Taxation and government revenue at micro level

Abstract

A common aspect is that higher tax-rates can increase supply elasticity; but nevertheless it may diminish the consumption of commodities which can result in smaller revenue to the government. The trade literature has shown empirically, the existence of a revenue-maximizing tariff. In this paper we shall show mathematically that, gradually increasing tax will attain a level at which the revenue function is at a maximum and beyond this level the revenue via taxation diminishes. For an analytical treatment, we set up a dynamic micro market model, in the usual notation, and we assume that for a single commodity with a price adjustment mechanism, the demand function and the supply function with taxation take the form <formula> and <formula> Here a,b,c,d are positive parameters;T is the tax-rate and j (>O) is the adjustment speed of P(t) .

Thus, the time path of the price function takes the form <formula> ; where <formula> , <formula> and <formula> . Noting that the Intertemporal Equilibrium is dynamically stable, the following results are obtained via algebraic techniques:

The selling price rises by <formula> , the consumption falls by <formula> and the government revenue is given by <formula> which is a quadratic function of T, representing a parabolic path for <formula> over T. Moreover,

(i) <formula> , provided that the demand curve is steeper than the supply curve; (ii) <formula> . Revenue maximizing tariff exists when <formula> (normal range) and the government revenue <formula>, taking the maximum at the end value of the normal range. Hence, we conclude that a relatively smaller portion of the levy can pass on to the consumer if the demand elasticity exceeds the supply elasticity, while the government revenue achieves a maximum.