each commodity. This approach allows producers to manage risk by varying their
allocation of land between commodities, in the same way as investors can
diversify portfolios.

Dichotomous choices can also be modelled using the tools of discrete stochastic
programming (Cocks 1968). Important applications of discrete stochastic
programming to Australian agriculture include Brown and Drynan (1986),
Kingwell (1994) and Kingwell, Pannell and Robinson (1993).

The approach adopted here, using the notion of state-contingent commodities,
does not require the introduction of explicit stochastic elements, and permits the
derivation of standard outputs of programming models such as shadow prices,
which have a direct economic interpretation. More generally, as discussed in

¹ Egan and Hammer (1996) determined that, in dryland production systems, between 70 and 80
per cent of total income over a ten year period is earned in the best three years and a net loss is
made in another three.

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