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3 - Public > 5 - Optimal Labour Income Taxation > Flashcards

5 - Optimal Labour Income Taxation Flashcards

1
Q

what are refundable tax credits

A
  • benefits received as long as they are working - doesnt benefit unemployed
  • rewarded with excess taxes that they otherwise would have been owed
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2
Q

assumptions of the simple model

A
  • U(C) is strictly increasing
  • U(C) is concave
  • Utility function is same for everyone
  • income is fixed Z for each individual (people cant change their behaviour)
  • assumes no behavioural responses
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3
Q

what does the simple model do

as long as assumptions hold

A
  • perfect equalisation
  • everyone gets the same post tax/transfer income
  • 100% redistributional
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4
Q

what does the simple model do
equation

A

maximises the sum of everyones utilities subject to the BC of the governments income (taxes=transfers)

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5
Q

what does the simple model prove

A

that maximising the utilities = the optimal tax solution is 100% MTR = perfect equalization

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6
Q

what are the issues with the simple model

A
  • no behavioural responses assumption = would destroy all incentive to work - assumption that incomes are fixed would be false as they would fall
  • people generally disagree with 100% redistribution = unfair
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7
Q

why should the simple model incorporate fairness

A
  • bounds on how much redistribution the gov can do
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8
Q

what is the equity efficiency trade off

A
  • redistribution = helps equity - reduces inequality
  • but at cost of economic inefficiency
  • high tax rates = economic inefficiency if there are behavioural responses to tax rates
  • behavioural responses limit the amount gov can redistribute
  • tradeoff between equity and efficiency
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9
Q

what factor limits the ability of gov to redistribute with taxes and transfers

A
  • the size of behavioural response limits ability to reduce inequality
  • equity efficiecny tradeoff
  • the more responsive individuals are to the tax - the less they work/more evade/avoid - the less taxes are generated
  • taxes create inefficiencies
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10
Q

what is -T(0)

A

transfer benefit with 0 earnings
lumpsum grant

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11
Q

what is T’(z)
what is 1 - T’(z)

A

MTR = how much an individual is being taxed for an additional $1 of earnings

1-T’(z) = how much an income they keep for each additional pound

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12
Q

what is the participation tax rate
why is it important

A

(T(z) - T(0)) / z

it is what fraction an individual keeps of earnings when moving from 0 earnings to z earnings (vertical line on graph)

its important for extensive labour supply responses - when people make decisions on whether to work or not

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13
Q

what is T(Z*)

A

the break even point

  • they get no benefit / loss from taxes or transfers
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14
Q

what is the difference between traditional means tested programs and refundable tax credits

A

traditional = reduce incentive to work for low income workers - benefit 0 hour workers

tax credit = incentive to work to gain from the benefits - but doesnt help 0 hour workers

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15
Q

what are the 2 different kind of models we can use to choose the optimal tax rate

A

without behavioural responses = simple model (horizontal line)

with behaviour responses (shallow slope)

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16
Q

what is the labour supply theory
equation

A

maximise utility (function of consumption and labour)
maxU(C,L)

subject to BC of income
C = w*l + R

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17
Q

what is the income effect

A

more income = increased consumption and decreased leisure

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18
Q

what is the substitution effect

A

increased income = the OC of leisure has increased, leisure is more expensive, so will increase labour

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19
Q

what is the difference between marshallian and hicksian labour supply

A

marshallian = maximise utility s.t BC

hicksian = minimise labour needed to reach utility given wage slope

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20
Q

what is uncompensated elasticity

A

substitution effect
considers only the response to price changes - doesnt consider the adjustment of consumers income

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21
Q

what is the Slutsky equation

A

eU = eC + income effect

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22
Q

what does
T(z) > 0
T(z) <0 mean

A
  1. net taxes
  2. net transfers
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23
Q

under what conditions is labour supply discouraged
(must mean that increases disposable income)

A

when z < z* = net transfers

T(z) < 0 = net transfers
T’(z) > 0 = being taxed for working

24
Q

what is the effect of net transfers on labour supply

A

unambiguous drop in pre-tax earnings
ambiguous effect on consumption

income effect = negative
* disposable income increases - net transfers
* increase C, reduce L

substitution effect = negative
* net wage decreased
* decrease C, decrease L

25
Q

what is the effect of net taxes on labour supply

A

z > z*

ambiguous effect on labour supply
unambiguous drop in consumption

income effect = positive
* disposable income decreased
* increase labour, decrease C and leisure

substitution effect = negative
* net of wage reduced
* increase leisure, decrease labour, decrease C

26
Q

what is the effect of taxes and transfers on labour supply for someone operating at z* before

A

they will choose to work fewer hours because the new tangency point is no longer maximising their utility, they can move up a curve

27
Q

what relationship does the laffer curve capture

A

the relationships between tax rates and tax revenue

what tax rate will max tax revenues

28
Q

what is the tax revenue function for laffer curve

what happens if t = 0 and t = 1

A

R(t) = t * Z(1-t)
- depends on tax rate and total income
- but average income is a function of net of tax rate

  • the tax revenue is 0, either no taxes, or no one works
29
Q

what is the optimal linear tax rate Rawlsian
equation

A

t* = 1/1+e

30
Q

what is the elasticity of average income wrt the net of tax rate

A

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

31
Q

what is the problem with t > t*

A

decreasing t would

make individuals better off - they pay fewer taxes
earn more revenue for the government - increase the amount of transfers they can give out

32
Q

under a Rawlsian gov which approach is better

A

optimising t* is best

because will make revenue as large as possible, making transfers larger

  • will help the poorest person in society more
33
Q

Rawlsian

A

choose t to maximise the tax revenue function

laffer curve

34
Q

utilitarian

A

choose t that will maximise the utilitarian SWF (sum of utilities)

  • diminishing MU = means that 1 dollar given to rich is valued less than given to poor
35
Q

what is the optimal linear tax rate
Utilitarian
equation

A

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

36
Q

what does the t* for utilitarian formula capture

and how

A

the equity efficiency tradeoff

increasing efficiency = decreasing t
increasing gov taste for redistribution = smaller g = t increases

37
Q

what does g- capture?

what does e capture?

A

equity
- captures the distributional part

efficiency
- efficiency in raising tax revenues and hours worked

38
Q

what does g=0 or g=1 represent

A

g = 0
- gov has high taste for redistribution

g = 1
- government does not want to redistribute
- wont tax
- already perfect equality
- everyone has the same income

39
Q

under what conditions is t close to the laffer rate t*?

A
  • g- is low
  • when inequality is high
  • MU decreases fast with income
  • gov has strong taste for redistribution
40
Q

what is the UK tax system like

A

individual tax is progressive with brackets with increasing MTR

41
Q

what will happen to labour supply if the optimal tax income rate changes for the highest bracket

A
  • normally ambiguous effect
  • rich = assume that the substitution effect will prevail because they are rich (income effect not that big)
  • they will decrease their hours supplied
42
Q

what are the 2 effects occuring when tax rate for top income bracket changes

A
  • there will be a mechanical increase in tax revenue, but behavioural response will reduce tax revenue

mechanical = tax increase
behavioural response = tax loss

43
Q

what is the mechanical increase

A

how much extra tax revenue would the tax change have generated if there was no behavioural response

44
Q

what is the mechanical increase
equation

A

dt * [z - z*]

change in tax * (how much they are earning above the threshold)

45
Q

what is the behavioural response

A
  • rich people will reduce the hours worked
  • fall in z
  • so there will be a loss in tax from increasing the tax rate
46
Q

what is the behavioural response
equation

A

-t/1-t * e * z * dt

47
Q

what is the optimal tax rate for top bracket equation

when DM = DB

A

t* = 1/ 1 + (a*e)

a = z / z - z*

48
Q

why does DM = DB need to equal in order to maximise tax revenue

what happens if DM > DB
what happens if DB > DM

A

DM>DB
* you can increase tax revenue by increasing the tax rate - you will be able to collect more

DB>DM
* you can increase tax revenue by decreasing the tax rate - less people will change their hours worked

49
Q

when does the optimal t value decrease?

A

decreases with:
* decrease in a = fewer people in top bracket - less worthwhile to tax them more

  • the more elastic rich people are - the greater efficiency loss will be so better to have lower tax
50
Q

what is a

A

the thinness of the top tail of income distribution

  • the higher the value of a - the thinner the tails = the fewer people in the upper tail of the income distribution
51
Q

what are all of the behavioural responses to income taxes

A
  1. reduced labour supply
  2. tax avoidance
  3. tax evasion
52
Q

what is tax avoidance

A

legal way to reduce tax liability by exploiting loopholes

53
Q

what is tax evasion

A

illegal under-reporting of income

54
Q

what can the government do to reduce these behavioural effects of income tax

A
  1. reduced labour supply
    - the government cant prevent this from happening
  2. evade/avoid = government can reduce this
55
Q

what ways is it possible from the gov to eliminate tax avoidance (legal way)

A
  1. better designed tax codes
  2. international cooperate = off shore tax evasion in tax havens

hard:
3. technological limitations of tax collection (how to tax informal cash business = hard)

56
Q

what are the limitations of the
t* = 1/ 1 + (ae) model

A
  1. model doesnt include extensive earnings responses - only includes intensive
  2. doesnt include fiscal externalities
  3. doesnt include classical externalities
    - charitable donations
    - positive spillovers (trickledown)

3 - Public (10 decks)

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