Three Sides of Harberger Triangles

Prevailing economic wisdom is highly critical of injudicious tax policies or government regulations, uncorrected externalities, unchecked monopolistic practices, and various other market failures.When economists are challenged to quantify the economic costs of associated price distortions, it is standard practice --and has been since the 1960s --to use a small number of assumptions and selected elasticities to estimate areas of the relevant "Harberger triangles."This simple and straightforward exercise has numerous applications and the virtue of producing answers rather than conjectures.Harberger triangles come in many shapes and sizes.Figure 1 offers an illustration of such a triangle for the simple case of an excise tax.Point A of Figure 1, at which the demand and supply schedules intersect, denotes market equilibrium in the absence of the tax, with quantity q 1 transacted at price p 1 .Introduction of an excise tax at rate J, payable by firms selling the commodity, shifts the supply schedule upward by J.At the new market equilibrium, firms sell q 2 units of the commodity at a market price of p 2 , receiving (after tax) p 3 = (p 2 -J).Market equilibrium at point A in Figure 1 has the feature that marginal consumption benefits equal marginal production costs.The excise tax drives a wedge between marginal benefits and marginal costs.At consumption level q 2 , consumers are willing to pay any amount up to p 2 for additional units of the good, and suppliers would readily provide additional units of the good for any price of p 3 or greater --but these additional transactions do not take place, due to the effect of the tax wedge.The loss associated with the foregone transaction of a single unit at q 2 is: p 2 -p 3 = J.Summing differences between the prices that consumers would pay, and the prices at which suppliers would provide goods, for all units between q 2 and q 1 , indicates the welfare loss due to the excise tax, and is represented by the shaded "Harberger triangle" in Figure 1.In this case, the height of the Harberger triangle is the tax rate, its base is the amount by which sales fall in reaction to the tax, and its area is one measure of the efficiency cost, or "deadweight loss," or "excess burden," associated with the excise tax. 1 These papers and others are reprinted, together with interpretive notes, in Harberger (1974).2 Harberger triangles, now common fare, were once rare delicacies.In two influential papers published in 1964, Arnold C. Harberger (1964a) offered a clear and persuasive derivation of the triangle method of analyzing deadweight loss, and (1964b) applied the method to estimate deadweight losses due to income taxes in the United States.Having earlier used the triangle method to calculate the size of monopoly-induced distortion in the U.S. economy (1954), corporate income taxes (1959a), and various and sundry distortions to the Chilean economy (1959b), Harberger shortly thereafter (1966) produced estimates of the welfare cost of U.S. capital taxes.In a subsequent survey, Harberger (1971) clarified various aspects of this method and addressed a number of its perceived shortcomings.1 While the theory of deadweight loss measurement was well established by the 1950s, economists very rarely estimated deadweight losses prior to the appearance of Harberger's work.Harberger's papers illustrated the techniques, the usefulness, and the realistic possibility of performing such calculations, and in so doing, ushered in a new generation of applied normative work.Deadweight loss triangles became known as "Harberger triangles" due to the broad influence of Harberger's papers on subsequent research.The new deadweight loss estimates, in turn, led to an important reevaluation of the welfare effects of multiple distortions in an economy, and consideration of the possibility that various market failures may transform Harberger triangles into even larger trapezoids.This essay examines Harberger triangles from three sides.The first is the place of the Harberger triangle in the historical development of the theory of consumer surplus and its use in evaluating the costs of economic distortions.The second is the theoretical controversy evoked by applications of Harberger triangles.And the third is the impact of Harberger triangles on subsequent empirical work and theories of market imperfections.

2The economics profession has Alfred Marshall to thank for putting quantity on the abscissa and price on the ordinate of supply-and-demand diagrams such as Figure 1, and, through his influence, institutionalizing this arrangement.Writing 46 years before Marshall, Dupuit used the more mathematically compelling alternative of price on the abscissa and quantity on the ordinate.