TAX HAVENS
FINAL PRESENTATION
Group 12:
Raluca Stanescu
Tiara Utomo
Tina Thomas
Yuxian Lun
MAIN ISSUE
What is the impact of tax havens on nonhaven countries in terms of foreign
investment?
Predicted result:
Economic activity in non-havens is diverted.
VARIABLES
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
Q(𝑲𝒏 ,𝑲𝒉 ) = Production function of firm’s output in countries outside of havens
𝑸(𝑲∗𝒉 )= Return to the tax haven earned in the tax haven itself
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax havens
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑲′𝒏 = Profit- maximising level of foreign investment
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝐾ℎ∗ = Fixed amount of capital given in tax haven
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
ASSUMPTIONS
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
Q(𝑲𝒏 ,𝑲𝒉) = Production function of firm’s output in countries outside of
havens
•To the extent that the firm is
able to use tax haven
investments to reduce
effective foreign tax rates on
income earned outside of
havens, it follows that 𝜏𝒕 ≤ 𝜏𝒏
𝑸(𝑲∗𝒉)= Return to the tax haven earned in the tax haven itself
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax
havens
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑲′𝒏 = Profit- maximising level of foreign investment
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝐾ℎ∗ = Fixed amount of capital given in tax haven
• Firms are assumed to invest equity capital for which
there is a shadow cost 𝝀.
EQUATIONS IN THE
MODEL
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
Q(𝑲𝒏 ,𝑲𝒉) = Production function of firm’s output in countries outside of
havens
𝑸(𝑲∗𝒉)= Return to the tax haven earned in the tax haven itself
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax
havens
If the firm elects not to invest in
the tax haven, its after-tax returns
are given by:
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑲′𝒏 = Profit- maximising level of foreign investment
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝜋1 ≡ 1 − 𝜏𝒏 𝑄 𝐾𝒏′ , 0 − 𝜆𝑐𝒏 𝐾𝒏′ .(1)
𝐾ℎ∗ = Fixed amount of capital given in tax haven
in which 𝐾𝑛′ = the profit-maximizing level of foreign investment,
characterized by the first-order condition:
1 − 𝜏𝑛
𝜕𝑄 𝐾𝑛′ ,0
𝜕𝐾𝑛
= 𝜆𝑐𝑛
(𝟐)
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
EQUATIONS IN THE
MODEL
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
Q(𝑲𝒏 ,𝑲𝒉) = Production function of firm’s output in countries outside of
havens
𝑸(𝑲∗𝒉)= Return to the tax haven earned in the tax haven itself
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax
havens
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑲′𝒏 = Profit- maximising level of foreign investment
If the firm instead chooses to invest in the tax
haven, its returns are given by:
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝐾ℎ∗ = Fixed amount of capital given in tax haven
𝜋𝒕 ≡ 1 − 𝜏𝒕 𝑄 𝐾𝒏∗ , 𝐾𝒉∗ + 𝑄 𝐾𝒉∗ − 𝜆(𝑐𝒏 𝐾𝒏∗ + 𝑐𝒉 𝐾𝒉∗ )
(3)
in which 𝐾𝑛∗ satisfies:
𝜕𝑄 𝐾𝑛∗ , 𝐾ℎ∗
1 − 𝜏𝑡
= 𝜆𝑐𝑛
𝜕𝐾𝑛
(𝟒)
EQUATIONS IN THE
MODEL
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
Q(𝑲𝒏 ,𝑲𝒉) = Production function of firm’s output in countries outside of
havens
𝑸(𝑲∗𝒉)= Return to the tax haven earned in the tax haven itself
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax
havens
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑲′𝒏 = Profit- maximising level of foreign investment
The first-order Conditions (2) and
(4) together imply that 𝐾𝑛′ and 𝐾𝑛∗
satisfy:
𝜕𝑄 𝐾𝑛∗ ,𝐾ℎ∗
𝜕𝐾𝑛
=
1−𝜏𝑛 𝜕𝑄 𝐾𝑛′ ,0
1−𝜏ℎ
𝜕𝐾𝑛
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝐾ℎ∗ = Fixed amount of capital given in tax haven
(5)
TWO CASES
We now consider two cases to demonstrate that the relationship between
𝜏𝑛 and 𝜏ℎ is theoretically ambiguous:
•
Case 1: firm can use tax havens to reduce foreign tax rates on income
earned outside of havens (𝜏𝑛 ≥ 𝜏ℎ ).
• Case 2: tax havens do not reduce foreign tax rates ( 𝜏𝑛 ⋍ 𝜏ℎ ).
1ST
𝝉𝟏 = Tax rate on the firm’s foreign investment
outside of tax havens
CASE
𝝉𝟐 = Tax rate on the profit if the firm also has a tax
haven operation
𝑲𝟏 = Level of capital investment in non-haven
𝑲𝟐 = Level of capital investment in haven
Q(𝑲𝟏 ,𝑲𝟐 ) = Production function of firm’s output in
countries outside of havens
Assumption:
𝑸(𝑲∗𝟐 )
= Return to the tax haven earned in the tax
haven itself

𝜕𝑄
𝐾𝑛 ,𝐾ℎ∗
𝜕𝐾𝑛
=
𝒄𝟏 = Cost per unit of capital investment in foreign
countries outside tax havens
𝜕𝑄 𝐾𝑛 ,0
𝜕𝐾𝑛
𝒄𝟐 = Cost per unit capital invested in the tax haven
𝑲′𝟏 = Profit- maximising level of foreign investment
𝝀
𝐾1∗ = Fixed amount of capital given in non haven
Because 𝜏𝑡 ≤ 𝜏𝑛
𝐾2∗ = Fixed amount of capital given in tax haven
1 − 𝜏𝑛 ≤ 1 − 𝜏𝑡
0<
=>
∗
𝝏𝑸 𝑲∗𝒏 ,𝑲𝒉
𝝏𝑲𝒏
= Shadow cost
≤
1−𝜏𝑛
1−𝜏𝑡
≤1
𝝏𝑸 𝑲′𝒏 ,𝟎
𝝏𝑲𝒏
(6)
1ST
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
CASE
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
The marginal product of capital
investment is subject to diminishing
returns => concavity.
Q(𝑲𝒏 ,𝑲𝒉) = Production function of firm’s output in countries outside of
havens
𝑸(𝑲∗𝒉)= Return to the tax haven earned in the tax haven itself
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax
havens
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑲′𝒏 = Profit- maximising level of foreign investment
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝐾ℎ∗ = Fixed amount of capital given in tax haven
Product of
capital
Investment
∗
𝝏𝑸 𝑲∗𝒏 ,𝑲𝒉
𝝏𝑲𝒏
≤
𝝏𝑸 𝑲′𝒏 ,𝟎
𝝏𝑲𝒏
(6)
So 𝑲∗𝒏 > 𝑲′𝒏
𝑲∗𝑛
𝑲′𝑛
Capital
investment
=> tax havens do not divert
investment in non - havens
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
2ND CASE
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
Q(𝑲𝒏 ,𝑲𝒉) = Production function of firm’s output in countries outside of
havens
1st Assumption: Tax havens do not
appreciably reduce effective foreign tax
rates
𝜏𝒏 ≅ 𝜏𝒕
𝑸(𝑲∗𝒉)= Return to the tax haven earned in the tax haven itself
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax
havens
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑲′𝒏 = Profit- maximising level of foreign investment
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝐾ℎ∗ = Fixed amount of capital given in tax haven
We have
𝜕𝑄 𝐾𝒏∗ ,𝐾𝒉∗
𝜕𝐾𝒏
=
1−𝜏𝒏 𝜕𝑄 𝐾𝒏′ ,0
1−𝜏𝒕
𝜕𝐾𝒏
(5)
So
𝜕𝑄 𝐾𝒏∗ ,𝐾𝒉∗
𝜕𝐾𝒏
=
𝜕𝑄 𝐾𝒏′ ,0
𝜕𝐾𝒏
If
𝑓 𝐾𝑛 , 𝐾ℎ
=
𝜕𝑄 𝐾𝑛 ,𝐾ℎ
𝜕𝐾𝑛
𝒇
Then
𝒇
𝐾𝑛∗ , 𝐾ℎ∗ = 𝑓 𝐾𝑛′ , 0
𝑲∗𝒏 , 𝑲∗𝒉 = 𝒇 𝑲′𝒏 , 𝟎 > 0
(7)
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
2ND
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
CASE
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
Q(𝑲𝒏 ,𝑲𝒉) = Production function of firm’s output in countries outside of
havens
2nd
Assumption: If the marginal product of
capital in non-havens falls as more capital
is invested in havens
𝑸(𝑲∗𝒉)= Return to the tax haven earned in the tax haven itself
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax
havens
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑲′𝒏 = Profit- maximising level of foreign investment
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝐾ℎ∗ = Fixed amount of capital given in tax haven
( specifically, if
𝜕2 Q K𝑛 ,Kh
𝜕Kn 𝜕Kh
< 0 (8) )
𝑓 𝐾𝑛∗ , 𝐾ℎ∗ = 𝑓 𝐾𝑛′ , 0 > 0
𝜕2 Q Kn ,Kh
𝜕Kn 𝜕Kh
<0
(7)
(8)
From 1st and 2nd assumption:
𝒇 𝑲′𝒏 , 𝟎 > 𝒇 𝑲′𝒏 , 𝑲∗𝒉 ∀ 𝑲∗𝒉 > 𝟎
(9)
2ND
𝝉𝒏 = Tax rate on the firm’s foreign investment outside of tax havens
CASE
𝝉𝒕 = Tax rate on the profit if the firm also has a tax haven operation
𝑲𝒏 = Level of capital investment in non-haven
𝑲𝒉 = Level of capital investment in haven
Q(𝑲𝒏 ,𝑲𝒉) = Production function of firm’s output in countries outside of
havens
𝑓
𝐾𝑛∗ , 𝐾ℎ∗
=𝑓
𝐾𝑛′ , 0
𝑸(𝑲∗𝒉)= Return to the tax haven earned in the tax haven itself
(7)
𝒄𝒏 = Cost per unit of capital investment in foreign countries outside tax
havens
𝒄𝒉 = Cost per unit capital invested in the tax haven
𝑓 𝐾𝑛′ , 0 > 𝑓 𝐾𝑛′ , 𝐾ℎ∗
𝑲′𝒏 = Profit- maximising level of foreign investment
(9)
𝛌 = Shadow cost
𝐾𝑛∗ = Fixed amount of capital given in non haven
𝐾ℎ∗ = Fixed amount of capital given in tax haven
Product of
capital
Investment
Then
𝑓 𝐾𝑛∗ , 𝐾ℎ∗ > 𝑓 𝐾𝑛′ , 𝐾ℎ∗
So..
𝑲∗𝑛 < 𝑲′𝑛
𝑲∗𝑛
𝑲′𝑛
Capital
investment
=> tax havens do divert investment in
non-havens
RESULT
1st CASE:
𝑲′𝒏 < 𝑲∗𝒏
=> tax havens do not divert
investment in non - havens
2nd CASE:
𝑲′𝒏 > 𝑲∗𝒉
in non-havens
=> tax havens do divert investment
We get two different results.
Conclusion? The result is theoretically ambiguous.
RESULT
So, the tax havens do not necessarily harm the economic
activity in non-havens.
In the end – it depends on tax rates, amount of capital
invested, shadow costs etc.
REFERENCES
• Desai, Mihir A. and Foley, C. Fritz and Hines Jr., James R.,
Do Tax Havens Divert Economic Activity? (April 2005).
Ross School of Business Paper No. 1024.