Consumer Utility Function: Initial Findings Through Lagrange Optimization Method

Abstract

The main problem in utility theory or its variant theory of consumer choice is that consumer is assumed capable of rational choice; yet, such choice is incapable of translating itself into rational numbers. On this account the assumption of rational choice remains dubious. This paper utilized Lagrange optimization method to approximate consumer utility function measured in cardinal units. The utility function was derived from the US deflated annual per capita consumption of pork and beef (United States department of Agriculture, USDA, 1998). This paper demonstrates that when quantities of pork are consumed, given the price, in effect gives diminishing marginal levels of pork consumption in opposite monotonic direction with beef consumption. Changes in the level of consumption approximate cardinally the consumer utility function consistent with the properties of indifference curve and with the axioms of consumer rational choice. This paper has two objectives: 1) to provide further insights on the measurability of consumer utility, and 2) to provide basis for forecasting the demand for pork and beef. This paper concluded that Pork-beef substitution of US consumers is an exponential function which exhibits pattern of the textbook-defined indifference curve and has the features of negative slope, convexity and asymptote. The function is also consistent with the axioms of consumer rational choice. Keywords - consumer utility function, lagrange optimization method