# MSCI 2150 Lecture Notes - Economic Equilibrium, Remittance

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7 Feb 2013

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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 PsTax = 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

=> Q1 = 920 and P1 = $56.40

Total Tax Revenue = Tax/unit * Q1 = $3 * 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+T) on the vertical axis and shift supply up at Qo by this

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amount. Most individuals shift supply up to intersect D at P0+T but 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

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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 at P0+T, which causes a fall in price to a new equilibrium P1 that is

usually less than P0+T though 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.

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