Using these slides
• These slides are used in a second year undergraduate
course, EC201, Microeconomic Principles I at the
London School of Economics.
• Details of the tax system change every year. The slides
give sources and websites for the information.
• The educational objective is to show students how
economic analysis, particularly the modelling of budget
constraints and income and substitution effects can be
used to understand the impact of taxes on households.
• The models used here oversimplify the tax system, but
students find them quite complicated enough.
• More details models are available on the Institute for
Fiscal Studies website.
© Margaret Bray
LSE
1
Taxes
• Start with a brief overview of the UK tax system
to give you context.
• You are not expected to remember the details of
this.
2
Income tax rates
• Data comes from HMRC (Her Majesty’s
Revenue and Customs)
• The home page is http://www.hmrc.gov.uk/
• Details of rates are at
http://www.hmrc.gov.uk/rates/it.htm
3
• Changes in tax rates are usually announced in
the budget in the spring.
• But some changes are often announced in the
pre-budget report in the autumn.
• See the Treasury website
http://www.hm-treasury.gov.uk/index.cfm
4
IFS
• The IFS (Institute for Fiscal Studies) website
http://www.ifs.org.uk/ has a large amount of useful
information on taxes.
• See particularly
Fiscal Facts http://www.ifs.org.uk/fiscalfacts.php for details
of the system
“Labour Supply and Taxes”, Costas Meghir and David
Phillips at http://www.ifs.org.uk/wps/wp0804.pdf IFS
Working Paper IFS Working Papers, W08/04
(March 2008) for an overview of the literature on labour
supply, taxes and benefits.
5
Stuart Adam, “A Survey of the UK Tax System”,
IFS Briefing Note BN09
This explains the system and gives rates for 20056.
You can find it on
http://www.ifs.org.uk/bns/bn09.pdf
6
Revenue raised by UK taxes
Total government receipts are projected to be
£516 billion in 2006-2007, which is 40.3% of GDP.
This Tax figure is equivalent to £12,740 for every
member of the working age population (15-65), or
to £8,515 per person.
Income tax, National Insurance and VAT are the
main source of revenue for the government,
together accounting for 60.1% of total receipts.
7
Sources of government revenues – projection for 2006-2007
£bn
% of total
Income tax
144.0
27.9
National Insurance
89.6
17.4
Value added
76.5
14.8
Fuel
24.0
4.7
Tobacco
8.0
1.6
Betting and gaming
1.4
0.3
Other indirect tax
13.6
2.6
Capital gains tax
3.8
0.7
Corporate tax
49.0
9.5
Council tax
22.0
4.3
8
Source: HM treasury, Budget Report, 2006
Taxes on Consumption
• VAT (value added tax) charged at 17.5% is the main tax
on consumption.
• Some goods are exempt from VAT.
(e.g. children’s clothes)
• Some goods are subject to additional taxes
(e.g. alcohol, tobacco, fuel, these are often
complicated as the next slides show)
9
Taxes on Alcohol (in addition to VAT)
Product and basis of duty
Duty
Rate per litre of pure alcohol
Spirits
£19.56
Rate per hectolitre (100 litres) per cent of
alcohol in the beer
Beer
£13.26
Rate per hectolitre (100 litres) of product
Wine and made-wine:
exceeding 1.2% - not exceeding 4%
£53.06
abv.
10
Source: http://www.hmrc.gov.uk/
Taxes on Tobacco (in addition to VAT)
Product
Duty
Cigarettes
22 %retail price plus £105.10
per thousand cigarettes
Cigars
£153.07 per kilogram
Hand-rolling tobacco
£110.02 per kilogram
Other smoking
tobacco
and
chewing tobacco
£67.30 per kilogram
Source: http://www.hmrc.gov.uk/
11
Taxes on Fuel (in addition to VAT)
Pence per litre
Sulphur-free petrol/diesel
Ultra low sulphur petrol/diesel
Biodiesel
Bioethanol
Duty rate
48.35p
48.35p
28.35p
28.35p
12
Source: http://www.hmrc.gov.uk/
UK Taxes on Income
• Income tax is paid on all income including
income from employment and income from
investments.
• National Insurance Contributions (NICs) are paid
on income from employment only.
13
Modelling the Effects of an
Income Tax
14
• Budget constraint without tax
Pc = W(T – n) or Pc + Wn = WT
or c + wn = wT
c = consumption, T = total time,
n = time outside paid employment “leisure”
W = money wage rate, P = price of consumption
w = W/p = real wage rate
15
The effects of a 20% proportional
income tax.
16
• Assume at first for simplicity that the only tax is a
proportional income tax of 20% or total earnings.
• Tax revenue = total tax paid = 0.2 W (T-n)
(W = money wage rate, T – n = hours worked)
• Budget constraint with tax
Pc = W (T – n) – 0.2 W(T-n)
or Pc = 0.8 W (T – n)
(P = price of good, c = consumption)
• Budget constraint with income tax can be written as
c + 0.8 wn = 0.8 wT
17
where w = W/p = real wage rate.
• Assume that the imposition of the income tax
does not change the wage rate W or the price of
goods P
so the real wage before tax w = W/P does
not change. (May not be realistic).
• Then the effect of the tax is to change the
budget constraint from
c + wn = wT
to c + 0.8wn = 0.8wT.
• In effect the 20% income tax changes the real
wage rate from w to 0.8w.
18
c
wT
This diagram is distorted to
make it easier to follow,
0.8wT should be much
closer to wT, and the slopes
of the lines should be much
closer to each other.
0.8wT
slope - w
slope – 0.8 w
0
T
n19
c
wT
budget constraint with no tax
slope - W/P = - w
budget constraint with tax
slope – 0.8 W/P = - 0.8 w
0.8wT
consumer’s
optimum with tax
(c*,n*)
0
T
n20
Tax revenue given T- n* and c* as labour and consumption
= 0.20 W (T – n*) (0.2 = tax rate, W wage, T – n* labour)
= W T – 0.8 WT - 0.2 n* W
= WT – (Pc* + 0.8 W n* ) – 0.2 n* W
(because from the budget constraint Pc* + 0.8Wn* = 0.8WT)
= WT – (Pc* + Wn*)
= WT – cost of (c*, n*) at pre tax prices P and W
21
wT
line through (c*,n*) with
slope - W/P = - w
and equation
c* + wn*
c – c* = - w (n – n*)
when n = 0 line meets the
vertical axis and
0.8wT
c = c* + wn*
(c*,n*)
0
T
n22
wT
From 2 slides back
tax revenue =
WT – (Pc* + Wn*)
c* + wn*
= P (wT – (c* + wn*) )
0.8wT
=P
(c*,n*)
0
T
n23
Definition: Equivalent Variation for a
price change
•
•
•
•
•
The price of good 1 starts at p1A.
At this price utility is uA.
The price of good 1 rises to p1B
p2 does not change.
Taking away the equivalent variation, EV, without
changing p1 from p1A has the same effect on
utility as increasing p1 from p1A to p1B without
changing income.
24
Definition: Equivalent Variation of a tax
• The tax changes the price of good 1 “leisure”
from W to 0.8W.
• Taking away the equivalent variation, EV, without
changing the price of “leisure” has the same
effect on utility as imposing the tax.
25
wT
Taking away the EV
(equivalent variation) from
the consumer has the
same effect on utility as
imposing the tax.
Show the budget line that
gives the EV.
0.8wT
(c*,n*)
0
T
n26
wT
Taking away the EV
(equivalent variation) from
the consumer has the
same effect on utility as
imposing the tax.
Show the budget line that
gives the EV.
0.8wT
slope – 0.8 w
(c*,n*)
0
T
n27
wT
EV = P
0.8wT
slope – 0.8 w
(c*,n*)
0
T
n28
wT
tax revenue = P
c* + wn*
EV = P
0.8wT
(c*,n*)
0
T
n29
wT
tax revenue = P
c* + wn*
EV = P
0.8wT
Tax revenue – EV
= P
(c*,n*)
0
T
n30
wT
Definition: Excess burden of a tax
= tax revenue
– equivalent variation
c* + wn*
= P
0.8wT
(c*,n*)
0
T
n31
wT
Taking
from the consumer as a
lump sum gives the
budget constraint
and the same tax revenue
as the income tax but is better for
the consumer.
c* + wn*
0.8wT
(c*,n*)
0
T
n32
This is a general argument.
A lump sum tax that reduces income by a fixed
amount that does not depend on anything the
consumer does reduces utility by less than a tax
where the revenue can be changed by changing
consumption, work or saving.
(e.g. excise tax, VAT, income tax…)
The only feasible lump sum tax is a “poll tax”
where everyone pays the same amount.
Is a poll tax ethically desirable?
Is a poll tax politically feasible?
33
The effects of a 25% proportional
consumption tax.
34
• Now assume at that the only tax is a
proportional tax on consumption at a rate of
25% on total consumption.
(e.g. a sales tax or VAT)
• Total tax paid = 0.25 P c
(P = price of consumption c)
• Budget constraint with consumption tax
Pc = W (T – n) – 0.25 Pc
or 1.25 Pc = W (T – n)
or 1.25 c + wn = wT
where w = W/p = real wage rate.
35
• Assume that the imposition of the consumption
tax does not change the wage rate W or the
price of goods P
so the real wage rate before tax P = W/p
does not change. (May not be realistic).
• Then the effect of the tax is to change the
budget constraint from
c + wn = wT to 1.25 c + wn = wT
or dividing by 1.25 and noting that 1/1.25 = 0.8
the budget constraint with a 0.25 % consumption
tax is
c + 0.8 wn = 0.8 wT.
36
• If the only tax is a proportional 20% income tax
the budget constraint is c + 0.8wn = 0.8wT.
• If the only tax is a proportional 25% consumption
tax the budget constraint is c + 0.8wn = 0.8wT.
• A proportional income tax at a rate of 25% has
exactly the same effect as a proportional
consumption tax at a rate of 20%.
• In effect the 20% income tax changes the real
wage rate from w to 0.8w.
37
In both cases the budget constraint is the same,
c + 0.8 wn = 0.8 wT
or as w = W/P multiplying by P
Pc + 0.8 W n = 0.8 WT
so standard consumer theory tells us that
consumers behave in the same way with the two
taxes.
Revenue from consumption tax is 0.25 Pc.
Revenue from income tax is 0.20 W (T – n).
But from the budget constraint Pc = 0.8 W ( T – n)
so consumption tax revenue is
0 .25 Pc = 0.25 x 0.8 W (T-n) = 0.2 W (T – n)
38
= income tax revenue.
c
wT
budget constraint with 20%
income tax or with 25%
consumption tax constraint
slope
- W/(1.25)P
0.8wT
= - 0.8 W/P = 0.8w.
slope - w
slope – 0.8 w
0
T
n39
• More generally, we get the same budget constraint
with a proportional income tax at rate tm as with a
proportional consumption tax at a rate tc if
(1 - tm ) (1+ tc ) = 1.
• Both taxes have the same effect on the budget
constraint and thus on consumer behaviour.
• The revenue raised by the two taxes is the same.
• All the arguments are exactly the same as before
with 0.20 replaced by tm and 0.25 replaced by tc so
(1 - tm ) (1+ tc ) = 0.8 x 1.25 = 1.
40
A more realistic model of income
tax
• More realistically income tax is not directly
proportional to income.
• Income tax schedule divide income into tax
brackets.
41
Suppose that there are three tax brackets
Bracket 1 £ 0 - £5000
Bracket 2 £5000 - £20 000
Bracket 3 > £20 000.
With an income of £15 000 you have
£ 5000 in bracket 1
£ 15 000 – 5000 = £10 000 in bracket 2.
42
bracket
3
income
£15 000
£20,000
bracket
2
£0
in bracket 3
£10 000
in bracket 2
£5,000
bracket
£0 1
£5000
in bracket 1
43
Suppose that there are three tax brackets
Bracket 1 £ 0 - £5000
Bracket 2 £5000 - £20 000
Bracket 3 > £20 000.
With an income of £30 000 you have
£ 5000 in bracket 1
£ 20 000 – 5000 = £15 000 in bracket 2.
£ 30 000 - 20 000 = £10 000 in bracket 3.
44
bracket
3
income
£30 000
£20,000
bracket
2
£10 000
in bracket 1
£15 000
in bracket 2
£5,000
bracket
£0 1
£5000
in bracket 1
45
• An income tax system gives a marginal tax rate
for each bracket, with higher brackets having
higher marginal tax rates.
• The system described in the next slide has
marginal tax rates
0 % bracket 1
20% bracket 2
40 % bracket 3
• Total income tax
=
0.00 (income in bracket 1)
+ 0.20 (income in bracket 2)
+ 0.40 (income in bracket 3).
46
Usual description of this tax scheme
total annual £
marginal tax income rate
< 5000
0
5000 - 20000
20 %
> 20000
40 %
47
tax
income
bracket
£15,000
£0
in 40% bracket
40%
£20,000
£10,000
in 20% bracket
20%
£5,000
£5,000
0%
in 0% bracket
£0
total tax = 0 x 5000 + .20 x 10,000 + 0.40 x 0
= £2,000
48
Definition: Marginal Income
Tax Rate
Marginal income tax rate is the number of extra
pennies tax you pay on £1 extra earnings.
With a 20% marginal income tax rate you pay
£ 0.20 = 20p
extra tax when you earn £1 more.
In the previous slide the marginal income tax rate
for someone earning £15000 is 20%.
49
Definition: Average Income
Tax Rate
Average Income Tax rate = total income tax
total income
In the previous someone earning £15000 pays
income tax
£ 0 x 5000 + .20 x 10,000 + 0.40 x 0
= £2,000
so average income tax rate = 2000 = 13%
15 000
50
tax
income
bracket
£15,000
£0
in 40% bracket
40%
£20,000
£10,000
in 20% bracket
20%
£5,000
£5,000
0%
£0
in 0% bracket
marginal tax rate 20%
average tax rate 2 000/15 000 = 13%
51
tax
income
bracket
£30,000
£10,000
in 40% bracket
40%
£20,000
£15,000
in 20% bracket
20%
£5,000
£5,000
0%
in 0% bracket
£0
total tax = 0 x 5000 + 0.20 x 15 000 + 0.40 x 10 000
52
= £7 000
tax
income
bracket
£30 000
£10 000
in 40% bracket
40%
£20,000
£15 000
in 20% bracket
20%
£5 000
£5,000
0%
£0
in 0% bracket
marginal tax rate 40%
average tax rate 7 000/30 000 = 23%
53
See consumer theory worked example 10 on
website for more explanation and details of how
to calculate the budget constraint.
54
annual consumption (£)
Budget Constraint
slope - 2.4
wage £4 per hour
17000
slope - 3.2
5000
8760
3760
7510
time outside employment (annual hours)
55
Important
Find the kinks by looking at hours and
after tax income at tax bracket boundaries.
56
With a wage of £4 per hour
earning £5000 takes
£5000/4 = 1250 hours
and leaves annual
time outside employment of
8760 - 1250 = 7510 hours.
8760 = 365 x 24 = hours in year.
With £5000 income tax paid = 0,
so (7510,5000) is the corresponding point on the
budget constraint. (5000 = income)
57
annual consumption (£)
Budget Constraint
slope - 2.4
wage £4 per hour
17000
slope - 3.2
5000
8760
3760
7510
time outside employment (annual hours)
58
With a wage of £4 per hour earning £20000 takes
£20000/4 = 5000 hours
and leaves annual time outside employment of
8760 - 5000 = 3760 hours.
8760 = 365 x 24 = hours in year.
With £20 000 income tax paid
= 0 x 5000 + 0.2 x 15000 = 3000
so (3760,17000) is the corresponding point on the
budget constraint. (17000 = after tax income =
20000 – 3000)
59
annual consumption (£)
Budget Constraint
slope - 2.4
wage £4 per hour
17000
slope - 3.2
5000
8760
3760
7510
time outside employment (annual hours)
60
Slope of the budget constraint
• The slope of the budget constraint = - w (1-tm)
where tm is the marginal income tax rate and
w is the hourly wage rate.
61
2006 – 7 Income Tax
total annual £
< 5035
marginal tax income rate
0
5035 - 7185
10 %
7185 - 38335
22 %
The UK tax
system
> 38335
40 %
The tax rates rarely change. From April 2000 until
April 2008 the rates were 10%, 22% and 40%.
The tax brackets change every year in April
(roughly at the inflation rate), don’t try to remember 62
them exactly.
2007 – 8 Income Tax
total annual £
marginal tax income rate
< 5435
0
5435 - 41 435
20 %
> 41 435
40 %
The UK tax
system
In April 2008 the 10% rate was abolished, and the
“basic rate” was cut from 22% to 20%.
63
2006 - 7 approximate tax brackets
total annual £
< 5000*
marginal tax income rate
0
5000 - 7000
10 %
7000- 38000
22 %
38000
40 %
The UK tax
system
* The level at which income starts to be taxed is called the
“personal allowance” which depends among other things
on age.
64
National Insurance Contributions (NIC)
• These function as an additional income tax
system.
• They are determined by weekly income. Income
Tax is determined by annual income.
The UK tax
system
65
weekly
income
£y
< 97
employee’s NIC
£
0
employer’s NIC
£
0
97 - 645
0.11(y – 97)
0.128( y – 97)
> 645
0.11(645 – 97)
+ 0.01(y – 645)
0.128( y – 97)
2006 – 07 NICs
66
weekly
income
£y
< 89
employee’s NIC
£
0
employer’s NIC
£
0
89 - 585
0.10(y – 89)
0.118( y – 89)
>585
0.10(585 – 89)
+ 0.01(y – 585)
0.118( y – 89)
0.118( y – 89)
2002 – 3 NIC
67
Why the change in structure of NIC?
In April 2003 NICs for both employers and
employees were increased by 1% NIC on
earnings above the NIC threshold.
This was announced in the March 2002
budget.
It has much the same effect as a 2% rise
in the income tax rate.
But there was a political commitment not
to change income tax rates.
68
Modelling budget constraints
69
Diagrams for seeing
budget constraints
consumption
The Economist’s
Diagram
c
The economists
diagram has the
advantage that
indifference
curves have
their usual
shape.
But non
economists
don’t
understand it.
budget set
0
“leisure” n
70
Flip the economists’ diagram horizontally.
income
after tax
indifference curves
slope the other
way.
0
hours worked
This diagram makes much more
sense to non economists.
71
You often see diagrams with
earnings before tax rather
than hours worked on the
horizontal axis.
Earnings
after tax
With this diagram the shape
of the graph does not depend
on the wage rate.
0
Contrast with previous
slides.
earnings
72
Flat Tax
• Introduced Russia 2001,
and in other transition economies
• Simpler than the UK income tax structure.
• Discussed UK, US, Germany
73
Flat Tax
• Simpler than the UK income tax structure.
• Exempts a fixed amount of income,
then has the same marginal tax rate at all
levels of income.
74
Example of a flat tax
• £10 000 tax exempt income
• 30% marginal tax rate
• Total tax payment
income y ≤ £10 000
income y > £10 000
tax 0
tax 0.30(y – 10 000)
75
Relative to existing tax
• A flat tax would decrease marginal tax rates at
the bottom of the income distribution (more
people tax exempt)
• and at the top (lower marginal tax rate).
76
Arguments for
a flat tax
• Reduces tax rates so increases labour supply.
(this argument is not right, see next slide)
• Simplification of the tax system reduces
administration costs and improves compliance.
77
• Labour supply may or may not increase when a
flat tax is introduced.
• Introducing a flat tax changes marginal and
average tax rates
• Analyse the effects on labour supply using
income and substitution effects.
78
You need to understand and
remember
• When the average income tax rate falls people
are better off, assuming “leisure” to be a normal
good the income effect reduces labour supply.
• When the average income tax rate rises people
are worse off, assuming “leisure” to be a normal
good the income effect increases labour supply.
79
earnings
after tax
 average income tax rate, makes
people better off.
assume time outside employment
normal good
income effect
 labour supply
w(1 – t)
earnings
80
You need to understand and
remember
• When the marginal income tax rate falls the
substitution effect increases labour supply.
• When the marginal income tax rate rises the
substitution effect decreases labour supply.
81
slope budget line w(1 – t)
earnings
t marginal income tax rate
after tax
Decrease marginal tax rate from t1 to
t2 steeper budget line,
subst effect  labour supply
w(1 – t2)
w(1 – t1)
earnings
82
Flat Taxes
• The UK has 4 tax brackets (marginal tax rates of
0%, 10%, 22% and 40%).
• In its simplest form a “flat tax” has only two tax
brackets, 0% and for example 30% marginal tax
rates.
• The next slides compare between a multi rate
system with 3 tax brackets and a flat tax system
with 2 brackets.
83
earnings
after tax
multi rate
income tax
Tax bracket
boundaries
earnings
84
earnings
after tax
flat tax
Tax bracket
boundary
earnings
85
effect of flat tax
earnings
after tax
multi rate
income tax
flat tax
earnings
86
• The next slides work through the effects of the
change to a flat tax both on utility and on the
labour supply and different levels of income.
• You are not expected to remember the details of
this argument.
• You are expected to be able to analyse a
change in the tax system in this way, using
income and substitution effects.
87
effect of flat tax
earnings
after tax
multi rate
income tax
flat tax
= earnings – total tax
Higher line has lower
average tax rate.
earnings
88
effect of flat tax
earnings
after tax
average
tax rates
In regions
the flat tax gives lower
average tax rate, utility increases.
earnings
89
effect of flat tax
earnings
after tax
multi rate
income tax
flat tax
Slope of line = 1 – tm where tm is marginal
income tax rate. Steeper line has lower
marginal tax rate.
earnings
90
effect of flat tax
earnings
after tax
Marginal
tax rates
In regions
flat tax gives lower
marginal tax rate.
earnings
91
effect of flat tax
earnings
after tax
lower average tax rate with flat tax,
lower marginal tax rate with flat tax
earnings
92
effect of flat tax
earnings
after tax
both average and marginal tax rates
fall with flat tax, effect on lab supply earnings
93
ambiguous (see next slide)
• When the average tax rate falls people are
better off, assuming “leisure” to be a normal
good the income effect reduces labour supply.
• When the marginal tax rate falls the substitution
effect increases labour supply.
• When both average and marginal tax rates fall
the effect on labour supply is ambiguous
94
effect of flat tax
earnings
after tax
both average and marginal tax rates
rise with flat tax, effect on lab supply earnings
95
ambiguous (see next slide)
• When the average tax rate rises people are
worse off, assuming “leisure” to be a normal
good the income effect increases labour supply.
• When the marginal tax rate rises the substitution
effect decreases labour supply.
• When both average and marginal tax rise the
effect on labour supply is ambiguous
96
effect of flat tax
earnings
after tax
average tax rate falls, marginal tax
rates rises with flat tax, labour supply
decreases (see next slide)
earnings
97
• When the average tax rate falls people are
better off, assuming “leisure” to be a normal
good the income effect reduces labour supply.
• When the marginal tax rate rises the substitution
effect decreases labour supply.
• When the average tax rate falls and the marginal
tax rates rises labour supply falls.
98
effect of flat tax
earnings
after tax
average tax rate rises, marginal tax
rate falls with flat tax, labour supply
increases
earnings
99
Summing up the Impact of a Change
in Income Tax
• You are definitely better off if a change to the
income tax schedule reduces your average tax
rate.
• The effect on labour supply depends on what
happens to both the marginal and average tax
rates. It is ambiguous if income and substitution
effects work in opposite directions.
• The effects of a change to income tax are
usually different at different levels of income.
100
Russia’s `Flat Tax`
• Ivanova, Keen, Klemm,
• Economic Policy June 2005
• Before top marginal tax rate 30%
• After marginal tax rate 13%.
• Revenue increased by 26%.
101
Russia’s `Flat Tax`
• Other changes in tax system
• better compliance
• No evidence for increased labour supply.
102
Possible Flat Tax in UK
• simplify income tax (one marginal
tax rate rather than three)
• but complications of tax system
are interaction of income tax, other
taxes and benefits.
103
Flat Tax in UK
• labour supply effects unclear
• top and bottom of income
distribution better off
• mid range income worse off
104
effect of flat tax
earnings
after tax
average
tax rates
Gainers from a flat tax
Losers from a flat tax
earnings
105
from
Economist
September
8 2005
106
Options for a UK ‘flat tax’
Stuart Adams and James Browne
Institute for Fiscal Studies, http://www.ifs.org.uk/
August 2006
This discusses various possibilities including the one we
have looked at.
The outcome depends greatly on the details of the system.
There is no simple story.
107