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EC320 PUBLIC POLICY > LECTURE 7 > Flashcards

LECTURE 7 Flashcards

1
Q

How does commodity tax distort consumer choice?

A

But affecting relative prices and causing demand to switch from one good to another.
Also affect total consumption/saving.

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2
Q

How do taxes affect consumer and producer prices?

A

drive a wedge between the 2

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3
Q

What type of tax is commodity tax usually? What does this mean?

A

Proportional, not lump sum = DISTORTIONARY

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4
Q

How does commodity tax affect IC/BC diagram?

A

BC PIVOTS INWARDS for good the tax is levied on.

Change in slope of BC.

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5
Q

EQUIVALENT VARIATION asks…

A

How much money would the consumer be WTP in advance to avoid the tax and be at constant original (pre-tax) prices?

i.e. How much does income need to change before the tax such that utility is equal to the level if the tax is implemented?

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6
Q

EV what hypothetical BL do we draw?

A

Draw BC parallel to OLD BC and tangent to NEW IC.

  • At original prices
  • Utility the same level as under the tax.
  • Consumers WTP this amount of income shift that brings utility no lower than that under the tax.
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7
Q

How do we calculate EV? What does it tell us?

A

EV = difference in income the original and hypothetical BLs represent. It tells us the $ value of the welfare loss of the price change induced by the tax.

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8
Q

Whats IE and SE with commodity tax on good 1?

A

IE: decreased disposable income = reduce consumption of both goods.
SE: good 1 relatively more expensive = substitute 2 for 1.

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9
Q

How do we show a lump sum tax on the same diagram that generates the SAME revenue as the commodity tax?

A

Draw BL parallel to original BC (no change in prices) that goes through the final commodity tax bundle (ensures generates same revenue)

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10
Q

How can we compare welfare effects of commodity tax and equivalent lump sum?

A

Lump sum = reaches higher IC

EV higher for commodity tax than lump sum

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11
Q

How do we define DWL of a commodity tax?

A

The welfare loss (measured in monetary terms) created by the commodity tax over and above the tax revenue generated.

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12
Q

DWL calculation in monetary units

A 
DWL = EV(commodity) - EV(lump sum)
DWL = EV(commodity) - tax revenue
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13
Q

How else can we calculate DWL apart from using EV?

A

Simple demand and supply diagram: DWL = change in CS + PS + government revenue

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14
Q

2 other words for DWL

A

excess burden / deadweight burden

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15
Q

Uniform tax rates for all goods are NOT optimal if…

A

consumer has different PED for the goods.

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16
Q

Ramsey optimal tax rule

A

Optimal tax rates where marginal DWL for the last $1 of tax collected is the SAME across all goods.

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17
Q

Does the Ramsey rule consider both efficiency and equity?

A

only efficiency - assume just 1 consumer so abstract from redistribution.

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18
Q

How does inverse elasticity rule relate to Ramsey rule? What assumption does it make?

A

It’s a simplified version of ramsey rule.

Assumes NO CROSS PRICE EFFECTS: demand for a good depends on own price only.

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19
Q

after tax price =

A

qi = pi + ti

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20
Q

IER BC for 2 goods

A

q1x1 + q2x2 = wL = L for w=1

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21
Q

What do we assume about individuals? Implication

A

Assume all individuals are homogenous = we can optimise for one representative individual/

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22
Q

Lagrangian for consumer optimisation

A

L = U(x1, x2, L) + alpha(L - q1x1 - q2x2)

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23
Q

What Lagrange Multiplier do we use for consumer optimisation?

A

alpha

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24
Q

3 FOCs for IER consumer optimisation

A

MU of consumption = lagrange multiplier * after-tax price for both goods.
MU of labour hours = - lagrange multiplier

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25
Q

For consumer IER optimisation, what does alpha represent?

A

alpha= shadow price = MU of income i.e. change in utility if income rises by $1

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26
Q

Gov revenue constraint in terms of p and q

A

R = t1x1 + t2x2
ti = qi - pi
R + p1x1 + p2x2 = q1x1 + q2x2

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27
Q

How does the gov obtain t*?

A

Maximise representative consumer’s utility while satisfying their revenue constraint

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28
Q

What are the government’s choice variables? Why?

A

x1 and x2

cannot choose L - this is endogenously determined from individual BC once x1 and x2 chosen.

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29
Q

What Lagrange Multiplier do we use for gov optimisation? What does it measure?

A

lambda = MU of income for the government

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30
Q

How are lambda and alpha related???

A

Distortionary taxes imply lambda > alpha
MU of Income for gov > MU of income for consumer
Gov valuation of rev > ind valuation of income

31
Q

What’s the inverse demand function?

A

qi=qi(xi)

demand only depends own price.

32
Q

How does the gov use consumer optimisation FOCs in their own?

A

They embed the consumer’s 3 FOCs into their own FOCs

33
Q

PED formula

A

PED = dxi/dqi * qi/xi

Use after-tax prices.

34
Q

INVERSE ELASTICITY RULE FORMULA

A

ti/(pi + ti) = - [(lambda - alpha)/lambda] * 1/PED

35
Q

What is the sign of IER tax and why?

A

Assume lamba > alpha as distortionary

So +VE proportional tax

36
Q

IER Relationship between tax and PED

A

Higher PED = more elastic = lower tax
Lower PED = more inelastic = higher tax
Inversely related!!

37
Q

How does the constant of proportionality vary across goods?

A

It is CONSTANT across goods - the taxes only vary across goods if PED different.

38
Q

IER implication for necessities and luxuries.

A 
Necessities = inelastic = higher tax
Luxuries = elastic -= lower tax
39
Q

Is IER equitable?

A

NO - higher tax on necessities = lower income individuals bear relatively more of the tax

40
Q

What does the ramsey rule introduce over IER?

A

CROSS PRICE EFFECTS i.e. goods can be substitutes or complements.

41
Q

Does Ramsey rule consider equity?

A

NO - abstract from redistribution by considering an economy with 1 consumer.

42
Q

Demand function for goods for Ramsey

A

xi = xi(q1, q2)

43
Q

Side check: what 2 taxes are equivalent??

A

Uniform commodity tax (2 goods taxed at same rate) & income tax

44
Q

What market structure does Ramsey assume? Implication.

A

Perfect competition: P=MC
SO: pi = w
pre tax price since this is the price the producer charges.

45
Q

When analysing the equivalence of uniform commodity tax and income tax, what kind of taxes do we assume for each?

A

Income tax = proportional

Commodity tax = proportional

46
Q

Compare after-tax price formula for IER and Ramsey

A

IER: qi = pi + ti - additive
Ramsey: qi = (1 + ti)pi - proportional

47
Q

Uniform commodity tax are income tax are equivalent when…

A

tow = t / (1 + t)
where tow = proportional income tax
t = uniform commodity tax

48
Q

A commodty tax only differs from an income tax when…

A

It is NON-UNIFORM

49
Q

How do uniform and non-uniform commodity taxes distort choice? Which is more distortionary?

A

Uniform = only distorts consumption-leisure choice.
Non-uniform = also distorts choice between x1 & x2
= more distortionary.

50
Q

Is a uniform tax better than a non-uniform one?

A

NO not necessarily - non-uniform taxes can exploit different PED for more revenue and lower DWL.

51
Q

For actual Ramsey rule, what do we assume about income tax?

A

NO INCOME TAX - this simplifies without loss of generality.

52
Q

BC for Ramsey rule

A

(1 + t1)p1x1 + (1+t2)p2x2 = wL
assume w = 1 therefore p = 1
(1 + t1)x1 + (1+t2)x2 = L

53
Q

What does the gov optimisation do for Ramsey?

A

MAX INDIRECT utility function of consumer s.t. revenue constraint.

54
Q

How do w find indirect utility function?

A

v(1 + t1, 1 + t2)

Sub optimal demand functions from consumer optimisation into x1, x2 and L to get as function of post-tax price.

55
Q

Sii shows

A

slutsky compensated demand.
first i = which good’s quantity changes.
second i = which good’s price changes

56
Q

What is Slutsky compensated demand?

A

Shows quantity a consumer buys if he is income compensated for a price change i.e. eliminates IE = SE remains. SE holds utility fixed.

57
Q

OWN PRICE SLUTSKY IDENTITY and interpretation

A

dXi/dqi = Sii - Xi*dXi/dM
Sii = SE - hold utility fixed
Last term = IE - hold prices fixed

58
Q

CROSS PRICE SLUTSKY IDENTITY

A

dXi/dqj = Sij - Xj*dXi/dM

59
Q

Approx of change in compensated demand due to tax =

When is it a good approx?

A

ti*Sii

Good approx if ti is small.

60
Q

Formula for change in compensated demand of good 1 due to introduction of taxes, as a proportion of pre-tax demand.

A

(t1S11 + t2S12) / X1

61
Q

Formula for change in compensated demand of good 2 due to introduction of taxes.

A

(t2S22 + t1S21) / X2

62
Q

RAMSEY RULE + EXPLAIN

A

(t1S11 + t2S12) / X1 = (t2S22 + t1S21) / X2
changes in compensated demand due to the taxes as proportions of pre tax demand should be EQUAL for the 2 goods. This minimises distortions in quantities due to non-uniform taxes.

63
Q

Implication of Ramsey Rule relating to elasticities

A

Good 1 = inelastic
Good 2 = elastic
If t1 changes, S11 < S21 by PED, so tax good 1 more and good 2 less.

64
Q

ADD ROY’S IDENTITY WE GET…

A

(t1S11 + t2S12) / X1 = (t2S22 + t1S21) / X2 = - THETA

65
Q

another name for ramsey rule

A

equal proportional reduction rule

66
Q

We can calculate actual taxes if we have…

A

utility function

production parameters.

67
Q

Ramsey rule minimises distortion in terms of what? Why?

A

QUANTITIES, NOT PRICES.

Because quantities are what determine utility - so prices only matter so far as they determine demands.

68
Q

SO: what does Ramsey rule suggest about uniform taxes?

A

NOT OPTIMAL - we want to minimise quantity, not price distortion.

69
Q

Ramsey equity implications. Why does this arise?

A

Inequitable - only considers efficiency.

Arises due to 1 household assumption.

70
Q

Another intuition from Ramsey

A

If there exists an untaxed good e.g. leisure, the optimal tax formula can be expressed in terms of complementarity or substitutability with the untaxed good. SO: efficiency can be improved by taxing more heavily goods that are more complementary with leisure.

71
Q

Optimal commodity tax implication for production

A

When optimal commodity taxes are employed, production must be efficient - optimum lies on PPF boundary.

72
Q

Condition for productive efficiency to be achieved

A

MRTS between any 2 inputs the SAME for all firms. This is achieved without the tax under perfect competition since each firm sets MRTS = p1/p2 and prices are taken from the market.

73
Q

Implication of productive efficiency result of commodity tax

A

Do NOT tax inputs or intermediate goods as it creates distortion and leads to a worse outcome than without the tax. So only tax final goods i.e. consumption.

74
Q

Limitations: the principle of not taxing intermediate goods is heavily dependent on 3 things…

A
  1. No pure private sector profits.
  2. Perfect competition
  3. Possibility to tax all final goods.

EC320 PUBLIC POLICY (7 decks)

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