Optimal Labour Income Tax (tough+important) Flashcards
2 types of transfer programs:
Universal transfers e.g public education
Means-tested transfers
Adjusted gross income (AGI)
Labour income + capital income
Taxable income equation
Taxable income = AGI - personal exemptions - deduction
Taxable income is… but marginal tax rates are…
B) individual income tax diagram
C) Marginal income tax diagram
Taxable income is continuous (smoothly increases as income increases) but marginal tax rates are constant; a step function (e.g goes from 20 to 40% in UK, no inbetween)
2 types of tax credits
Non-refundable (cannot reduce taxes below zero) e.g child care expenses
Refundable (can reduce taxes below zero i.e net transfers) e.g EITC (earned income tax credit) offers working families income based on how many kids they have
Refundable tax credits is thus a form of means tested transfers!
Like EITC, based on means i.e must be a working family and based on number of kids
EITC structure for individual with one child
If 0 income, cannot claim EITC (so have to work! - means tested)
EITC payout increases at rate of 34 cents for every additional dollar earnt until 10k
From then the payout is constant, and then at 18k, they’ll begin to decrease/phase-out their payments (reduce the amount you get)
Phased out fully at 40k.
US: tax filing
B) what system do they use
Taxes on year t, will be filed in Feb-April of year t+1 (the next year)
B) 3rd party reporting: Payers (employers, banks etc) send income information to government (since self-reporting could lie)
US main means-tested transfer programs (2), and what’s the main difference
Traditional transfers: by welfare agencies, paid on monthly basis
Refundable income tax credits e.g EITC: by tax administration, paid as an annual lump sum in year t+1
Main difference is traditional paid monthly, tax credits annually
Take up rates between the 2 means-tested transfer programs
Low take up for traditional, high for refundable tax credits
UK means-tested transfer program
Universal credit: allows part-time work without losing their entitlement to benefits
Budget set
Along 45 degree line: pre-tax income = post tax income i.e 0% tax rate: you are not paying tax
Above 45 degree line = post tax income>pre tax income (we are receiving transfers)
Below 45 degree line = pre tax income>post tax income i.e we are getting taxed
Z : pre-tax income
Z - T(Z) : post-tax income (disposable income)
Pg 20 - explain the budget set line intuition
B) slope of budget set line
C) participation tax rate
Lumpsum grant: we start at -T(0) i.e
A) Constant MTR; same tax rate for everyone. Point we intersect the 45 degree line (z) means no longer receive transfers. From z we pay tax at T’(z): so individual keeps 1-T’(Z) for every extra $1.
B) Constant marginal tax rate with slope 1-T’(z)
C) Participation tax rate (tp): proportion of income taxed when moving from not working to earning amount Z (after taxes and benefit reductions)
so tp is amount they pay, (1-tp)Z is
what they keep
So previous budget sets show constant MTR since budget line is constant.
US vs France budget set
For zero earners - We can see France is more
generous (higher -T(0)
but less generous than US with earners, they tax out the benefits quicker than US. US incentivise work
Once around 30k. MTR is larger in France, so they pay higher taxes (further away from 45 degree line i.e zero tax)
Problem with traditional means-tested programs
Reduce incentives to work for low income workers
E.g like France, rewards those not working!
How to solve
And Eval:
Refundable tax credits increase incentive to work for low income workers.
However refundable tax credit doesn’t benefit those with zero earnings (trade-off between helping zero earners vs workers)
How to find optimal taxation: assume government have utilitarian objective: what is their social welfare function
What assumption also
We assume everyone has the same utility function
SWF = Σu(zi - T(zi))
Sum of utilities of individuals (which is a function of their disposable income/consumption)
Remember z-T(z) is disposable income/consumption
This utilitarian government are subject to budget constraint:
Σ T(zi) = 0
I.e since some tax rates are negative, some are positive, so overall =0 which means all revenue is used for redistribution
So at what point do they maximise social welfare
Maximise social welfare where MU across individuals is equal. (And given they have the same utility function, this will occur at the same level of income for everyone)
Why is this utilitarian objective of government unrealistic
Since this states maximising social welfare requires equal incomes!
Which means 100% tax rate and redistribution. (Take all money and redistribute evenly!) IRL would have have behavioural response - equity-efficiency trade off, people would work less etc!!
Derivation with 2 individuals rather than ‘everyone’ is easier…
What would their max SWF (and subject to BC)
B) then solve
Max SWF = u[z₁-T(z₁)] + u[z₂ - T(z₂)]
Subject to
T(z₁) + T(z₂) = 0
B) rearrange BC to T(z₁) = -T(z₂) , then sub into SWF
SWF = u[z₁ + T(z₂)] + u[z₂ - T(z₂)]
(Turns into + T(z₂) as double negative —)
Then differentiate FOC with respect to T(z₂)
dSWF/dT(z₂) = u’[z₁ + T(z₂)] - u’[z₂ - T(z₂)] = 0
(Just a dashed version lol)
Then replace T(z₂) back with -T(z₁) , which shows
u’[z₁ - T(z₁)] = u’[z₂ - T(z₂)] !!!! (MU equal)
so also z1 - Tz(z1) = z2 - T(z2)
I.e SWF is maxised where MU is constant across the 2 individuals!
Diagram of utiliarian objective of government
Utility function same for everyone, concave.
Before tax rate, first person consumes c1, and individual 2 was consuming more at c2.
Now with tax, took money from individual 2 with low MU (since consumes more), and give to individual 1 with low MU, to make consumption is equal
Result: new utility is higher than the previous average
So what is government ability to redistribute constrained by
Behavioural responses! Unrealistic to try to achieve full equity, since inefficiency if individuals respond
Labour supply theory:
Utility is a function of what
B) what is their budget constraint
Consumption c (positive)
Labour supply l (negative, since increased l means less leisure so less utility)
Max u(c,l)
B) subject to c = wl + r
Consumption = net of tax wage rate (wages after tax) x hours worked + non-labour income
