THE IMPLICATIONS OF DECREASING BLOCK PRICING FOR INDIVIDUAL DEMAND FUNCTIONS: AN EMPIRICAL APPROACH

Abstract

Decreasing block pricing refers to the practice of selling a product at successively lower marginal prices as the amount purchased in any one time period increases. In more familiar terms, this practice can be thought of as any quantity discount scheme as long as marginal price does not vary continuously with quantity. Decreasing block pricing results in a faceted, non-convex budget set, and under standard assumptions concerning consumer preferences, yields several nonstandard theoretical implications. The central goal of this paper is to formulate an estimation technique which is consistent with these implications. When the budget set is not convex, the uniqueness of consumer equilibrium is no longer guaranteed. It also follows that discontinuities in demand occur whenever consumer equilibrium shifts from one facet of the budget constraint to another. Prior empirical studies have not made use of demand functions consistent with these results. In Chapter 2, a utility-maximizing algorithm was developed to determine consumer equilibrium given the declining block pricing schedule and income for a Cobb-Douglas utility function. In developing this algorithm, it was made clear that the proper approach for estimating individual demand was through the use of a block-dependent independent variable. The coefficient of this block-department independent variable provided an estimate of a utility function parameter which completely specified the Cobb-Douglas form. Incorporating this utility function estimate into the utility-maximation algorithm made it possible to obtain estimates of consumption given changes in any or all of the rate schedule components. While the use of a block-dependent independent variable is the theoretically correct method for estimating demand, it poses an inescapable problem of errors-in-variables. A Monte Carlo study was performed in Chapter 2 to investigate, among other things, the seriousness of the errors-in-variables bias. The results were quite encouraging. When using data incorporating extremely large error variances, amazingly precise estimates were obtained. Another encouraging Monte Carlo result was when comparing samples not containing a discontinuity with those with one, it was found that the latter produced estimates with statistically significant superiority. Chapter 3 generalized the estimation technique of the previous chapter to allow the estimation of demand using cross-sectional data. The data base recorded monthly electricity consumption for households from a number of cities whose utilities had decreasing block rates. Seven of these cities were selected for analysis. The data also included various demographic characteristics and electric appliance stock information. The generalization was accomplished by assuming that all households had a Stone-Geary utility function. Also, the utility function parameter representing the minimum required quantity of electricity was assumed to depend linearly on the household's appliance stock and demographic characteristics. This allowed demand to vary across households on the basis of this parameter and income. The results of applying this regression technique to the cross-sectional data were then compared with results from a conventional, non-theoretically based demand specification. The data were used in pooled and individual month form with the former yielding much better statistical results. The Stone-Geary form provided a greater number of significant coefficients for price and income variables than the conventional version. The predominant failure of the conventional version was that the coefficient of marginal price was rarely significant and when significant, frequently of the wrong sign. For the same samples, the Stone-Geary results were quite acceptable except for the regressions involving one of the cities. Thus, it was demonstrated that a method consistent with the theoretical implications of decreasing block pricing is easily applied to cross-sectional data and produces better results than conventional techniques.