Optimal Labour Income Tax II Flashcards
(45 cards)
If no taxes c = z (consumption is our earnings)
With taxes c = z -T(z)
What if
A) T’(z)>0, what happens and effect
B) T(Z)> 0, what happens and effect
C) T(z) < 0, what happens and effect
D) so what transfer program always discourages labour supply
A) T’(z) > 0
Marginal tax rate is positive so reduces net wage rate and reduces labour supply through substitution effects (leisure cheaper)
B) 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)
C) T(z) < 0
increases disposable income so reduced labour supply due to income effects (can work less to receive same amount)
D) transfer program with T(z) < 0 and T’(z) > 0
Assume we start with no tax/transfer system, so along the 45 degree line.
then suppose the tax/transfer system we just looked at (transfer for non-workers, then constant tax imposed.
What is the net effect on labour supply and z, if z<z*?
pg 5
individual receives transfers in net:
T(z) < 0 , income effect: so they work less
also
T’(z) > 0 so net wage rate fallen, (leisure cheaper) so substitute work for leisure
so net effect is a fall in labour supply and z! (same as D from previous FC)
What if income above z* (z>z*)
Assume we start with no tax/transfer system, so along 45 degree line.
Then impose system. What is net effect on labour supply and z pg6
Individual now pays taxes in net:
now T(z) > 0 , income effect means labour supply and z increases.
T’(z) > 0 , so sub effect means since net-wage rate has fallen, leisure is cheaper so sub work for leisure, so labour supply and z falls!
So net effect is ambiguous
So marginal tax rate T’(z) is for substitution effect (adjusts net-wage rate)
Tax/transfer rate T(z) is for income effects (adjusts disposable income)
How to find the optimal linear tax rate
Laffer curve
Laffer curve:
first derive consumption equation
B) R equation (universal transfer)
c = (1-t)z + R
R is fixed universal transfer (so transfer given to everyone) funded by taxes
b) R = tz
Tax revenue per person R(t)
b) what happens when R(t=0)
c) R(t=1)
d) what does these 2 results show us
R(t) = t x Z(1-t)
b) R(t=0) means tax revenue when tax rate is 0, is obviously 0
c) R(t=1) means we are charging 100% tax rate, so nobody works, so we also get 0 tax revenue!
d) both extremes get 0 tax revenue, so U shaped! This is the laffer curve! Tax cannot be 0% or 100%, as both get no revenue R(t)!
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.
If government is rawlsian, what would they do?
B) what if utilitarian
They want to maximise welfare of worst-off person, make R(t) (tax revenue per person) as large as possible for bigger transfer
B) maximise utility of ALL individuals (do not care about maximising tax revenue)
So utiliarian SWF maximises utility of all individuals
SWF = Σ u(disposable income, labour supply) pg10
Then maximise by FOC, we get equation. Don’t bother learning equation, just remember the meaning
Government want more tax revenue to maximise social welfare (Z-zi : change in income following tax, i.e revenue)
However face behavioural response - efficiency cost of increasing taxes. (EQUITY-EFFICIENCY)
So utiliarianists want more tax rev to redistribute evenly but face behavioural response
What is the optimal linear tax rate formula under utilitarian government?
B) main benefit of this adjusted formula
t = 1-gbar / 1-gbar+e
Where gbar is 0<g<1
B) it capture equity-efficiency trade off
if gbar=0 values redistribution
if gbar =1 , does not value redistribution
use equation and let gbar=1 we get t=0: optimal tax is none when noone cares about redistribution!
When should gbar be low and t be close to the laffer rate 1/1+e (2)
When inequality is high (thus will want more distribution so low g)
When marginal utility decreases fast with income (thus good to tax rich, who don’t get much utility from their additional consumption, to give to poor with a higher MU from consumption!)
Suppose the government wants to maximise tax revenue collected from top bracket
(since MU of consumption for rich is small thus better to tax).
What would a increase in the top bracket look like in diagram pg 13
Slope flatter moving away from 45 degree line, showing a higher tax rate
What 2 effects do we get as a result of increasing tax rate for the top bracket? pg 14
b) draw this to the diagram
Mechanical response: a fall in disposable income for these earners, and an increase in tax rev
Behavioural response: a fall in labour supply, reducing tax revenue!
So with these counteracting effects, where is optimal tax government sets
b) optimal tax rate for top bracket
Increase tax of top earners till
Mechanical effect of tax = size of behavioural response (dM+db=0)
b) t = 1 / 1+ae
where a is thinness of top tail= z/z-z*
higher a = not many people in top bracket, so benefit of increasing tax may not be a lot since not many people affected and paying the tax rate (empirically a=1.5)
So the top bracket people reduce labour supply in response to tax rises.
This is not the only behaviour response; which others (2)
tax avoidance (legal loopholes) or evasion (underreporting income illegally)
Why does distinguishing between labour supply responses vs the other 2 behavioural responses matte
Can’t do much with behaviorual responses
but they can address the other 2, e.g close loopholes, punishment
Issues with addressing tax evasion/avoidance (3)
System poorly designed (allows legal loopholes)
Hard - needs international cooperation (prevent 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 i.e lumpsump grant -T(z) > 0
(Since there won’t be lazy people who leave work, since only intensive response, so okay to transfer… I think
what does negative income tax (lumpsum grant) require to work
b) what does this look like (on pg 20 i drew)
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? (2)
Only targets transfer to the most needy (RMB we assume only intensive response!)
Intensive labour supply response at bottom does not generate large output losses to society anyways
When will people prefer a negative MTR at the bottom
b) what does this look like (i drew pg 20)
If society sees people with zero income as less deserving than average, so give to low income earners rather than non-workers
Draw transfer for non-workers, and high MTR at bottom to phase out, then a lower MTR after z*
b) then gov reduce genoristy of lumpsum, but reduce phase out rate pg22. Who benefits/loses, and as a result when pursue this policy? (Reducing generosity and phase out rate)
b) this is worse for non-workers, however workers get to keep their earnings more, then it is phased out (at the kink)
Workers: benefit from slower phase-out rate (keep more of earning), increases incentive to join workforce.
Gov: save revenue + more earnt from increased labour market participation
(rmb tho: only desirable if society low weight for zero earners, otherwise reducing generosity not good
Are participation labour supply responses (whether to work or not) are large/small at bottom?
b) What does their participation depend on?
Large at bottom (extensive margin big)
b)
Participation tax rate
I.e proportion of income taxed when moving from no earnings to earning z
