Price elasticity of demand always increases with price
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Reference literature and economic theory demonstrate that price elasticity of demand does not always increase with price, noting that straight-line demand curves show decreasing elasticity as prices drop and that alternative models allow elasticity to move in either direction.
Abstract In 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.
Along a straight-line demand curve the percentage change, thus elasticity, changes continuously as the scale changes, while the slope, the estimated regression coefficient, remains constant. Going back to the demand for gasoline. A change in price from $3.00 to $3.50 was a 16 percent increase in price. If the beginning price were $5.00 then the same 50¢ increase would be only a 10 percent increase generating a different elasticity. Every straight-line demand curve has a range of elasticities starting at the top left, high prices, with large elasticity numbers, elastic demand, and decreasing as one goes down the demand curve, inelastic demand. In order to provide a meaningful estimate of the elasticity of demand the convention is to estimate the elasticity at the point of means. Remember that all OLS regression lines will go through the point of means. At this point is the greatest weight of the data used to estimate the coefficient. The formula to estimate an elasticity when an OLS demand curve has been estimated becomes:
Where and are the mean values of these data used to estimate , the price coefficient.
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