Functions with Linear Price Elasticity for Forecasting Demand and Supply

Abstract

AbstractIn theoretical demand and supply analyses, functions with constant price elasticity are still frequently used although price elasticity is known to change in response to price. We relax the assumption of constant price elasticity to linear price elasticity which allows us to model demand and supply that decreases or increases with price. Quantity functions with linear price elasticity have been used in economics before but only to a limited extent since they have not been sufficiently theoretically studied. This paper overcomes this gap by identifying and studying all possible functional forms with linear price elasticity as well as their inverses, actually plotted as demand and supply curves. We find that quantity (demanded or supplied) as a function of price with linear price elasticity is a product of an exponential and a power function of price, while the price as a function of quantity involves the Lambert W function. Hence, the class of functions with linear price elasticity is heterogeneous: it contains reversible and irreversible functional forms as well as convex and non-convex functional forms. The class’ heterogeneity provides several modelling and research opportunities.