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MSCI 3400 (16)


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Management Science
MSCI 3400
Sean Mac Donald

SALES TAXES Our understanding of elasticity will help us analyze the impact of sales taxes or subsidies on equilibrium price and quantity. 1. Per Unit Tax The simplest sales tax is a fixed tax per unit sold, regardless of the price or quantity of the units sold. Whether sellers or buyers collect the tax for remission to the government is irrelevant to the impact of the tax on buyers and sellers but we will assume that sellers collect the tax since this is the more common occurrence due to the greater ease of remission. Since the sellers impose the tax on each unit sold, the sellers add the amount of the tax to the price of each unit sold. This means that the supply function shifts up by the amount of the tax. If the equation for supply was Ps = S(Q), the Ps Tax= T + S(Q) where T = tax/unit. e.g. Suppose P = 84 – 0.03Q and P = 26 + 0.02Q describe the market for opera tickets per day. Initial Equilibrium => 84 – 0.03Q = 26 + 0.02Q => Qo = 1160 and Po = $49.20 What is the effect (short-run) of a tax of $12/unit? => Supply: P = 12 + 26 + 0.02Q After Tax Equilibrium => 84 – 0.03Q = 38 + 0.02Q => Q 1 920 and P = $16.40 Total Tax Revenue = Tax/unit * Q = $31* 1100 = $3300 NOTE: The equilibrium price after the tax increased by $7.20 ($56.40 - $49.20) not $12. A graph of these equilibria helps us understand why. Graph the after-tax equilibrium by shifting up the supply curve by the amount of the tax. Indicate the original price plus the tax (P0+Ton the vertical axis and shift supply up at Qo by this - 1 - amount. Most individuals shift supply up to intersect D0+Tbut this is incorrect since Supply clearly shifts by more than the amount of the tax at that point. P = 84 - 0.02Q, P = 26 + 0.03Q, Tax = $12/unit Price ($) 80 S1 Po+t So 60 P1 Po 40 D 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 40 60 80 10 10 10 10 10 20 22 24 Q1 Qo Quantity Sellers add the tax to the price that they charge customers but customers do continue to buy Qo at the higher price due to the Law of Demand. The higher price results in a fall in quantity demanded leading to a surplus at0+T, which causes a fall in price to a new equilib1ium P that is usually less than0+Tthough greater than Po. The increase in price and decrease in quantity as a result of the tax is a function of the relative elasticities of Demand and Supply. We will see later that a comparison of the relative slopes of Demand and Supply suffices to determine the change in price for linear Demand. - 2 - Incidence (or Burden) of a Tax Economists call the share of the tax paid by Buyers and Sellers the incidence, or burden, of the tax. Definition: The Buyers’ share of a tax is the difference between the pre-tax and post-tax price paid by Buyers. Buyers’ Share (BS) = 1 – Po Definition: The Sellers’ share of a tax is the difference between the pre-tax and post-tax price received by Sellers. Sellers’ Share (SS) = Po – (P – Tax) 1 Note: The Sellers’ PriceSel =1P – Tax) is the price sellers receive after they deduct the tax from the after-tax price paid by buyers. Note: The tax revenue collected by the government (or total tax paid) is graphically the area with the tax as the vertical dimensio1 (P1– (P – tax)), which is the difference between the pre- tax and post-tax Supply curves a1 Q . A. Tax collected by Sellers (Tax shifts Supply) P ST So Po +T P 1 BS Tax Revenue SS Po PSel P 1T Do Q Qo 1 - 3 - e.g
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