IN THIS PAPER a non-additive dynamically varying version of the Stone-Geary utility function is proposed. Dynamic demand functions are derived by maximizing this utility function subject to an expenditure constraint. Habit formation by the consumer is taken into account. The demand functions obtained are ,estimated for each of the four meat types consumed in South Africa, viz. beef, mutton, pork and chicken. Analysis of the results indicates that in order to estimate the demand for meat in South Africa, it is necessary to utilize consumption data broken down according to population group. The standard double-log demand model for meat consumption in South Africa is of the form where i = 1, ..., 4 corresponds to beef, mutton, pork and chicken respectively; ci is the annual per capita consumption of meat type i (kg); k i is a constant; p i is the deflated annual weighted average retail price of all cuts of meat type i (rands per kg); e ij is the elasticity of demand for meat of type i with respect to the price of meat of type j; l is the deflated annual per capita income (rands); b i is the income elasticity for meat of type i.To avoid multicollinearity and autocorrelation in such a model, sophisticated econometric techniques are required. Unfortunately, results achieved to date by various researchers (Broom, 1964;Hancock, 1983), who have attempted this estimation, have not been entirely satisfactory. In particular, certain of the elasticities obtained have incorrect signs. More important, neither Broom nor Hancock was able to obtain reliable estimates for the demand function for mutton. The assumption that the various elasticities are constant over an extended period of time probably accounts for this failure. There have been substantial changes, however, in the consumption patterns of meat over the past three decades. The per capita consumption of beef has declined from 35,5 kg in 1948/50 to 22,3 kg in 1980/81, a drop of 37 per cent on the 1948/49 consumption.
SAJE v54(2) p208Pork and mutton have shown similar trends, with consumption falling by 22 per cent and 35 per cent respectively. The consumption of chicken, on the other hand, has increased by a dramatic 458 per cent (Abstract of Agricultural Statistics, 1983). Such large shifts in consumption must surely be accompanied by significant changes in the demand functions. Consumers have become accustomed to higher levels of consumption of chicken, and have grown to accept lower levels of consumption of beef and mutton. The market for meat at the beginning of this period differed from that for the end of the period. Just as the markets for meat in the USA and Australia display different characteristics, as measured by elasticities, it can be expected that the respective elasticities for the demand for meat in South Africa today should be different from what they were three decades ago. Hancock (1983) detected that a change in the demand functions had indeed taken place.A dynamic model appears to be called for. The alternative to using some modification of an ad ho...