Apply tools of logical reasoning, graphical methods and mathematics to solve basic decision problems faced by consumers and firms.

Assignment 2
Tax revenue consequences from the 2021 new top personal tax rate
Peer Ebbesen Skov
ECON620 – Microeconomics: Markets and Welfare

Learning outcome 1:
Apply tools of logical reasoning, graphical methods and mathematics to solve basic
decision problems faced by consumers and firms.
Learning outcome 3:
Measure the social welfare generated by different market outcomes or Government
interventions.
Learning outcome 4:
Apply the “economic way of thinking” to a range of applications.
Learning outcome 5:
Present economic analysis in written and verbal form.
1
1 Background
On 30 November 2020, the New Zealand government enacted a new top personal income tax
rate of 39% on annual income exceeding $180,000 for the year ending 31 March 2022 (2022
tax year) and later income years. Part of the reason behind this new higher marginal tax
rate was a revenue objective (The Government needed to reduce the fiscal impact of higher
operating allowances).1
Table 1 below shows the tax schedule for each of the two tax years 2021 (column 2) and 2022
(column 3). The 2021 tax schedule includes four brackets with the lowest tax rate 10.5%
applied to income below $14,000 and the highest 33% tax rate applied to income above
$70,000. The 2020 reform introduced a new, fifth, income bracket and tax rate whereby
income above $180.000 is taxed at 39%.
Tax Rates by Income Bracket for 2021 and 2022
ddIncome Bracketdd dddTax Rateddd dd2021 Tax Yeardd dd2022 Tax Yeardd
$0 – $14,000 t1 10.5% 10.5%
$14,001 – $48,000 t2 17.5% 17.5%
$48,001 – $70,000 t3 30% 30%
$70,001 – $180,000 t4
33% 33%
$180,001 – t5 %39
In the following case study, you are part of a small consultancy group that are asked to
predict the revenue implications of this new tax bracket and rate: how much (extra) revenue
will the Government collect.
1See page 10 (Labour’s 2020 Election Manifesto).
2
Part A: Stylised Illustration of a Tax Reform
Consider a simple two-bracket tax system with a marginal tax rate t1 on pre-tax income (z)
below a threshold K and a marginal tax rate t2 > t1 on the income exceeding K. Illustrate
in a diagram (with pre-tax income (z) on the x-axis and after-tax income (c) on the y-axis)
the budget set created by the tax system. Show how the budget set changes when the top
tax rate (t2) is increased and explain the link between the marginal tax rate and the slope
of the budget line. Discuss how the increase in t2 could affect individuals’ labour supply
decisions.
[Hint: Chapter 2 Budget Constraints Workshop]
Part B: Tax Revenue Impact
The tax revenue from the new 39% top income tax (t5) is given by:
R = t5(z − K)N
where z is the average pre-tax income for the individuals above the threshold K (NZD
180,000) and N is the number of top threshold taxpayers. The associated excel data includes
the 2019 taxable income distribution, use those data to find N and calculate z. Predict the
total revenue collected from this new tax rate and bracket. How much additional tax revenue
is collected as a result of the new tax rate and bracket?
[Hint: Chapter 2 Budget Constraints Workshop]
3
Part C: Revenue Effects from Marginal Tax Changes
The effect of a marginal increase in (t5) on the government’s revenue can be expressed as2
:
dR

dt5

1
α
−
t5
1 − t5
ε

Nz, where α =
z
z − K
Estimates of the elasticity of taxable income ε suggest this parameter is equal to 0.15 (NB.
previous version incorrectly gave the ε as -0.15). Use your data set to calculate α and find
dR
(dt5)
(i.e. plug in all the parameters in the above formula and report the resulting dollar
amount). Provide an interpretation of α and comment on how dR
(dt5)
depends on α. Compare
and contrast the revenue consequences calculated in Part C with those in Part B.
[Hint: Chapter 8 Slutsky Equation Workshop]
2This derivation assumes that z depends positively on the after-tax rate (1−t5) with a constant elasticity.
The appendix shows the full derivation for completeness, however, it is not required to solve the question.
4
Appendix: Derivation of dR
dt
R = t(z − K)N
Assume that z depends positively on the after-tax rate (1 − t) with a constant elasticity ε.
dR
dt = (z − K)N + t
dz
dt N
Where the first component is the “mechanical effect” and the second is the “behavioural

effect”.

z − K
z
+
t
1 − t
dz
d(1 − t)
d(1 − t)
dt
1 − t
z

Nz
where we’ve used the chain rule to express dz
dt as dz
d(1−t)
d(1−t)
dt . Using d(1−t)
dt = −1 along with
the definition of the elasticity of taxable income (wrt. to net-of-tax rate) ε =
dz
d(1−t)
1−t
z
, we
obtain:
dR
dt = (z − K)N + t
dz
dt N

z − K
z
−
t
1 − t
ε

Nz =

1
α
−
t
1 − t
ε

Nz
5