LECTURE 6 Flashcards
3 uses of income tax by government
- Fund public services.
- redistribute income
- Provide insurance
3 sources of taxable income
- earned income
- non-earned income e.g. property income
- taxable benefits e.g. state pension
The UK PIT system is approx UNITARY. What does this mean?
Income is aggregated and tax is calculated on the aggregate.
basic, higher and additional rates in UK.
20%, 40% and 45%
The UK PIT system consists of 2 things…
- Tax: income and NICs
2. Tax credits - form of benefits.
Average tax rate formula
total tax paid / income = T(Y)/Y = tax paid per unit of income
Marginal tax rate formula
change in total tax paid / change in income = change in tax paid for 1 unit increase in income.
MTR under progressive system
MTR increases with income so higher income individuals pay a greater proportion of their income in tax.
MTR under regressive system
MTR decreases with income so higher income individuals pay a smaller proportion of their income in tax. Same tax amount e.g. sin taxes.
MTR under proportional system
MTR same for all levels of income so all individuals pay same proportion of their income in tax. Pay same tax rate = flat tax.
Extensive margin of labour supply
whether to be in LF or not.
Intensive marginal of labour supply
How many hours to work conditional on being in LF.
Consumer utility function and BC in consumption leisure optimisation problem
Max U(c, l) s.t. C = (1-t)wL + R
What’s the opportunity cost of leisure?
Wage
Effective wage =
(1 - t)w = post-tax wage.
What’s another constraint for consumer consumption leisure optimisation besides BC?
TIME constraint: L + l = T
How do consumption, leisure and labour affect utility?
U’(c) > 0
U’(l) > 0
U’(L) < 0 - utility decreases in labour
Labour-consumption trade off
U’(c) > 0, U’(L)<0 but need to work to earn money to consume.
What’s R in consumer c-l optimisation?
R = non-labour income. c = R if do not work still have some money.
Slope of BC in consumption-leisure space
slope = –(1-t)w = opportunity cost of leisure in terms of post-tax wage and so consumption lost.
What’s the SE if tax rate decreases?
Lower t = higher effective wage = higher opportunity cost of leisure. BC pivots so steeper. Substitute leisure for labour as leisure becomes relatively more expensive.
What’s the IE if tax rate decreases?
Tax rate decreases = higher disposable income. Assume consumption and leisure both normal goods = consume more of both.
SO: how does a decrease in t affect labour incentives through SE and IE?
SE: lower t = greater incentive to work
IE: lower t = more leisure since normal good = disincentive to work.
SO: how does an increase in t affect labour incentives through SE and IE?
SE: higher t = less incentive to work
IE: higher t = less leisure since normal good = incentive to work.
Tax function T(Z) =
How does tax depend on income?
T(Z) = T bar + tz
T bar = autonomous part
tax linearly depends on income.
Tax function if zero earnings but transfer benefits.
- T(0) = T bar < 0
- ve taxation = transfer.
Another name for MTR
phasing out rate
Formula for how much of a $1 increase in income you get to keep as disposable income.
D = Z - T(Z) dD/dZ = 1 - T'(Z) = 1 - MTR
the MTR affects what type of labour supply response?
INTENSIVE
Participation tax rate formula and explanation.
Tp = T(Z) - T(0) / z
Difference between taxes paid if z>0 and transfer receive if z=0, as a proportion of income.
1 - participation rate shows
proportion of earnings retained when moving from out of LF to into LF and earning Z.
Disposable income formula relating to participation rate.
Z - T(Z) = -T(0) + z(1 - Tp)
Break even earnings point is where…
T(z) = 0, pre-tax income = post-tax income. Neither net subsidy receiver nor net tax payer.
A graph with consumption on Y axis and pre-tax income on X axis aims to show us…
What’s the 45 degree line?
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
Slope of consumption function =
1 - T’(Z) = 1 - MTR
IE how much of $1 increase in income you keep as disposable income.
How do the slopes of the consumption function and 45 degree line compare and why?
Consumption function slope flatter and < 1 for MTR > 0. When income rises by $1, get to keep
What does it mean when pre-tax income is before the break even point?
Z < Z* means T(Z) < 0 i.e. net subsidy receiver.
consumption > pre-tax/transfer earnings
What does it mean when pre-tax income is after the break even point?
Z > Z* means T(Z) > 0 i.e. net tax payer.
consumption < pre-tax/transfer earnings
How do we find the participation tax rate on c-z graph?
(1 - Tp)*Z = vertical distance between consumption at z=0 and consumption at a given z>0
How do utility functions compare in diagrams in consumption-leisure and consumption-pre-tax income space?
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.
How does wage compare into c-l and c-z diagrams?
c-l: wage comes into BC and (1-t)w = slope of BC
c-z: wage not in BC, but affects utility.
How to inputs of utility functions compare into c-l and c-z diagrams?
c-l: U(c, l)
c-z: U(c, L=z/w)
How do ICs compare into c-l and c-z diagrams?
They’re equivalent
c-l: C = (1 - t)wL + R
c-z: C = z - T(z) = (1 - t)z + T bar
2 aims of US EITC
- redistribute income to low wage earners.
2. Promote labour supply among low wage earners since they’re in work benefits.
efficiency equity trade-off with tax and transfer system.
Equity: redistribution to reduce inequality
Efficiency: taxes and transfers create disincentives to work.
Effect of T(z)<0 on labour supply and through which effect?
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.
Why does it make sense intuitively that transfers reduce incentive to work via IE?
Because with transfers, can now work less and earn the same disposable income.
Effect of T(z)>0 on labour supply and through which effect?
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.
Why does it make sense intuitively that taxes increase incentive to work via IE?
Because with taxes, now have to work more to earn the same disposable income.
Effect of MTR i.e, T’(Z) > 0 on labour supply and through which effect?
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
Summarise IE and SE on incentives to work for net subsidy payer
IE = disincentive to work SE = disincentive to work
Summarise IE and SE on incentives to work for net tax payer
IE = incentive to work
SE = disincentive to work
= AMBIGUOUS overall effect.
How do taxes and transfers affect utility for zz*?
Zz*: taxes decrease utility = move to lower IC via IE
The optimal income tax rate balances what 2 incentives?
equity and efficiency
How are consumers similar and how are they different in Mirrlees?
identical preferences
Different skills and so wages.