Some  Tax  Basics  

2

Tax Incidence, Efficient and Fair Taxation

• Who bears the burden of a tax?

• Commodity Taxation and Deadweight Loss

• Why we cannot use lump-sum taxes

3

Tax Incidence

•  Who bears the burden of any given tax? –  We’ll show that the burden of a tax is generally

split between consumers and producers –  Interesting point: In general, it doesn’t matter who

pays the tax (consumer, or producer)--tax incidence will be determined by supply and demand interaction

–  In other words, it’s no more “fair” to tax gas producers than to tax gas consumers…it makes no difference to who bears the burden of the tax

4

Tax Incidence

•  Who bears the burden of a tax? –  The person who hands the tax over to Revenue

Canada? –  The consumer? –  Businesses? –  Workers?

•  This is the question of tax incidence –  Statutory incidence says who is responsible for

handing the tax over –  Economic incidence tells us who really bears the

burden

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Example--Per Unit Tax

•  Consider the market for cell phones Qd=4500-20P Qs=25P –  In equilibrium, we know Qs=Qd, so P=$100 and

Q=2500. •  Suppose the government imposes a $9 per

unit tax on cell phones. –  Assume the tax is imposed on suppliers (so sellers

have to pay the tax to RevCan. Qd=4500-20P Qs=25(P-tax)=25(P-9)=25P-225

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Example--Per Unit Tax

•  First, recognize that if there is a per unit tax, then the price consumers pay must differ from the price producers receive Pc: price consumers pay Ps: price producers receive Pc=Ps+t or Ps=Pc-t

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Example--Per Unit Tax

•  Recognizing that prices will differ, so that Ps=Pc-t, Qd=4500-20Pc Qs=25(Ps)=25(Pc-t)=25(Pc-9)=25Pc-225

•  In equilibrium, Qs=Qd, so 4500-20Pc=25Pc-225 or Pc=105; so Q=2400 and Ps=105-9=96

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Example--Per Unit Tax

•  Think of supply curve as “willingness to accept” curve –  Now suppliers must

receive an extra $9 per unit to be willing to produce it; implies

a shift up in supply curve by $9.

•  Find new (taxed) equilibrium where S’ and D intersect; gives Pc –  Read Ps off old supply

curve

Incidence of per unit tax on supplier

225

4500

D

S

100

2500

t

9

S’ (w/tax)

Orig. Equil.

New Equil.

Pc=105

Ps=96

2400

$$

Q

9

What’s the incidence?

•  Of the $9 tax, consumers pay $5 (in higher price paid), and producers pay $4 (in lower price received) – Originally, consumers paid $100, now pay

$105. – Originally, producers received $100, now

receive $96.

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Does it Matter Who Actually Hands the Tax to the Government?

•  Suppose the cell phone tax is charged to consumers instead of producers – Each time you buy cell phone, you receive

a bill for $9 from the government – Does this change anything? Redo analysis Pc=Ps+t Qd=4500-20Pc=4500-20(Ps+9) Qs=25Ps

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Does it Matter Who Actually Hands the Tax to the Government?

•  Tax on consumer lowers willingness to pay by amt. of tax –  Represent this by shifting

D curve down by amt of tax

•  Find new taxed equilibrium at intersection of S and D’ –  This gives new Ps; read

Pc by going straight up to old D curve.

•  Notice: Result is identical to taxing producer $9 per unit!

Incidence of per unit tax on consumer

225

4500

D

S

100

2500

t 9

D’ (w/tax)

Orig. Equil.

New Equil.

Pc=105

Ps=96

2400

216

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Statutory Incidence Doesn’t Matter!

•  This example illustrates that it doesn’t matter who is legally responsible for paying the tax –  Producers and consumers bear same burden of

the tax, regardless of who hands it over to the government

–  In both cases, consumer bears $5 of the $9 burden, and producer bears $4 of the $9 burden.

•  Economic incidence (who really bears burden) is unrelated to statutory incidence (who physically hands the tax over)

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Does it Matter Who Actually Hands the Tax to the Government?

•  Why is this important? –  Think about something like a gas tax. Some

people say charging consumers gas taxes is unfair because poor people pay a larger share of their income on gas than rich people (this is true)

–  But, does it solve the problem to charge gas taxes to gas station owners, instead?

–  No,it makes no difference. Tax will be just as unfair as if govt charges consumers at the pump.

•  Politicians are always ignoring this. –  Example: if CPP contribution rates are going to

rise, who should pay? Worker or Employer? It doesn’t matter!

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Determinants of Economic Incidence

•  Relative elasticity of supply and demand –  What do elasticities tell us? –  How responsive Qs and Qd are to changes in price –  If supply is relatively elastic, it increases a lot as

price rises –  If demand is relatively elastic, it falls a lot as price

rises –  If Qs and Qd are relatively inelastic, quantities

change a small amount for a given price change •  Burden of tax falls on the less elastic side of

the market

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What Determines Price Elasticity of Demand?

•  Substitutability (more alternatives, more elastic) –  Insulin; no good substitutes, demand is price

inelastic –  Coke; Pepsi good substitute, demand relatively

price elastic •  Luxury vs. necessity (demand more elastic for

luxuries) •  Long run vs. short run

–  If you need something now, your demand will be relatively price inelastic; if you have the option to wait, you can afford to be more price sensitive

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What Determines Price Elasticity of Demand?

•  Budget Share “The importance of being unimportant.” –  For something like salt (tiny part of your budget)

the price could probably double without you significantly reducing your purchases

–  Smaller share items, less elastic demand –  Example: price elasticity of demand for cigarettes

is higher for teenagers (relatively poor) than for adults (relatively rich)

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Ad Valorem Tax

•  If tax is a fraction of the price of a good (say 14%), we call it an ad valorem tax. –  Tax lowers consumer

WTP if applied to consumers

–  Raises firms’ WTA if applied to producers

•  Either way, incidence is same (redo with tax on suppliers)

•  Question: Why does demand curve pivot?

An Ad Valorem Tax on Consumers

S D

D’(w/tax)

Ps

Pc

Q

P

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Balanced Budget Incidence

•  A more sophisticated view of tax incidence takes into account how the tax revenues are spent – Suppose the cell phone producers in our

earlier problem live in Alberta; the consumers live in BC

–  If the tax revenues are given to BC schools, then we might view the burden of the tax differently

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Criteria for Evaluating Taxes--Efficiency

•  Holding other things constant, we want taxes that cause as little deadweight loss as possible (i.e. as little welfare loss as possible)

•  This means – Taxes that cause minimal distortion – Taxes that are cheap to administer

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Substitution Effect (SE)

•  Basic point on substitution effect –  Increasing the price of a good will cause

substitution away from that good, even if utility is held constant

– This applies in both the model analyzed here and the income-leisure model analyzed previously

– This substitution is the cause of DWL when we apply a commodity tax in the model here.

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Substitution Effect and Demand

•  The consumer demand of a good depends on both the SE and the income effect.

•  In the demand and supply diagram of the partial equilibrium model we get an approximation of deadweight loss, but not the exact measure (except for the special case of quasi-linear preferences) because demand keeps income the same, not utility.

•  We’ll see once again why income effect does not create distortion.

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DWL and Commodity Tax

•  Assume a simple 2 good consumer choice model –  Consumer gets utility from goods x and y –  Each consumer has income, M and faces prices

Px and Py –  Consumers maximize utility subject to budget

constraint •  Assume supply is completely elastic

consumers bear burden of the tax.

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Recall what the Substitution Effect is •  When the price changes (for instance,

because of a per unit tax or ad valorem commodity tax), there are two effects –  When consumer price of x rises,

1)  the consumer is poorer. If the good is normal they consume less of it--this is the income effect.

2)  the relative price of x rises, causing consumer to substitute away from x toward y. This is the substitution effect.

–  In this case, an increase in Px causes consumers to unambiguously reduce consumption of x, because both SE and IE go in same direction.

–  Only if good x is inferior do income and substitution effects go in opposite directions.

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Effect of Taxing x on Consumer’s Bundle

•  What is the overall effect of a commodity tax (tax on x)?

•  Assume both goods are normal. –  Price increase causes

quantity demanded (of x) to fall.

–  How much of this fall is income effect?

–  How much is subs effect?

• •

x

y

A C

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Equivalent Variation and DWL

•  Equivalent Variation of a tax: Start at A. A commodity tax on x causes utility loss (AC). Now suppose, instead of the tax, we just take cash away until we’ve caused the same utility loss as the tax (AB). This amount is the EV of the tax.

–  Why is there DWL at C?

Assume price of good y is $1y-axis measures dollars spent on y.

• •

y

A C

• B

x ie on x

EV

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Why Does SE cause DWL?

•  The equivalent variation (EV) of a commodity tax is the utility cost of that tax measured in dollar terms –  If government revenue (GR) equals EV,

there’s no DWL, because gain in government welfare (revenues) equals loss in consumer welfare; social welfare stays the same

–  If we just took cash from this person (instead of the commodity tax) then at point B, GR=EV, so no DWL

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Why is there DWL at C?

•  There is DWL at C –  GR at C is equal to

vertical distance between point C and the old budget constraint. Compare social welfare associated with C to social welfare associated with A, then government is made better off by GR, but consumer is made worse off by EV. DWL=EV-GR>0.

• •

y

A C

• B

x

GR

EV

From B to C: substitution effect

•  At B and C utility stays the same, but B is optimal choice with old prices, C is optimal choice with new prices

•  What changes from B to C is the relative price ratio, but utility stays the same.

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• •

y

A C

• B

x se of x

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Alternative Way to Think About Substitution Effect than How You

First Learned It! •  Using EV, we take away

income before changing the price –  From A to B is income

effect –  B to C is substitution

effect •  We just hold the “after”

utility level constant; whereas typically the “before” utility level is held constant to determine SE

• •

se

y

A C

• B

x ie

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Why Does SE cause DWL? •  Going from A to B is pure income effect

–  No DWL from pure income effects (consumer loss exactly offset by government revenue gain)

–  The move we get from A to B is equivalent to a lump sum tax with same loss in consumer utility as with per unit tax that results in choice C.

•  Only get DWL moving from B to C (because now dollar gain in govt revenue is less than dollar cost in utility)

•  So DWL only kicks in due to substitution effect

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Suppose Tax Doesn’t Change Quantity of x? No DWL?

•  Unfortunately not, only possible if IE and SE cancel each other out for x! So there is a SE. –  Original choice: A –  Taxed choice: C –  Amt of lump-sum tax that

would generate equivalent utility loss: AD

–  Revenue from per unit tax: AC

–  DWL: CD –  Only possible if x is an

inferior good Good X

Good Y

A

C B

•

• D

U1

U2

Original BC

BC w/tax on X BC w/lump sum tax

• •

As long as there is a substitution effect, there will be DWL

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There’s DWL even if Quantity of x Doesn’t Change

•  In supply-demand analysis when there is no change in quantity of x, we’d think excess burden is zero. That’s not true! – Here we see that it’s possible to have no

change in consumption of a taxed good, but still have DWL.

– The problem with our supply-demand analysis is that we didn’t consider what was occurring in other markets

– Partial eqm vs General eqm analysis.

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Does a Non-Distortionary Tax Exist?

•  To find a non-distortionary tax, we must find one that does not change the relative prices of any goods –  Lump-sum tax would do this (no substitution effect!) –  Revenue from a lump-sum tax equals the equivalent

variation of the tax –  This means the value of the revenue generated exactly

equals the loss of welfare to the consumer paying the tax –  No DWL (no excess burden)

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No DWL with pure Income Effect •  We can’t find any other

budget line cutting through B that raises same revenue but gives greater utility (try to find one!) –  $ gain to government

equals $-equivalent loss to consumers

–  GR=EV •  Once we switch to a per

unit tax, the SE will kick in and GR will be lost (so DWL occurs)

No DWL from lump-sum tax (only inc effect)

•

y

A •

B

x ie of x

GR EV

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Why Don’t Govts use taxes that only produce IE?

•  Margaret Thatcher tried to implement a “poll tax”, essentially a lump-sum tax – Led to riots, downfall of her government

•  Very regressive – Everyone pays same dollar amount in

taxes – Poor would pay huge fraction of their

income, while rich would pay tiny fraction

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Is There a Fair Way to Implement a Lump-Sum Tax?

•  Could charge different lump-sum taxes to people in different income brackets –  But then this isn’t really lump-sum taxation, it’s an

income tax! –  People have incentive to keep their income low to

avoid tax (behaviour is distorted)