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.)

Results:

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 - 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.