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

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

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

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

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

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

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

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

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

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

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

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

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