Optimal Labour Income Tax II Flashcards
If no taxes c = z (consumption = earnings)
With taxes c = z -T(z)
What if T(z)
A) >= 0 or <=0
B) T’(z)>0
B) > 0
A) T(z) ≥ 0 if individual pays taxes on net, 𝑇(𝑧) ≤ 0 if individual receives transfers on net.
B) marginal tax rate is positive so reduces net wage rate and reduces labour supply through substitution effects
C) T(z) > 0 reduces disposable income and increase labour supply through income effects (less money so need to work more to earn the same amount)
D) increases disposable income so reduced labour supply due to income effects (can work less to receive same amount)
What if income below z* (z<z*) (breakeven level of income)
Positive marginal tax rate T(z)’ > 0 , so
What if income below z* (z<z*)
Optimal linear tax rate:
Tax revenue per person (R)
R = t x Z(1-t)
Where t is tax rate
Z is earnings
Optimal tax rate formula (t)
t* = 1/1+e
Where e is elasticity - responsiveness of individuals to taxes
E.g if e=0 , means unresponsive i.e individuals would have no behavioural response, so thus optimal tax rate is 1.
Laffer curve diagram pg 8
If government et is rawlsian (maximise welfare of worst-off person)
t* = 1/1+e is optimal to make transfer R(t) as large as possible
What if government is utiliarian (so doesn’t care all about tax revenue, but utility too)
Pg 10 SWF
Government first order condition under utilitarian (bottom of pg10)
Optimal linear tax rate formula
B) main benefit of this adjusted formula
t = 1-g/1-g+e
Where g is 0<g<1
B) it capture equity-efficiency trade off
When is g low and t close to optimal laffer rate (t*=1/1+e)
When inequality is high
When marginal utility decreases fast with income
Suppose the government wants to maximise tax revenue collected from top bracket taxpayers (marginal utility of consumption of top 1% earners is small).
Optimal top income tax rate (FOR TOP EARNERS)
t = 1/1+a x e
a is the thinness top tail
e is efficiency
Other forms of behavioural response (not reduced labour supply)
Tax avoidance
Tax evasion
Why is labour supply vs tax avoidance/evasion distinction matter when considering behavioural response
Since if people reduce labour supply and work less when tax rates increase, not much government can do about it
However if people tax evade/avoid, gov can address this e.g by closing tax loopholes, enforcement etc
Issues with addressing tax evasion/avoidance
Tax avoidance occurs as tax codes system is poorly designed so allows people to find legal loopholes
Hard - forms of tax avoidance/evasion needs to be addressed with international cooperation (to address off-shore tax evasion in tax havens)
Also technological limitations e.g impossible to tax informal businesses
If individuals respond to taxes only through intensive margin (how much they work rather than whether they work),
What is the optimal transfer at bottom income group?
Negative income tax
What is the negative income tax expressed as
Lumpsum grant -T(0)>0
Characteristic of the negative income tax (lumpsum grant)
High marginal tax rates (MTRs i.e T’(z) ) at the bottom to phase out the lumpsum grant quickly
Why is high MTRs (phasing out lumpsum grants quickly) at bottom efficient?
Target transfer to the most needy (those with no earnings)
Earnings at bottom are low to start with, so intensive labour supply response does not generate large output losses
What about a negative MTR at bottom, what is the intuition
Here society prefers to give transfers to those who work but on low income, rather than those with no earnings at all
Society sees people with zero income as less deserving than average
Pg 22 diagram of high MTR
Pg 23 shows situation where society values zero earners less than those earning
Why is negative MTR beneficial for government
B) pg24 diag
Saves their revenue, since now only gives it for those who work, rather than those with no earnings
Participation labour supply responses (whether to work or not) are large at bottom (much larger response compared to intensive i.e how much to work)
What does participation depend on?
Participation tax rate
Participation tax rate
B) how much does individual keep when moving from no earnings to earnings
Tp = [T(z) - T(0)] / z
B) keeps fraction 1-Tp
Key result: in-work subsidies with 𝑇′ 𝑧 < 0 are optimal when labour supply
responses are concentrated along extensive margin and govt cares about low
income workers.
Pg 26 diagram to show participation tax rate
Why is participation response good a win-win reform (2)
B) diagram of it pg 29
Saves gov revenue (rewards earning rather than no earnings, incentivises people to get into work)
but also benefits IF intensive response to the subsidy is small i.e people don’t reduce their labour hours a lot since they can now technically earn the same for less since transfers.
B)
Blue arrow is the saving gov rev
Dotted line represents benefit if intensive margin small
Recap:
So if society views 0 earners as less deserving, what is optimal
B) what if more deserving and labour supply responses regarding extensive margin (work or not)
C) when is generous lumpsum with high MTR at bottom justified (2)
Low lumpsum grant and low phasing out rate at bottom
B) low phasing out rate at bottom is optimal
C)
if society views 0 earners as deserving,
and if there is little extensive margin response (people who are in work would NOT stop working following the lumpsum)
Previously what were real life transfer systems like
Used to have high phasing out rates i.e no incentive to work!
Why so high?
Since initially designed for groups not expected to work e.g widows, but it became problematic as groups that could work began to exploit it e.g single mothers
What has been done since then
More in-work benefits i.e like EITC which incentivises people to work! E.g more help for low income workers opposed to those who dont work at all
Basic income definition
All people receive a unconditional sum of money regardless of earnings
The R in the linear tax system c = (1-t) x z + R
Or the -T(0) > 0 in nonlinear tax system c = z - T(z)
Basic income is equivalent to what?
Means-tested transfer phased out with earnings!
Since has higher taxes (higher MTR) to fund basic income for everybody
Pros and cons of basic income
Pro: Less stigmatising than means-tested
Con: requires higher nominal taxes to fund since for everyone
Note: basic income can be in other forms e.g
Universal Healthcare
Public Education
Pg 33 basic income diagram
Issues with this program
Whether people are willing to fund transfers for everyone
Is in-kind transfers e.g healthcare, education as good as cash transfer?
Views
Rational individual perspective
Social perspective
Rational individual perspective on whether in-kind is equivalent to cash
If inkind transfer is tradable at market price, equivalent to cash
If non tradable, inferior to cash
So cash most likely preferable according to this perspective.
Social perspective on in-kind vs cash
4 sub views
Commodity egalitarianism: some goods are seen as rights and should be provided to all e.g education and health
Paternalism: recipients prefer cash
Behavioural (individual failures): they’d have biases, self control etc if they were to have cash may use incorrectly, so better to have in-kind
Efficiency: in-kind is good as can prevent those who dont really need them from getting them e.g rich people wouldn’t queue for free soup, so more efficient
Income tax for couples: 3 desirable properties
B) issue
Income tax should be:
based on resources (base on family income if they fully share income)
Marriage neutral (no higher/lower whether married or not)
Progressive
B) impossible to have system that satisfies all 3
Why is it impsosble to have all 3 satisfied
For it to be based on family income and marriage neutral, income tax has to be linear, not progressive!!!
If couples do not share income which is better
Individual tax is better if not shared, family taxation is better if couples share income
What should gov do if marriage responds to tax/transfer differential (if number of marriage decreases if taxes are higher for married people)
Reduce the penalty of marriage i.e move toward individualised system
If Labour supply of secondary earners is more elastic than labour supply of primary earners
Secondary earnings should be taxed less (since secondary earners are more responsive in their labour hours, thus tax less to get them to work more/prevent them from working less!)
What should transfers for children (Tkid) be? Positive or negative?
And why? (2)
Positive, as children
Reduce family income (e.g stay at home mum)
Increase marginal utility of consumption
Should Tkid(z) (transfer for kid) increase with income z?
Yes: as rich spend more on kids than lower income families
No: lower income families need child transfers the most, so should be the other way round, high transfer for low Z
In reality what is Tkid relation with Z
B) EU vs US Tkid policies
Fairly constant with Z
B) EU focus on pre-kindergarten child care benefits, US focus on tax credits for families with children
