economics assignment

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

ECO 364 - International Trade Lecture 3: The Ricardian Model

ECO 364 - International Trade Fall 2018 Ricardian Model 1

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Motivation

Why do economists generally think that international trade is a good thing?

ECO 364 - International Trade Fall 2018 Ricardian Model 2

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Motivation

Why do countries trade what they do?

US

exports

(2016)

Chinese

exports

(2016)

Source: The Observatory of Economic Complexity. http://atlas.media.mit.edu

ECO 364 - International Trade Fall 2018 Ricardian Model 3

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Overview

I Last week (exchange economies):

I trade allows countries to gain by exchanging endowments I countries export goods in which they have a comparative advantage I i.e. goods that they have relatively more of

I What was missing:

I where do endowments come from? I how do things like productivity and technology shape trade patterns? I how does trade affect wages and employment?

I To study this, extend exchange economy model by introducing production

I one factor of production: labor I abstract from other factors: capital, land, etc.

ECO 364 - International Trade Fall 2018 Ricardian Model 4

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Overview

(1) (2) (3) (4)

exchange Ricardian specific Hecksher-Ohlin

economy model factors model model

# countries 2 2 2 2

# goods 2 2 2 2

# factors - 1 2 2

factors mobile no yes 1 yes, 1 no yes

across sectors?

ECO 364 - International Trade Fall 2018 Ricardian Model 5

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Overview

I Etymology: David Ricardo, 1772-1823, British economist I Prevailing international trade theory of the time - Mercantilism:

I exporting is good because it generates wealth for the country I importing is bad because it drains wealth from the country I therefore high import tariffs are desirable I trade is a zero-sum game

I Ricardo argued that this theory was incorrect

I On the Principles of Political Economy and Taxation (1817) I all countries can gain from trade... I by exporting goods in which they have a comparative advantage I trade is not a zero-sum game

ECO 364 - International Trade Fall 2018 Ricardian Model 6

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Overview

I Key ideas:

I trade can be beneficial because countries differ in terms of technology I differences in technology can be a source of comparative advantage I so countries export what they are relatively better at producing

I Adam Smith, Wealth of Nations, Book IV, Chapter II:

It is the maxim of every prudent master of a family never to attempt to make at home what it will cost him more to make than to buy.

ECO 364 - International Trade Fall 2018 Ricardian Model 7

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Closed Economy Model

I First consider a single country “Home”

I Two sectors (goods): 1 and 2

I both goods produced using only labor I labor is mobile across the two sectors I market structure is perfect competition

I Representative household in Home:

I endowed with LH units of labor I consuming C1, C2 of the two goods yields utility U (C1, C2) I U has standard properties of a utility function

ECO 364 - International Trade Fall 2018 Ricardian Model 8

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Budget Set

I Let w H denote the wage I Let pH1 , p

H 2 the prices of goods 1 and 2, with relative price p

H r ≡ pH1 /p

H 2

I Household has income I H derived from its labor income:

I H = w H LH

I Household’s budget constraint:

pH1 C H 1 + p

H 2 C

H 2 ≤ I

H

ECO 364 - International Trade Fall 2018 Ricardian Model 9

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Utility Maximization

I Given prices, household chooses consumption to maximize utility:

max C H

1 ,C H

2

U (

C H1 , C H 2

) s.t. pH1 C

H 1 + p

H 2 C

H 2 ≤ I

H

I First-order conditions imply:

MRS H ≡ U H1 /U H 2 = p

H 1 /p

H 2

ECO 364 - International Trade Fall 2018 Ricardian Model 10

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Production

I Production technology available to firms in Home:

I 1 unit of labor produces aH1 units of good 1 I 1 unit of labor produces aH2 units of good 2

I aH1 , a H 2 referred to as the marginal product of labor (MPL) for each good

I Note that constant MPLs ⇒ no diminishing returns to scale I Marginal costs of production (cost of producing 1 unit):

mc H1 = w H /aH1 , mc

H 2 = w

H /aH2

where w H is the wage level

ECO 364 - International Trade Fall 2018 Ricardian Model 11

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Production Possibilities Frontier

I How much of each good can be produced given the available technology? I Let X H1 , X

H 2 denote total output of goods 1 and 2

I Total labor used to produce goods 1 and 2:

LH1 = X H 1 /a

H 1 , L

H 2 = X

H 2 /a

H 2

I Home’s production possibilities frontier (PPF):

X H1 /a H 1 + X

H 2 /a

H 2 ≤ L

H

ECO 364 - International Trade Fall 2018 Ricardian Model 12

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Profit Maximization

I Market structure is assumed to be perfect competition

I firms take prices as given and choose output to maximize profits

I Formally, profit-maximization problem for a firm producing good i ∈{1, 2} is:

max X H

i

{ pHi X

H i − mc

H i X

H i

} I What must the price of each good be in equilibrium?

ECO 364 - International Trade Fall 2018 Ricardian Model 13

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Market Clearing

I Case 1: pH i

> mc H i

I return to producing good i is greater than its cost I optimal supply of good i is +∞ I market for good i cannot clear

I Case 2: pH i

< mc H i

I return to producing good i is less than its cost I optimal supply of good i is 0 I market for good i cannot clear

I Case 3: pH i

= mc H i

I return to producing good 1 is equal to its cost I firms make zero profits and are indifferent about producing any quantity I market for good i can clear

ECO 364 - International Trade Fall 2018 Ricardian Model 14

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Market Clearing

I Perfect competition implies prices must equal marginal costs of production:

pH1 = w H 1 /a

H 1 , p

H 2 = w

H 2 /a

H 2

I Since labor is freely mobile...wages must be equal across sectors:

w H1 = w H 2 = w

H

e.g. if w H1 > w H 2 , no workers in sector 2 and market for this good cannot clear

I Therefore the relative price is equal to the inverse of relative MPL, aHr ≡ aH1 /a H 2 :

pHr = 1/a H r

I Real wages are equal to MPLs:

w H /pH1 = a H 1 , w

H /pH2 = a H 2

ECO 364 - International Trade Fall 2018 Ricardian Model 15

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Equilibrium

I At the equilibrium prices, the PPF and the household’s budget set are identical:

Budget Set PPF

ECO 364 - International Trade Fall 2018 Ricardian Model 16

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Demand Production Market Clearing Equilibrium

Equilibrium

I Equilibrium consumption is then determined by the household’s utility maximization problem at the equilibrium prices:

ECO 364 - International Trade Fall 2018 Ricardian Model 17

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

The pattern of specialization The effect of trade on wages

Small Open Economy

I Now suppose that Home can trade at world prices pW1 , p W 2

I i.e. as in previous lecture, assume that Home is a small open economy

I Recall that if Home produces both goods, then the zero-profit conditions require:

pW1 = w H /aH1 , p

W 2 = w

H /aH2

I Therefore the world relative price pWr ≡ pW1 /p W 2 must satisfy:

pWr = a H 2 /a

H 1

i.e. pWr must be the same as the autarky relative price p H r

I However, with trade, it is possible for all workers to be hired in one sector

I i.e. for complete specialization to occur... I because demand for the other good can be satisfied by foreign imports

ECO 364 - International Trade Fall 2018 Ricardian Model 18

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

The pattern of specialization The effect of trade on wages

Case 1: Home specializes in production of good 1

I In this case, the profit conditions require:

pW1 = w H /aH1 , p

W 2 < w

H /aH2

I The world relative price must therefore satisfy:

pWr > a H 2 /a

H 1

I Home produces at point A I Trade allows it to consume at point B , achieving higher utility

ECO 364 - International Trade Fall 2018 Ricardian Model 19

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

The pattern of specialization The effect of trade on wages

Case 2: Home specializes in production of good 2

I In this case, the profit conditions require:

pW1 < w H /aH1 , p

W 2 = w

H /aH2

I The world relative price must therefore satisfy:

pWr < a H 2 /a

H 1

I Home produces at point A I Trade allows it to consume at point B , achieving higher utility

ECO 364 - International Trade Fall 2018 Ricardian Model 20

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

The pattern of specialization The effect of trade on wages

The effect of trade on wages

I Note that trade also leads to an increase in real wages

I Case 1 : Home specializes in good 1

I real wages: w H /pW1 = a

H 1 , w

H /pW2 > a H 2

I real wage in terms of good 2 exceeds MPL for good 2

I Case 2: Home specializes in good 2

I real wages: w H /pW1 > a

H 1 , w

H /pW2 = a H 2

I real wage in terms of good 1 exceeds MPL for good 1

I Intuition: real wages increase because trade allows workers to specialize....

I in producing the good in which the country has a comparative advantage

ECO 364 - International Trade Fall 2018 Ricardian Model 21

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Two-country Model

I Now introduce another country “Foreign”

I Foreign differs from Home only in terms of its:

I labor endowment LF

I technology (MPLs) aF1 , a F 2

I In particular, we will assume that...

I Home has an absolute advantage in both goods:

aH1 > a F 1 , a

H 2 > a

F 2

I but Home has a comparative advantage in good 1 and Foreign has a comparative advantage in good 2:

aH1 /a H 2 > a

F 1 /a

F 2

ECO 364 - International Trade Fall 2018 Ricardian Model 22

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Two-country Model

I Recall that in autarky:

Home Foreign

ECO 364 - International Trade Fall 2018 Ricardian Model 23

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Two-country Model

I Now suppose Home and Foreign are allowed to trade

I Key questions:

1. Will the countries trade? 2. Which country will export/import which good? 3. Which country will gain/lose from trade? 4. How much will be traded and at what prices?

ECO 364 - International Trade Fall 2018 Ricardian Model 24

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Comparative Advantage

I Key to the analysis: the concept of comparative advantage

I Recall that a country has a comparative advantage in a good if...

I its autarky relative price is lower than the world relative price under trade I autarky relative price = relative price that results in autarky, i.e. pHr , p

F r

I From closed economy analysis, autarky prices depend on relative MPLs:

pHr = a H 2 /a

H 1 , p

F r = a

F 2 /a

F 1

I In this model, comparative advantage is therefore equivalent to...

I having a relative MPL greater than that of the other country

I “Law of Comparative Advantage”:

I countries export goods in which they have a comparative advantage

I Intuition: lower autarky relative price ≈ good is relatively less scarce

ECO 364 - International Trade Fall 2018 Ricardian Model 25

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Will the countries trade?

I From analysis of the SOE case, we know that:

I Home will specialize in good 1 if pWr > 1/a H r

I Home will specialize in good 2 if pWr < 1/a H r

I same logic applies to exports/imports by Foreign

I Also recall that aHr > a F r by assumption

I Therefore to determine if trade occurs, we can consider several possible cases

ECO 364 - International Trade Fall 2018 Ricardian Model 26

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Will the countries trade?

I Case 1:1/aHr < 1/a F r < p

W r

I both countries specialize in good 1 I world market for good 2 cannot clear

I Case 2: pWr < 1/a H r < 1/a

F r

I both countries specialize in good 2 I world market for good 1 cannot clear

I Case 3: 1/aHr < p W r < 1/a

F r

I Home specializes in good 1 I Foreign specializes in good 2 I potential for trade

ECO 364 - International Trade Fall 2018 Ricardian Model 27

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Will the countries trade?

I Note that it is also possible for incomplete specialization to occur

I Case 4: 1/aHr = p W r < 1/a

F r

I Home produces both goods I Foreign specializes in good 2 I potential for trade

I Case 5: 1/aHr < p W r = 1/a

F r

I Home specializes in good 1 I Foreign produces both goods I potential for trade

ECO 364 - International Trade Fall 2018 Ricardian Model 28

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Which country will export/import which good?

I In any case, the pattern of trade is dictated by comparative advantage

I By assumption: aH1 /a

H 2 > a

F 1 /a

F 2

I That is, the opportunity cost of producing good 1 in terms of good 2 is lower in Home than in Foreign, and therefore:

I Home produces good 1 and exports it to Foreign I Foreign produces good 2 and exports it to Home

I Does the pattern of trade depend on:

I absolute advantage, i.e. levels of a1 and a2?No! I differences in labor endowments, LH and LF ?No!

ECO 364 - International Trade Fall 2018 Ricardian Model 29

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Which country will gain/lose from trade?

I From SOE analysis:

I a country gains from being able to trade... I at any relative price different from its autarky relative price

I Immediately implies that both Home and Foreign must gain from trade!

I Calculation of welfare is exactly the same as in SOE given pWr

ECO 364 - International Trade Fall 2018 Ricardian Model 30

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Real wages

I As in SOE case, trade leads to increases in real wages

I Since Home produces good 1, the zero profit condition requires:

w H

pW1 = aH1

so that Home’s real wage in terms of good 1 is the same as in autarky

I Since Foreign produces good 2, the zero profit condition requires:

w F

pW2 = aF2

so that Foreign’s real wage in terms of good 2 is the same as in autarky

ECO 364 - International Trade Fall 2018 Ricardian Model 31

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Real wages

I However, since 1/aHr ≤ pWr ≤ 1/aFr , then:

w H

pW2 =

( w H

pW1

) pWr = a

H 1 p

W r ≥ a

H 2

w F

pW1 =

( w F

pW2

) 1

pWr =

aF2 pWr ≥ aF1

I Trade can lead to an increase in:

I Home’s real wage in terms of good 2 I Foreign’s real wage in terms of good 1

I With complete specialization, both real wages strictly increase

ECO 364 - International Trade Fall 2018 Ricardian Model 32

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

How much will be traded and at what prices?

I Export supply and import demand depend on world relative price pWr

Home Foreign

I As pWr increases from a H 2 /a

H 1 to a

F 2 /a

F 1 :

I Home increases both exports of good 1 and imports of good 2 I Foreign reduces both imports of good 1 and exports of good 2

ECO 364 - International Trade Fall 2018 Ricardian Model 33

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

How much will be traded and at what prices?

I pWr must be such that export supply equals import demand

I For example, in the good 1 market:

ECO 364 - International Trade Fall 2018 Ricardian Model 34

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices?

Formal solution

I To determine trade volumes and prices, need to solve the equilibrium conditions

I You will explore this step by step in this week’s problem set!

ECO 364 - International Trade Fall 2018 Ricardian Model 35

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Empirical Evidence Summary

Empirical Evidence

Source: MacDougall, Donald. 1951. “British and American Exports: A Study Suggested by the

Theory of Comparative Costs. Part I,” Economic Journal, 61, pp. 697–724.

ECO 364 - International Trade Fall 2018 Ricardian Model 36

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Empirical Evidence Summary

Empirical Evidence

Source: Balassa, Bela. 1963. “An Empirical Demonstration of Classical

Comparative Cost Theory,” Review of Economics and Statistics, 45(3), pp. 231-238.

ECO 364 - International Trade Fall 2018 Ricardian Model 37

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Empirical Evidence and Summary

Empirical Evidence Summary

Summary

I Studied trade between two countries with different production technologies

greater relative MPL

⇒ lower autarky relative price ⇒ comparative advantage

I Countries export goods in which they have a comparative advantage

I both countries gain through specialization

I Theory illustrates the problem with some common arguments against trade:

I “trade is good only if your country is strong enough to compete” I “foreign competition is unfair when it is based on low wages” I “trade exploits workers if they receive low wages”

I Next lecture: introduce additional factor of production immobile across sectors

I i.e. a specific-factors model I will allow us to see how some factors gain/lose from trade... I even though gains from trade are positive on average

ECO 364 - International Trade Fall 2018 Ricardian Model 38