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EC320 PUBLIC POLICY > LECTURE 6 > Flashcards

LECTURE 6 Flashcards

1
Q

3 uses of income tax by government

A
  1. Fund public services.
  2. redistribute income
  3. Provide insurance
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2
Q

3 sources of taxable income

A
  1. earned income
  2. non-earned income e.g. property income
  3. taxable benefits e.g. state pension
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3
Q

The UK PIT system is approx UNITARY. What does this mean?

A

Income is aggregated and tax is calculated on the aggregate.

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4
Q

basic, higher and additional rates in UK.

A

20%, 40% and 45%

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5
Q

The UK PIT system consists of 2 things…

A
  1. Tax: income and NICs

2. Tax credits - form of benefits.

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6
Q

Average tax rate formula

A

total tax paid / income = T(Y)/Y = tax paid per unit of income

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7
Q

Marginal tax rate formula

A

change in total tax paid / change in income = change in tax paid for 1 unit increase in income.

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8
Q

MTR under progressive system

A

MTR increases with income so higher income individuals pay a greater proportion of their income in tax.

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9
Q

MTR under regressive system

A

MTR decreases with income so higher income individuals pay a smaller proportion of their income in tax. Same tax amount e.g. sin taxes.

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10
Q

MTR under proportional system

A

MTR same for all levels of income so all individuals pay same proportion of their income in tax. Pay same tax rate = flat tax.

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11
Q

Extensive margin of labour supply

A

whether to be in LF or not.

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12
Q

Intensive marginal of labour supply

A

How many hours to work conditional on being in LF.

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13
Q

Consumer utility function and BC in consumption leisure optimisation problem

A

Max U(c, l) s.t. C = (1-t)wL + R

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14
Q

What’s the opportunity cost of leisure?

A

Wage

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15
Q

Effective wage =

A

(1 - t)w = post-tax wage.

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16
Q

What’s another constraint for consumer consumption leisure optimisation besides BC?

A

TIME constraint: L + l = T

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17
Q

How do consumption, leisure and labour affect utility?

A

U’(c) > 0
U’(l) > 0
U’(L) < 0 - utility decreases in labour

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18
Q

Labour-consumption trade off

A

U’(c) > 0, U’(L)<0 but need to work to earn money to consume.

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19
Q

What’s R in consumer c-l optimisation?

A 
R = non-labour income.
c = R if do not work still have some money.
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20
Q

Slope of BC in consumption-leisure space

A

slope = –(1-t)w = opportunity cost of leisure in terms of post-tax wage and so consumption lost.

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21
Q

What’s the SE if tax rate decreases?

A

Lower t = higher effective wage = higher opportunity cost of leisure. BC pivots so steeper. Substitute leisure for labour as leisure becomes relatively more expensive.

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22
Q

What’s the IE if tax rate decreases?

A

Tax rate decreases = higher disposable income. Assume consumption and leisure both normal goods = consume more of both.

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23
Q

SO: how does a decrease in t affect labour incentives through SE and IE?

A

SE: lower t = greater incentive to work
IE: lower t = more leisure since normal good = disincentive to work.

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24
Q

SO: how does an increase in t affect labour incentives through SE and IE?

A

SE: higher t = less incentive to work
IE: higher t = less leisure since normal good = incentive to work.

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25
Q

Tax function T(Z) =

How does tax depend on income?

A

T(Z) = T bar + tz
T bar = autonomous part
tax linearly depends on income.

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26
Q

Tax function if zero earnings but transfer benefits.

A
  • T(0) = T bar < 0

- ve taxation = transfer.

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27
Q

Another name for MTR

A

phasing out rate

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28
Q

Formula for how much of a $1 increase in income you get to keep as disposable income.

A 
D = Z - T(Z)
dD/dZ = 1 - T'(Z) = 1 - MTR
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29
Q

the MTR affects what type of labour supply response?

A

INTENSIVE

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30
Q

Participation tax rate formula and explanation.

A

Tp = T(Z) - T(0) / z

Difference between taxes paid if z>0 and transfer receive if z=0, as a proportion of income.

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31
Q

1 - participation rate shows

A

proportion of earnings retained when moving from out of LF to into LF and earning Z.

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32
Q

Disposable income formula relating to participation rate.

A

Z - T(Z) = -T(0) + z(1 - Tp)

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33
Q

Break even earnings point is where…

A

T(z) = 0, pre-tax income = post-tax income. Neither net subsidy receiver nor net tax payer.

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34
Q

A graph with consumption on Y axis and pre-tax income on X axis aims to show us…
What’s the 45 degree line?

A

How the tax and transfer system affects the relationship between pre-tax income and disposable income/consumption. It shows the budget constraint / consumption function. The 45 degree line is where consumption=pre-tax income so T(Z)-0

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35
Q

Slope of consumption function =

A

1 - T’(Z) = 1 - MTR

IE how much of $1 increase in income you keep as disposable income.

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36
Q

How do the slopes of the consumption function and 45 degree line compare and why?

A

Consumption function slope flatter and < 1 for MTR > 0. When income rises by $1, get to keep

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37
Q

What does it mean when pre-tax income is before the break even point?

A

Z < Z* means T(Z) < 0 i.e. net subsidy receiver.

consumption > pre-tax/transfer earnings

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38
Q

What does it mean when pre-tax income is after the break even point?

A

Z > Z* means T(Z) > 0 i.e. net tax payer.

consumption < pre-tax/transfer earnings

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39
Q

How do we find the participation tax rate on c-z graph?

A

(1 - Tp)*Z = vertical distance between consumption at z=0 and consumption at a given z>0

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40
Q

How do utility functions compare in diagrams in consumption-leisure and consumption-pre-tax income space?

A

C-l: ICs slope downwards as usual and higher to NE
C-Z: ICs slope upwards as more pre-tax income i.e. more labour (z=wL) requires more consumption as compensation. Higher to NW when more C but less work.

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41
Q

How does wage compare into c-l and c-z diagrams?

A

c-l: wage comes into BC and (1-t)w = slope of BC

c-z: wage not in BC, but affects utility.

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42
Q

How to inputs of utility functions compare into c-l and c-z diagrams?

A

c-l: U(c, l)

c-z: U(c, L=z/w)

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43
Q

How do ICs compare into c-l and c-z diagrams?

A

They’re equivalent
c-l: C = (1 - t)wL + R
c-z: C = z - T(z) = (1 - t)z + T bar

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44
Q

2 aims of US EITC

A
  1. redistribute income to low wage earners.

2. Promote labour supply among low wage earners since they’re in work benefits.

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45
Q

efficiency equity trade-off with tax and transfer system.

A

Equity: redistribution to reduce inequality
Efficiency: taxes and transfers create disincentives to work.

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46
Q

Effect of T(z)<0 on labour supply and through which effect?

A

Initially on 45 degree line, then receive subsidy in net so c > z. Increase in disposable income = increase leisure and consumption via IE since both normal goods = decrease labour = z decreases.

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47
Q

Why does it make sense intuitively that transfers reduce incentive to work via IE?

A

Because with transfers, can now work less and earn the same disposable income.

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48
Q

Effect of T(z)>0 on labour supply and through which effect?

A

Initially on 45 degree line, then pay taxes in net so c < z. Decrease in disposable income = decrease leisure and consumption via IE since both normal goods = increase labour = z increases.

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49
Q

Why does it make sense intuitively that taxes increase incentive to work via IE?

A

Because with taxes, now have to work more to earn the same disposable income.

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50
Q

Effect of MTR i.e, T’(Z) > 0 on labour supply and through which effect?

A

SE: MTR > 0 = lower effective wage = lower opportunity cost of leisure = increase leisure, reduce labour and so Z through SE. Regardless of whether z>z* or z

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51
Q

Summarise IE and SE on incentives to work for net subsidy payer

A 
IE = disincentive to work
SE = disincentive to work
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52
Q

Summarise IE and SE on incentives to work for net tax payer

A

IE = incentive to work
SE = disincentive to work
= AMBIGUOUS overall effect.

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53
Q

How do taxes and transfers affect utility for zz*?

A

Zz*: taxes decrease utility = move to lower IC via IE

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54
Q

The optimal income tax rate balances what 2 incentives?

A

equity and efficiency

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55
Q

How are consumers similar and how are they different in Mirrlees?

A

identical preferences

Different skills and so wages.

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56
Q

Whats the wage in Mirrlees

A

wage = skill assuming competitive economy

57
Q

Income = f() mirrlees

A

Income = f(skill, hours worked)

58
Q

Does Mirrlees look at extensive/intensive margin?

A

Assumes everyone works = NO EXTENSIVE

ONLY INTENSIVE

59
Q

What’s the 1st best tax policy? Why is this not feasible for the government?

A

1st best = lump sum tax on individual characteristics = skill - like an initial endowment. BUT: skill = private information and cannot be observed by the gov - they only know distribution of skills.

60
Q

In Mirrlees model, government are trying to determine…

A

Optimal T(Z)

61
Q

What’s the 2nd best tax policy when 1st best isn’t feasible?

A

2nd best = tax behaviour i.e income since this is observed. While income depends on skill, it also depends on hours worked –> distortionary.

62
Q

2 constraints in government’s problem Mirrlees. Explain them.

A
  1. revenue requirement
  2. incentive compatibility - no 2 consumers want to swap allocations, they find the allocations given U maximising so no incentive to change/pretend to be someone else.
63
Q

In Mirrlees, the government assigns an allocation of what to each consumer?

A

Consumption pre-tax income allocation

64
Q

Formula for pre-tax income Mirrlees

A

Z = wL
w=skill, s
SO: z = sL

65
Q

In Mirrless, what functions depend on skill?

A

z(s)

c(z(s)) = z(s) - T(z(s))

66
Q

U=f() in Mirrless

A

U(c, L=z/s) = U(c, z, s)

67
Q

How do ICs of low and high skill consumers compare? WHY?

A

At any (z, c), LOW SKILL IC = STEEPER than high skill. Because income = f(skill, hours worked) so to achieve a given level of income, low skilled must put in relatively more labour hours = require higher consumption as compensation

68
Q

What’s the agent monotonicity condition?

A

This requires ICs of low skilled to be steeper than ICs go high skilled at any (c, z)

69
Q

Diagrammatically, a consumer’s optimum (c, z) is where…

A

Consumption function is tangent to highest IC

70
Q

Consequence of agent monotonicity for (c, z) allocations of high vs low skilled.

A

cH > cL
zH > zL
HS optimum will never be to the left of LS optimum as LS would also find this preferable.

71
Q

If we have a quasilinear utility function u(c) - z/s for Mirrlees, what’s the MRSz,c ? How does MRS vary with skill?

A

MRSz,c = MUz/MUc = -1/s/u’(c) = - 1/su’(c)

Higher skill = lower MRS = flatter IC = agent monotonicity satisfied.

72
Q

Would a low skill ever mimic a high skill?

A

NO as it would be costly they’d have to undergo training.

73
Q

Would a high skill ever mimic a low skill?

A

YES - could find it preferable to lower consumption and have more leisure instead by putting in less effort.

74
Q

incentive compatibility constraint mirrlees

A

Only HS IC is binding.
u(cH) - zH/sH = u(cL) - zL/sH
sH regardless as high skilled.

75
Q

How does a utilitarian government optimise for Mirrless? what are it’s choice variables?

A

MAX utility HS + utility LS
s.t. incentive compatibility constraint
s.t. aggregate resource constraint
4 choices = cH, cL, zH, zL

76
Q

We simplify the government Mirrlees optimisation to make it unconstrained. Give the maximisation formula nw.

A

Max betaH u(cH) + betaL u(cL) - (sH + sL / 2sHsL) (cH + cL)

77
Q

What’s beta h in Mirrlees?

A

Bh = sH + sL / 2sL

i.e. weight on HS utility function

78
Q

What’s beta l in Mirrlees?

A

Bl = 3sL - sH / 2sL

i.e. weight on LS utility function

79
Q

Range for sH in terms of sL. What does this ensure?

A

sL < sH < 3sL

Ensures + VE weight on LS utility.

80
Q

How to weights on LS and HS utilities compare? What does this mean for outcomes?

A

beta H > beta L
HS always has more weight on utility function.
SO: cH > cL at the optimum.

81
Q

Mirrlees FOC wrt cH + interpret

A

u’(cH) = 1/sH
MU of consumption of HS is inversely related to skill
Since u’‘(c) < 0, higher skill = lower MU of consumption = higher consumption. consumption proportional to skill.

82
Q

At the optimum, what’s MRSz,c for HS ??

A

u’(cH) = 1/sH
MRS = 1/sHu’(cH)
So MRS = 1 at the optimum.

83
Q

At the optimum, what’s MTR for HS? Explain.

A

We found MRS=1 at the optimum.
Optimum where consumption function tangent to IC.
1 - T’(z) = 1 –> T’(Z) = MTR = ZERO

84
Q

MTR = 0 for high skilled is called…

A

No distortion at the top result

85
Q

Mirrlees FOC wrt cL + interpret

A

u’(cL) = (sH + sL) / sH(3sL - sH)

86
Q

At the optimum, what’s MRSz,c for LS ??

A

MRS = sH(3sL - sH) / sL(sH + sL) < 1

87
Q

At the optimum, what’s MTR for LS? Explain.

A

MRS < 1
1 - T’(Z) < 1 –> T’(Z) = MTR > 0
+VE MTR for LS

88
Q

SO: what’s the Mirrless MTR range?

A

0 <= t* < 1

89
Q

What does Mirrless imply about progressive tax schemes?

A

That they cannot be optimal since progressive require MTR to rise with income so MTR is highest for highest income, not zero.

90
Q

Mirrlees no distortion at the top result is only valid for…

A

The HIGHEST skill consumer - no prediction for 2nd highest.

91
Q

How do Diamond and Saez adapt Mirrless?

A

They use ELASTICITIES

92
Q

How do applied optimal income tax models differ to results on Mirrless?

A

They find:

  1. top MTR not zero.
  2. MTR < 0 for low earners i.e. subsidise
93
Q

Optimal linear income tax AKA

A

LAFFER CURVE

94
Q

Laffer curve show relationship between…

A

Tax revenue and tax rate

95
Q

In Laffer, what do we assume the government do with revenue?

A

R = t*average Z

This R goes back to individuals in the form of a transfer: C = (1 - t)Z = R

96
Q

What’s the only channel from tax rate to pre-tax earnings?

A

Lower tax rate = higher net-of-tax rate = higher effective wage = higher opportunity cost of leisure = SE increases labour = higher pre-tax earnings.

97
Q

Tax revenue formula Laffer

A

R(t) = t*Z(1 - t) where Z = f(1 - t), not multiplied.

98
Q

What’s R when t=0 and t=1?

A

t=0 R=0

t=1 R=0 since no-one works.

99
Q

Elasticity of AVERAGE pre-tax income wrt net of tax rate

A

e = dZ/d(1-t) * (1-t)/Z

100
Q

Mechanical effect of higher t on R

A

Higher t = higher R holding Z constant

101
Q

Behavioural effect of higher t on R

A

Higher t = lower Z = lower R

102
Q

How do we find the revenue maximising t* i.e. the peak of Laffer curve? What is it?

A 
dR/dt = 0
t* = 1 / 1 + e
103
Q

Why is the revenue maximising t* not necessarily optimum t*?

A

Because government objective is NOT to maximise revenue - its to maximise SWF. They must account for behavioural effect of higher t on Z.

104
Q

Gov’s optimisation to find optimum t* for Laffer curve?

A

Assume all individuals have same U(c, L)
Sub in consumption function
d(SWF=sum Ui)/dt

105
Q

What’s the optimum t* from Laffer method?

A

t* = (1 - g bar) / (1 - g bar + e)

106
Q

In laffer, e represents… and how does t* depend on e and why?

A

EFFICIENCY parameter
Higher e = 1% change in net of tax rate has a greater effect on Z i.e. greater behavioural effect = high efficiency cost of taxation = lower t*

107
Q

In laffer, g bar represents… and how does t* depend on g bar and why?

A

EQUITY parameter: How much social value gov places on increasing consumption of 1 person by 1 unit vs distributing 1 unit among everyone.
g bar = inversely related to redistribute tastes and so inequality.
Higher g bar = less redistribution = lower t*

108
Q

Laffer MAX redistribution values of g bar and t*

A

Max redistribution when g bar = 0.

g bar =0, t* = 1 / 1 + e i.e. revenue maximising laffer.

109
Q

Government have higher redistributive tastes when…

A

Higher inequality.

MU of income decreases fast with income.

110
Q

Laffer MIN redistribution values of g bar and t*

A

Min redistribution when g bar = 1.

t* = 0 - zero tax rate, zero revenue, zero transfers.

111
Q

Government have lower redistributive tastes when…

A

Little inequality.

112
Q

When we say tax rate, what kind of tax rate do we mean?

A

always MARGINAL tax rate

113
Q

Pertubation method for top income tax rate

A

Consider the effects of a small increase dt on SW by ONLY looking at effects on individuals with income > certain threshold.

114
Q

Explain mechanical effect and its sign

A

Higher MTR = increase in revenue, holding behaviour (labour hours) constant = +VE effect

115
Q

Explain behavioural effect and its sign

A

Higher MTR = decrease in labour hours through SE = lower average earnings = lower revenue = -VE effect

116
Q

Explain utility/welfare effect and its sign

A

Higher MTR = decreased utility for high income individuals holding behaviour constant.

117
Q

How do we find optimum for top income tax rate?

A

mechanical effect + behavioural effect = utility effect

Must sum to zero so tax reform has no first order SW effects.

118
Q

To simplify top income tax analysis, what do we assume?

A

NO IE - only SE of higher tax rate on labour supply.

119
Q

For individuals over threshold, how do MTR compare?

A

Assume CONSTANT linear tax rate, t, above the threshold z bar.

120
Q

Do we look at intensive/extensive for top tax?

A

Intensive only - assume everyone works.

121
Q

What’s the effect of a small increase dt on taxes paid by 1 individual above z bar?

A

(z - z bar)dt

122
Q

What’s the mechanical effect of dt on taxes paid, assuming population above z bar = 1?

A

M = (zm - z bar)dt

where zm = average income above threshold

123
Q

Formula for reduction in pre tax earnings of one individual due to dt (using elasticity)

A

dz = -ez dt/(1 - t)

124
Q

Formula for reduction in revenue due to behavioural effect of one individual due to dt (using elasticity)

A

dT(z) = t*d(Z)

125
Q

Behavioural effect for all individuals

A

B = -e bar Zm tdt/(1 - t)

126
Q

How do we show small increase dt for top earners on c-z diagram?

A

Slope = 1 - T’(z) so Higher MTR = flatter slope beyond z bar.

127
Q

How do we show mechanical effect on c-z diagram?

A

At same z, reduction in disposable income from old to new consumption function = increase in tax receipts

128
Q

How do we show behavioural effect on c-z diagram?

A

Show z decreasing in response to the reform.

129
Q

Overall effect of tax reform on revenue: M + B =

A

[Zm/z bar - 1 - t/(1-t) * e bar * zm/z bar]

If M > B, raises revenue.

130
Q

What’s the welfare effect of the tax reform driven by?

A

Increased tax liability so its driven entirely by the mechanical effect.

131
Q

Utility effect =

A

g bar M

  • M = increased tax liability
  • g bar = SWF weight on top income individuals relative to weight on government revenue
132
Q

The definition of g bar implies…

A

The government is indifferent between $1 more consumed by top income individuals and $g bar more government revenue

133
Q

When we set M + B = g bar M, we get the optimal top income tax rate =

A

t* = (1 - g bar)/(1 - g bar + a*ebar)

134
Q

How does g bar affect top t*?

A

Higher g bar = more social value on top income individuals = less redistributive taste = lower t*

135
Q

How does e affect top t*?

A

Higher e = greater behavioural effect & so efficiency loss of tax = lower t*

136
Q

What is a in top t* formula?

A

a = thinness of tail of income distribution

Higher a = thinner tail = fewer people in top half.

137
Q

How does a affect top t*? Why?

A

Higher a = thinner tail = fewer people in top = lower revenue potential = lower t*. Also when a higher, more worried about B > > M.

138
Q

How does top t* relate to Mirrlees result?

A

When zm=z bar i.e. only 1 person in top, a–>infinity, t* = 0. The same no distortion at the top result.

139
Q

a formula:

A 
a = zm / zm - z bar
a = [zm/zbar] / [zm/zbar - 1]

EC320 PUBLIC POLICY (7 decks)

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