# Lecture Note 6.19.pdf - Economics 230a Fall 2019 Lecture...

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Economics 230a, Fall 2019 Lecture Note 6: Basic Tax Incidence Tax incidence refers to where the burden of taxation actually falls, as distinguished from who has the legal liability to pay taxes. As with deadweight loss, it is a concept for which the intuition is clear, but for which actual measurement requires the specification of a precise conceptual experiment. It is not enough simply to ask, “What is the incidence of a tax on good x?” We must specify what is done with the revenue, because that will affect incidence, not just through its direct effect on well-being but also through influences on equilibrium product and factor prices. To illustrate the concept of incidence, consider a small tax introduced in some competitive market, in which the initial price is p0and the initial quantity x0. We introduce a tax, which reduces output, increases the consumer price q,and reduces the producer price p, in the manner shown below. For simplicity, we will assume that the revenue is spent by the government in the same manner that the consumer would spend it. Thus, total demand (by the consumer plus the government) is the same as it would be if the consumer were given the revenue. Starting at an undistorted equilibrium, this is roughly equivalent to compensated demand, since there is no first-order deadweight loss. pq1p0p1 x1x0x The relative burdens on the demand and supply sides will depend on relative elasticities. Defining the term 𝑧𝑧̂= d log(z), and letting the demand and supply elasticities (defined to be non-negative) be ηDand ηS, we know that 𝑥𝑥=−𝜂𝜂𝐷𝐷𝑞𝑞=𝜂𝜂𝑆𝑆𝑝𝑝̂. Further, if we let T= (1+τ), where the ad valoremtax imposed on the producer price, we have q = Tp, so that 𝑞𝑞=𝑇𝑇+𝑝𝑝̂. (Also, assuming that we are starting at a value of τ= 0, 𝑇𝑇= 𝑑𝑑𝑑𝑑.) Thus, setting the two expressions for 𝑥𝑥equal we have −𝜂𝜂𝐷𝐷�𝑇𝑇+𝑝𝑝̂�=𝜂𝜂𝑆𝑆𝑝𝑝̂ ⇒ 𝑝𝑝̂=−𝜂𝜂𝐷𝐷𝜂𝜂𝐷𝐷+𝜂𝜂𝑆𝑆𝑇𝑇; 𝑞𝑞=𝜂𝜂𝑆𝑆𝜂𝜂𝐷𝐷+𝜂𝜂𝑆𝑆; the ratio of the shares of the burden on consumers and producers is S/ηD, i.e., is proportional to the inverse ratio of the respective elasticities – the greater the responsiveness, the lower the burden. Note: it does not matter whether the tax is imposed on the buyer or the seller, assuming that prices are flexible. C B S D A The burden of the tax falling on the demand side is the loss of consumer’s surplus A+B, while the burden on the producer is the loss of producer’s surplus C+D, the sum exceeding revenue (A+C) by the deadweight loss B+D. For a small change starting at a Pareto optimum, the first-order excess burden is small relative to the revenue cost and we can approximate burdens by xqfor the consumer and -xpfor the producer, with the total burdens equal to revenue in this first-order approximation. τis ηD
2Application: Payroll Tax Reform in Sweden The U.S. social security payroll tax is assessed partially on employees and employers, up to an annual earnings ceiling (now \$132,900). A standard prediction is that the payroll tax’s incidence should be the same whether assessed on employees or employers.
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