1. Multi-Market Analysis by Alan V. Deardorff University of Michigan 2018
PubPol/Econ 541
Multi-Market Analysis by Alan V. Deardorff University of Michigan 2018

2. Outline Large country tariff
Differentiated-Product Import, Small Country
Import Input to Production of Nontraded Final Good
Tariff on Imports from One Country but Not Another

3. Recall: Small-Country Tariff
Domestic Market
P D
SD(PD)
Welfare Effects of Tariff:
Dom sup’s +a
Dom dem’s –(a+b+c+d)
Dom gov’t +c
Dom cty –(b+d)
(1+t)PW a c b d PW
DD(PD)
𝑆 0 𝐷
𝑆 1 𝐷
𝐷 1 𝐷
𝐷 0 𝐷
𝑄 𝐷
Figure 1
Tariff in a Small Country on a Homogeneous Good

4. Outline Large country tariff
Differentiated-Product Import, Small Country
Import Input to Production of Nontraded Final Good
Tariff on Imports from One Country but Not Another

5. Recall: Large-Country Tariff
Domestic Market
Foreign Market PD PF
SD(PD)
DF(PF)
SF(PF)
1+𝑡)𝑃 1 𝑊 a
𝑃 0 𝑊 b c d
𝑃 0 𝑊 e g f h i
𝑃 1 𝑊
𝑃 1 𝑊
DD(PD)
𝑄 𝐷
𝑄 𝐹
𝑆 0 𝐷
𝑆 1 𝐷
𝐷 1 𝐷
𝐷 0 𝐷
𝐷 0 𝐹
𝐷 1 𝐹
𝑆 1 𝐹
𝑆 0 𝐹
Welfare Effects of Tariff:
Dom sup’s +a
Dom dem’s –(a+b+c+d)
Dom gov’t (c+e)
Dom cty e–(b+d)
For sup’s –(f+g+h+i)
For dem’s +f
For gov’t 0
For cty –(g+h+i)
World –(b+d+g+i)
This was a multi-market analysis
Figure 2
Tariff in a Large Country (“Domestic”) on a Homogeneous Good

6. Outline Large country tariff
Differentiated-Product Import, Small Country
Import Input to Production of Nontraded Final Good
Tariff on Imports from One Country but Not Another

7. Differentiated-Product Import, Small Country
Domestic Good
Import PD PM
𝑆 𝐷 𝑃 𝐷
𝑃 1 𝐷 b b
𝑃 1 𝑀 =(1+𝑡 𝑃 0 𝑀 a f c h d
𝑃 0 𝐷 e g
𝑃 0 𝑀
𝑆 𝑀
𝐷 𝑀 𝑃 𝑀 , 𝑃 1 𝐷
𝐷 𝐷 𝑃 𝐷 , 𝑃 1 𝑀
𝐷 𝑀 𝑃 𝑀 , 𝑃 0 𝐷
𝐷 𝐷 𝑃 𝐷 , 𝑃 0 𝑀
𝑄 𝐷
𝑄 𝑀
Welfare Effects of Tariff:
Dom sup’s (a+b)
Dom dem’s –(a+b+c+d)
& –(e+g)
Dom gov’t (e+f)
Dom cty –(c+d+g–f)
But (c+d) = (f+h)
(Why? Trust me.) So
Dom cty –(f+h+g–f)
= – (h+g)
Figure 4
Tariff on Imported Imperfect Substitute for Domestic Good

8. Differentiated-Product Import, Small Country
Domestic Good
Import PD PM
𝑆 𝐷 𝑃 𝐷
𝑃 1 𝐷 b
𝑃 1 𝑀 =(1+𝑡 𝑃 0 𝑀 a f h c d
𝑃 0 𝐷 e g
𝑃 0 𝑀
𝑆 𝑀
𝐷 𝑀 𝑃 𝑀 , 𝑃 1 𝐷
𝐷 𝐷 𝑃 𝐷 , 𝑃 1 𝑀
𝐷 𝑀 𝑃 𝑀 , 𝑃 0 𝐷
𝐷 𝐷 𝑃 𝐷 , 𝑃 0 𝑀
𝐷 𝑀 𝑃 𝑀 , 𝑃 𝐷 ( 𝑃 𝑀 )
𝑄 𝐷
𝑄 𝑀
Is “ceteris paribus” demand curve
𝐷 𝑀 𝑃 𝑀 , 𝑃 0 𝐷
Welfare Effects of Tariff:
Dom sup’s (a+b)
Dom dem’s –(a+b+c+d)
& –(e+g)
Dom gov’t (e+f)
Dom cty –(c+d+g–f)
But (c+d) = (f+h)
(Why? Trust me.) So
Dom cty –(f+h+g–f)
= – (h+g)
𝐷 𝑀 𝑃 𝑀 , 𝑃 𝐷 ( 𝑃 𝑀 )
Is “mutatis mutandis” demand curve
Figure 4
Tariff on Imported Imperfect Substitute for Domestic Good

9. Outline Large country tariff
Differentiated-Product Import, Small Country
Import of Input to Production of Final Good
Tariff on Imports from One Country but Not Another

10. Tariff on Input to Production of Traded of Final Good
Imported Input
𝑆 𝐹 𝑃 𝐹 , 𝑃 1 𝐼 PF PI
𝑆 𝐹 𝑃 𝐹 , 𝑃 0 𝐼
𝑃 𝐹 a
𝑃 1 𝐼 =(1+𝑡 𝑃 0 𝐼
𝑃 0 𝐹 b c
𝑃 0 𝐼
𝑆 𝑀
𝐷 𝐹 𝑃 𝐹
𝐷 𝐼 𝑃 𝐼 , 𝑃 1 𝐹
𝑄 𝐹
𝑄 𝐼
𝑄 1 𝐹
𝑄 0 𝐹
𝑄 1 𝐼
𝑄 0 𝐼
Welfare Effects of Input Tariff:
Dom sup’s –a = –(b+c)
Dom dem’s 0
Dom gov’t b
Dom cty –c
Why?
𝑆 𝐹 shifts up by cost increase.
If PF
Rises to 𝑃 𝐹 then suppliers are unharmed.
Their loss from price not rising is area a
Note: In this case the position of DF does not matter, since PF does not change.
Figure 5
Tariff on Imported Input to Traded Final Good Production

11. Tariff on Input to Production of Non-Traded of Final Good
Imported Input
𝑆 𝐹 𝑃 𝐹 , 𝑃 1 𝐼 PF PI
𝑆 𝐹 𝑃 𝐹 , 𝑃 0 𝐼
𝑃 𝐹 d e
𝑃 1 𝐹 a
𝑃 1 𝐼 =(1+𝑡 𝑃 0 𝐼 b c i
𝑃 0 𝐹 f g h j
𝑃 0 𝐼
𝑆 𝑀
𝐷 𝐼 ?
𝐷 𝐼 𝑃 𝐼 ,PF ( 𝑃 𝐼 )
𝐷 𝐼 𝑃 𝐼 , 𝑃 0 𝐹
𝐷 𝐹 𝑃 𝐹
𝐷 𝐼 𝑃 𝐼 , 𝑃 1 𝐹
𝑄 𝐹
𝑄 𝐼
𝑄 1 𝐹
𝑄 0 𝐹
𝑄 1 𝐼
𝑄 0 𝐼
Welfare Effects of Input Tariff:
Dom sup’s –(d+e)
Dom dem’s –(a+b+c)
Dom gov’t f
Dom cty –(a+b+c+d+e)+f )
But (a+d+e) = (f+g+h+i)
= what suppliers would have lost if PF had not risen
So Dom cty –(a+b+c+d+e)+f = –(b+c+g+h+i)
And (b+c) = i = j
The extra loss to the private sector due to price rise from 𝑃 0 𝐹 to 𝑃 1 𝐹
So Dom cty – (g+h+i+j)
Figure 5
Tariff on Imported Input to Production of Non-traded Final Good

12. Outline Large country tariff
Differentiated-Product Import, Small Country
Import Input to Production of Nontraded Final Good
Tariff on Imports from One Country but Not Another

13. Tariff on One Country but Not Another
with countries exporting imperfect substitutes
Imports from Country B
Imports from Country C
(1+𝑡𝐵 𝑃 0 𝐵 a b
𝑃 0 𝐶
𝑆 𝐶
𝑆 𝐵
𝑃 0 𝐵
𝐷 𝑀𝐶 𝑃 𝐶 , 𝑃 1 𝐵
𝐷 𝑀𝐵 𝑃 𝐵 , 𝑃 0 𝐶
𝐷 𝑀𝐶 𝑃 𝐶 , 𝑃 0 𝐵
Welfare Effects of Tariff on B:
Dom pvt –(a+b)
Dom gov’t +a
Dom cty –b
Figure 6
Tariff on imports from only Country B,
imperfect substitute for imports from Country C