5 - Optimal Labour Income Taxation Flashcards
what are refundable tax credits
- benefits received as long as they are working - doesnt benefit unemployed
- rewarded with excess taxes that they otherwise would have been owed
assumptions of the simple model
- 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
what does the simple model do
as long as assumptions hold
- perfect equalisation
- everyone gets the same post tax/transfer income
- 100% redistributional
what does the simple model do
equation
maximises the sum of everyones utilities subject to the BC of the governments income (taxes=transfers)
what does the simple model prove
that maximising the utilities = the optimal tax solution is 100% MTR = perfect equalization
what are the issues with the simple model
- 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
why should the simple model incorporate fairness
- bounds on how much redistribution the gov can do
what is the equity efficiency trade off
- 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
what factor limits the ability of gov to redistribute with taxes and transfers
- 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
what is -T(0)
transfer benefit with 0 earnings
lumpsum grant
what is T’(z)
what is 1 - T’(z)
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
what is the participation tax rate
why is it important
(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
what is T(Z*)
the break even point
- they get no benefit / loss from taxes or transfers
what is the difference between traditional means tested programs and refundable tax credits
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
what are the 2 different kind of models we can use to choose the optimal tax rate
without behavioural responses = simple model (horizontal line)
with behaviour responses (shallow slope)
what is the labour supply theory
equation
maximise utility (function of consumption and labour)
maxU(C,L)
subject to BC of income
C = w*l + R
what is the income effect
more income = increased consumption and decreased leisure
what is the substitution effect
increased income = the OC of leisure has increased, leisure is more expensive, so will increase labour
what is the difference between marshallian and hicksian labour supply
marshallian = maximise utility s.t BC
hicksian = minimise labour needed to reach utility given wage slope
what is uncompensated elasticity
substitution effect
considers only the response to price changes - doesnt consider the adjustment of consumers income
what is the Slutsky equation
eU = eC + income effect
what does
T(z) > 0
T(z) <0 mean
- net taxes
- net transfers
under what conditions is labour supply discouraged
(must mean that increases disposable income)
when z < z* = net transfers
T(z) < 0 = net transfers
T’(z) > 0 = being taxed for working
what is the effect of net transfers on labour supply
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
what is the effect of net taxes on labour supply
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
what is the effect of taxes and transfers on labour supply for someone operating at z* before
they will choose to work fewer hours because the new tangency point is no longer maximising their utility, they can move up a curve
what relationship does the laffer curve capture
the relationships between tax rates and tax revenue
what tax rate will max tax revenues
what is the tax revenue function for laffer curve
what happens if t = 0 and t = 1
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
what is the optimal linear tax rate Rawlsian
equation
t* = 1/1+e
what is the elasticity of average income wrt the net of tax rate
dZ/d(1-t) * (1-t)/Z
what is the problem with t > t*
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
under a Rawlsian gov which approach is better
optimising t* is best
because will make revenue as large as possible, making transfers larger
- will help the poorest person in society more
Rawlsian
choose t to maximise the tax revenue function
laffer curve
utilitarian
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
what is the optimal linear tax rate
Utilitarian
equation
t = 1-(g-) / 1-(g-) + e
what does the t* for utilitarian formula capture
and how
the equity efficiency tradeoff
increasing efficiency = decreasing t
increasing gov taste for redistribution = smaller g = t increases
what does g- capture?
what does e capture?
equity
- captures the distributional part
efficiency
- efficiency in raising tax revenues and hours worked
what does g=0 or g=1 represent
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
under what conditions is t close to the laffer rate t*?
- g- is low
- when inequality is high
- MU decreases fast with income
- gov has strong taste for redistribution
what is the UK tax system like
individual tax is progressive with brackets with increasing MTR
what will happen to labour supply if the optimal tax income rate changes for the highest bracket
- 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
what are the 2 effects occuring when tax rate for top income bracket changes
- there will be a mechanical increase in tax revenue, but behavioural response will reduce tax revenue
mechanical = tax increase
behavioural response = tax loss
what is the mechanical increase
how much extra tax revenue would the tax change have generated if there was no behavioural response
what is the mechanical increase
equation
dt * [z - z*]
change in tax * (how much they are earning above the threshold)
what is the behavioural response
- rich people will reduce the hours worked
- fall in z
- so there will be a loss in tax from increasing the tax rate
what is the behavioural response
equation
-t/1-t * e * z * dt
what is the optimal tax rate for top bracket equation
when DM = DB
t* = 1/ 1 + (a*e)
a = z / z - z*
why does DM = DB need to equal in order to maximise tax revenue
what happens if DM > DB
what happens if DB > DM
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
when does the optimal t value decrease?
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
what is a
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
what are all of the behavioural responses to income taxes
- reduced labour supply
- tax avoidance
- tax evasion
what is tax avoidance
legal way to reduce tax liability by exploiting loopholes
what is tax evasion
illegal under-reporting of income
what can the government do to reduce these behavioural effects of income tax
- reduced labour supply
- the government cant prevent this from happening - evade/avoid = government can reduce this
what ways is it possible from the gov to eliminate tax avoidance (legal way)
- better designed tax codes
- international cooperate = off shore tax evasion in tax havens
hard:
3. technological limitations of tax collection (how to tax informal cash business = hard)
what are the limitations of the
t* = 1/ 1 + (ae) model
- model doesnt include extensive earnings responses - only includes intensive
- doesnt include fiscal externalities
- doesnt include classical externalities
- charitable donations
- positive spillovers (trickledown)
