Does Excluding Cross-commodity Interactions Matter? Beef and Lamb in Australia

Australian broadacre agriculture is typified by strong cross-commodity relationships, where sheep and cattle grazing enterprises compete for pasture and both compete with wheat and other crops for land. Further, some commodities produced by multi-product farms are also used in the production of final products that are substitutes in demand, such as beef and lamb. Economic analyses of the beef market, for example, should also include consideration of the market for the related product, lamb. In this paper the effects of exogenous demand and supply shifters on the wholesale-farm price ratio in two closely related industries, beef and lamb, are examined in a Gardner type of model and the effects of excluding consideration of the cross-commodity interactions is measured. Parameter values were chosen based on previous empirical estimates and the judgement of the authors. Due to uncertainty about many of these parameters, a stochastic approach to sensitivity analysis was adopted where an appropriate probability distribution for each of the unknown parameters was chosen and 5,000 values from each of these distributions were drawn to construct estimated frequency distributions of results. It was found that the value for the general equilibrium elasticity of the beef wholesale to farm price ratio with respect to an exogenous demand shift was slightly larger with lamb cross-commodity effects imposed than without. Therefore the inclusion of cross-commodity relationships increases the responsiveness of the beef/cattle price ratio to the demand shift, but only slightly. The results further suggest that the demand and supply cross-price effects are additive rather than counteracting. Therefore incorrectly excluding the cross-commodity effects may result in large errors