Much previous work on agricultural stabilization has emphasized price stabilization. Stabilization is given a different meaning here. Additive error terms are attached to linear supply and demand functions, and the effects on consumers' and producers' surpluses of reducing these error terms are studied. That is, the error terms are assumed to have their variances reduced, and the expected values of the surpluses are derived and compared with their expected values corresponding to the original error term variances. The results are not favourable, and suggest that, with the particular criterion used here, stabilization of supply and demand functions is not as desirable as generally believed. Further results, allowing for shifts in the functions and the introduction of risk aversion are less unequivocal, and require empirical knowledge for conclusions to be reached.