Taxes, Subsidies, and Other Government Policies
Christopher Makler
Stanford University Department of Economics
Econ 50: Lecture 23
Today's Agenda
- Taxes
- Who pays the tax?
- Is it based on quantity or value?
- Subsidies
- Like a negative tax
- Price Controls
- Price ceilings
- Price floors
List price includes all taxes.
Taxes are based on quantity (cents per gallon)
List price does not include taxes.
Tax is a percentage of the price.
Payroll taxes (SS and medicare):
15% of income paid by worker
15% of income paid by employer
Steel Tariffs
In 2018, Trump imposed a 25% tariff on imported steel
(Biden largely kept these.)
24% decrease in quantity of steel imports
22% increase in price of imported steel
(therefore, 3% decrease in price foreign companies receive)
P = \text{“List price”}
P_F = \text{Price received by firms}
P_C = \text{Price paid by consumers}
If consumers pay the tax:
If firms pay the tax:
If they split it evenly:
Imposing a Tax
P + t
P
P
P - t
P + \tfrac{1}{2}t
P - \tfrac{1}{2}t
D(P_C) = 100 - 3P_C
S(P_F) = 2P_F
Equilibrium price and quantity with no tax.
Equilibrium quantity and prices
faced by consumers and firms if
consumers pay a tax of t = 10.
Equilibrium quantity and prices
faced by consumers and firms if
firms pay a tax of t = 10.
Tax burden for consumers:
the amount of the tax that results in an increase in the price paid by consumers,
relative to the equilibrium price
Tax burden for firms:
the amount of the tax that results in an decrease in the price received by firms,
relative to the equilibrium price
What is the burden in this case?
How does tax burden relate to the relative elasticities of demand and supply?
Elasticity and Tax Incidence
The equilibrium quantity, price paid by consumers, and price received by firms doesn't depend on who pays the tax
It does depend on the relative elasticity of demand and supply.
Doing the math on elasticity
\epsilon_{Q,P} = {\% \Delta Q \over \% \Delta P}
\% \Delta Q = \% \Delta P \times \epsilon_{Q,P}
Multiply both sides by \(\% \Delta P\):
Definition of elasticity:
The change in quantity demanded if the price consumers pay increases by \(\%\Delta P_C\):
\% \Delta Q_D = \% \Delta P_C \times \epsilon_{Q_D,P}
PRICE ELASTICITY OF DEMAND
The change in quantity supplied if the price firms pay decreases by \(\%\Delta P_F\):
\% \Delta Q_S = \% \Delta P_F \times \epsilon_{Q_S,P}
PRICE ELASTICITY OF SUPPLY
(note: we're treating all numbers as magnitudes, since we know the direction!)
The change in quantity demanded if the price consumers pay increases by \(\%\Delta P_C\):
\% \Delta Q_D = \% \Delta P_C \times \epsilon_D
PRICE ELASTICITY OF DEMAND
The change in quantity supplied if the price firms pay decreases by \(\%\Delta P_F\):
\% \Delta Q_S = \% \Delta P_F \times \epsilon_S
PRICE ELASTICITY OF SUPPLY
In the new equilibrium, these two changes in quantities must be the same:
\% \Delta P_C \times \epsilon_D
\% \Delta P_F \times \epsilon_S
=
\displaystyle{{\Delta P_C \over \Delta P_F} = {\epsilon_S \over \epsilon_D}}
{\Delta P_C \over P} \times \epsilon_D
{\Delta P_F \over P} \times \epsilon_S
=
If before the tax, \(P_C = P_F = P\), then:
\displaystyle{{\Delta P_C \over \Delta P_F} = {\epsilon_S \over \epsilon_D}}
Suppose supply is more elastic than demand.
Who pays more of the tax, consumers or producers?
pollev.com/chrismakler
\displaystyle{{\Delta P_C \over \Delta P_F} = {\epsilon_S \over \epsilon_D}}
Note: the total change in price must be equal to the amount of the tax:
\Delta P_C + \Delta P_F = t
\Delta P_F = t - \Delta P_C
\displaystyle{{\Delta P_C \over t - \Delta P_C} = {\epsilon_S \over \epsilon_D}}
\displaystyle{\Delta P_C = {\epsilon_S \over \epsilon_S + \epsilon_D} \times t}
(after some algebra)
\displaystyle{\Delta P_F = {\epsilon_D \over \epsilon_S + \epsilon_D} \times t}
\displaystyle{\Delta P_C = {\epsilon_S \over \epsilon_S + \epsilon_D} \times t}
\displaystyle{\Delta P_F = {\epsilon_D \over \epsilon_S + \epsilon_D} \times t}
Suppose demand and supply are given by
\(D(P) = 37553P^{-2}\)
\(S(P) = 243P^4\)
What would the effect of a $12 per unit tax be?
pollev.com/chrismakler
Subsidies
Price Controls
Price Controls and Elasticity
Summary
Taxes and subsidies drive a "wedge" between supply and demand.
Instead of facing the same prices, firms and consumers face different prices.
Equilibrium still occurs at the point where the quantity demanded at the price consumers pay equals the quantity supplied at the price firms receive.
Price controls, when they are binding, prevent the market from arriving at the equilibrium price
at which supply equals demand, leading to persistent shortages or surpluses.
In all of these cases, the impact of the policy on the market depends crucially on the
price elasticities of demand and supply.
Econ 50 | Lecture 23
By Chris Makler
Econ 50 | Lecture 23
Bringing supply and demand together
