5 - Optimal Labour Income Taxation

Question 1

what are refundable tax credits

Answer 1

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

Question 2

assumptions of the simple model

Answer 2

• 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

Question 3

what does the simple model do

as long as assumptions hold

Answer 3

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

Question 4

what does the simple model do
equation

Answer 4

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

Question 5

what does the simple model prove

Answer 5

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

Question 6

what are the issues with the simple model

Answer 6

• 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

Question 7

why should the simple model incorporate fairness

Answer 7

• bounds on how much redistribution the gov can do

Question 8

what is the equity efficiency trade off

Answer 8

• 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

Question 9

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

Answer 9

• 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

Question 10

what is -T(0)

Answer 10

transfer benefit with 0 earnings
lumpsum grant

Question 11

what is T’(z)
what is 1 - T’(z)

Answer 11

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

Question 12

what is the participation tax rate
why is it important

Answer 12

(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

Question 13

what is T(Z*)

Answer 13

the break even point

• they get no benefit / loss from taxes or transfers

Question 14

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

Answer 14

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

Question 15

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

Answer 15

without behavioural responses = simple model (horizontal line)

with behaviour responses (shallow slope)

Question 16

what is the labour supply theory
equation

Answer 16

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

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

Question 17

what is the income effect

Answer 17

more income = increased consumption and decreased leisure

Question 18

what is the substitution effect

Answer 18

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

Question 19

what is the difference between marshallian and hicksian labour supply

Answer 19

marshallian = maximise utility s.t BC

hicksian = minimise labour needed to reach utility given wage slope

Question 20

what is uncompensated elasticity

Answer 20

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

Question 21

what is the Slutsky equation

Answer 21

eU = eC + income effect

Question 22

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

Answer 22

1. net taxes
2. net transfers

Question 23

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

Answer 23

when z < z* = net transfers

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

Question 24

what is the effect of net transfers on labour supply

Answer 24

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

Question 25

what is the effect of net taxes on labour supply

Answer 25

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

Question 26

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

Answer 26

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

Question 27

what relationship does the laffer curve capture

Answer 27

the relationships between tax rates and tax revenue what tax rate will max tax revenues

Question 28

what is the tax revenue function for laffer curve what happens if t = 0 and t = 1

Answer 28

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

Question 29

what is the optimal linear tax rate Rawlsian equation

Answer 29

t* = 1/1+e

Question 30

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

Answer 30

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

Question 31

what is the problem with t > t*

Answer 31

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

Question 32

under a Rawlsian gov which approach is better

Answer 32

optimising t* is best because will make revenue as large as possible, making transfers larger - will help the poorest person in society more

Question 33

Rawlsian

Answer 33

choose t to maximise the tax revenue function laffer curve

Question 34

utilitarian

Answer 34

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

Question 35

what is the optimal linear tax rate Utilitarian equation

Answer 35

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

Question 36

what does the t* for utilitarian formula capture and how

Answer 36

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

Question 37

what does g- capture? what does e capture?

Answer 37

equity - captures the distributional part efficiency - efficiency in raising tax revenues and hours worked

Question 38

what does g=0 or g=1 represent

Answer 38

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

Question 39

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

Answer 39

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

Question 40

what is the UK tax system like

Answer 40

individual tax is progressive with brackets with increasing MTR

Question 41

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

Answer 41

- 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

Question 42

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

Answer 42

- there will be a mechanical increase in tax revenue, but behavioural response will reduce tax revenue mechanical = tax increase behavioural response = tax loss

Question 43

what is the mechanical increase

Answer 43

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

Question 44

what is the mechanical increase equation

Answer 44

dt * [z - z*] change in tax * (how much they are earning above the threshold)

Question 45

what is the behavioural response

Answer 45

- rich people will reduce the hours worked - fall in z - so there will be a loss in tax from increasing the tax rate

Question 46

what is the behavioural response equation

Answer 46

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

Question 47

what is the optimal tax rate for top bracket equation when DM = DB

Answer 47

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

Question 48

why does DM = DB need to equal in order to maximise tax revenue what happens if DM > DB what happens if DB > DM

Answer 48

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

Question 49

when does the optimal t value decrease?

Answer 49

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

Question 50

what is a

Answer 50

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

Question 51

what are all of the behavioural responses to income taxes

Answer 51

1. reduced labour supply 2. tax avoidance 3. tax evasion

Question 52

what is tax avoidance

Answer 52

legal way to reduce tax liability by exploiting loopholes

Question 53

what is tax evasion

Answer 53

illegal under-reporting of income

Question 54

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

Answer 54

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

Question 55

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

Answer 55

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)

Question 56

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

Answer 56

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)