ECON 2167: International Economics

Curtis Aquino

Department of Economics
University of Western Ontario
 Week 1: The Ricardian Model (1/24)

I We will begin this course with “old” trade theory over the next four weeks

I In these models, trade arises from differences in technology and factor endowments across countries

I Today, we will study the Ricardian model of international trade

I This model is one of the oldest in trade theory and even economics as a whole

I As one of the first theories in trade, it is motivated by a relatively simple observation:

I Empirical Fact 1: Advanced countries import products they could easily produce themselves

I This observation motivated Ricardo to ask the following question:

I Question: Why do technologically advanced countries import from less advanced countries?
 Week 1: The Ricardian Model (2/24)

I The basic set-up of the Ricardian model of international trade is as follows:

1. Agents: two countries, domestic D and foreign F

2. Endowments: countries have L̄C , C ∈ {D, F } labor available

3. Technology: labor L is the only input in production with constant marginal returns

4. Preferences: utility for D and F is strictly increasing in apples A and bananas B

5. Markets: perfectly competitive with free labor mobilitity between industries

I We will start by solving the model without trade then allow trade between the countries

I Our goal is to derive the supply and demand of traded goods and the welfare gains from trade
 Week 1: The Ricardian Model (3/24)

I Representing the Ricardian model mathematically, we have:

AC = αC × LC,A , C ∈ {D, F } (1)

BC = βC × LC,B , C ∈ {D, F } (2)

L̄C = LC,A + LC,B , C ∈ {D, F } (3)

I From equations 1 and 2, the MPL for apples and bananas are constants αC and βC , respectively

I The marginal product of labor (MPL) is the change in output from a change in labor

I These MPL are constant because, e.g., ∆AD = αD × ∆LD,W =⇒ M P LD,A = αD

I Equation 3 is a resource constraint — total labor demand cannot exceed total labor supply
 Week 1: The Ricardian Model (4/24)

I With these equations in hand, we can draw the production possibilities frontier (PPF)

I The PPF shows all combinations of outputs that can be produced using all available resources

I If country C only produced apples (or bananas) they could make αC × L̄C apples (or βC × L̄C bananas)
 Week 1: The Ricardian Model (5/24)

I We know that production in country C must take place on (or inside of) the PPF

I For example, suppose (αD , βD , L̄D ) = (4, 2, 25) and (αF , βF , L̄F ) = (1, 1, 100)
 Week 1: The Ricardian Model (6/24)

I The slope of the PPF tells us how many bananas we have to give up to get one more apple

I Likewise, the inverse of the slope tells us how many apples to get one more banana

I We know two points on these PPFs — the x- and y-intercepts — let’s compute the slope directly:

βC × L̄C − 0
Slope of the PPF = (4)
0 − αC × L̄C

βC
=− (5)
αC

M P LC,B
=− (6)
M P LC,A
 Week 1: The Ricardian Model (7/24)

I For our linear PPF, the slope is constant at −βC /αC . What if our PPF was non-linear?

I Consider (A0 , B0 ) and the change in apple labor ∆LA needed to produce (A1 , B1 )

B1 − B0
Slope of the PPF = (7)
A1 − A0

B1 − B0 ∆LA
= × (8)
A1 − A0 ∆LA

M P LB
=− (9)
M P LA

I The slope of the PPF is always the (negative of the) ratio of MPLs

I Negativity comes from B1 − B0 and ∆LA always having the opposite sign
 Week 1: The Ricardian Model (8/24)

I Differences in M P LA and M P LB reflect differences in production technologies across countries

I e.g., if αD > αF then domestic is said to have an absolute advantage in producing apples

I e.g., if αD /βD > αF /βF then domestic is said to have a comparative advantage in producing apples

I Recall: the opportunity cost (OC) of something is the highest valued foregone alternative

I In our two-good economy, this makes the OC of an apple the slope of the PPF by definition

I e.g., domestic has a comparative advantage in apples if its OC is lower than foreign’s

I In general, the OCX is the ratio of M P LY to M P LX and the slope of the PPF
 Week 1: The Ricardian Model (9/24)

I So far, we have pinned down the set of production possibilities in each country

I Now we’ll add in firms. By Assumption 3, firms in each country are perfectly competitive

I Recall: perfect competitors produce where marginal revenue (equals price) equals marginal cost

I To pin down marginal cost, ∆T C/∆Q, consider the MC for domestic apple producers:

M CD,A = ∆(T V C + T F C)/∆AD (10)

= wD,A × ∆LD,A /∆AD (11)

= wD,A /M P LD,A (12)

= PD,A (13)
 Week 1: The Ricardian Model (10/24)

I This allows us to identify the price ratio of apples to bananas. For example, for domestic:

PD,A wD,A βD
= × (14)
PD,B wD,B αD

I By freely mobile labor, wages will equalize in a country wC,A = wC,B . Hence:

PD,A βD
= (15)
PD,B αD
 
= Slope of the PPF (16)
 

PC,A
I Perfectly competitive profit-maximizing firms produce where = |Slope of the PPF|
PC,B
 Week 1: The Ricardian Model (11/24)

I Now we know the set of production possibilities and the perfectly competitive equilibrium prices

I Without trade, all that remains is to find which point on the PPF consumers in each country choose

I Domestic and foreign consumers find (AD , BD ) and (AF , BF ) that maximize their respective utility
 Week 1: The Ricardian Model (12/24)

I Consumers find the indifference curve that provides the highest utility while still being feasible

I Recall: an indifference curve (IC) collects all bundles for which the consumer is equally well-off

I All points on ICs farther from the origin are strictly preferred to those that are closer
 Week 1: The Ricardian Model (13/24)

I Points too far (e.g., Y ) are not feasible and points too close are not utility-maximizing (e.g., Z)

I Given these hypothetical ICs, consumers are most well-off when the IC is tangent to the PPF

I This outcome — at X and X 0 — illustrates an autarkic no-trade equilibrium

 Week 1: The Ricardian Model (14/24)

I Now let’s allow these countries to trade and see how the model rationalizes our empirical observation

I Conjecture: even if αD > αF and βD > βF both countries can gain from trade. How?

I Idea: each country can specialize by only producing if they have a comparative advantage

I To determine comparative advantages, we need to compute each good’s opportunity cost

I Recall: OCX = M P LY /M P LX , so the OC of apples is β/α and the OC of bananas is α/β

 Week 1: The Ricardian Model (15/24)

I Using our example that (αD , βD , L̄D ) = (4, 2, 25) and (αF , βF , L̄F ) = (1, 1, 100):

Apples Bananas
M P LD,B 1 M P LD,A
Domestic M P LD,A
= 2
banana M P LD,B
= 2 apples
M P LF,B M P LF,A
Foreign M P LF,A
= 1 bananas M P LF,B
= 1 apple

I Domestic has an absolute advantage in both goods since αD > αF and βD > βF

I Domestic (or foreign) has a comparative advantage in apples (or bananas)

I Domestic must sacrifice more apples to produce a single banana compared to foreign

I Equivalently, domestic must sacrifice fewer bananas to produce a single apple compared to foreign
 Week 1: The Ricardian Model (16/24)

I By specializing, domestic produces 4 × 25 = 100 apples and foreign produces 1 × 100 bananas

W , P W — what could they buy?

I Suppose both countries sold everything at the world prices PA B

P W × 100 + PB
W W
× 0 = PA W
× AD + PB × BD (17)
|A {z } | {z }
Domestic’s “Income” Domestic’s Consumption

W W W W
PA × 0 + PB × 100 = PA × AF + PB × BF (18)
| {z } | {z }
Foreign’s “Income” Foreign’s Consumption

I Notice the distinction: domestic produces 100 apples but need not consume 100 apples

I This will become more clear when we see a graphical example

 Week 1: The Ricardian Model (17/24)

W , P W become:
I Re-arranging, the PPFs with trade and world prices PA B

No-Trade Free-Trade
W W
1 PA PA
Domestic BD = 50 − 2
× AD BD = 100 × W − W × AD
PB PB
W
PA
Foreign BF = 100 − AF BF = 100 − W × AF
PB

I Some world prices expand the set of feasible alternatives to both countries

W
I If PA W
/PB is greater than 1/2, the set of feasible alternatives to domestic expands

I If P W /P W is less than 1, the set of feasible alternatives to foreign expands

A B
 Week 1: The Ricardian Model (18/24)

W /P W = 2/3 ≤ 1 expands the PPFs of both countries

I For example, 1/2 ≤ PA B
 Week 1: The Ricardian Model (19/24)

I This unambiguously makes both countries better off by reaching higher indifference curves

I Domestic produces 100 apples, consumes 40 apples and exports 60, and imports 40 bananas

I Foreign produces 100 bananas, consumes 60 bananas and exports 40, and imports 60 apples
 Week 1: The Ricardian Model (20/24)

W /P W ≤ 1 could have worked as well. What will equilibrium prices be?

I Other prices 1/2 ≤ PA B

I We determine this by the intersection of export supply and import demand. Consider domestic apples

I When P W /P W < 1/2, domestic would supply 0 apples

A B

I When P W /P W = 1/2, domestic would supply 50 apples

A B

I When P W /P W = 2/3, domestic would supply 60 apples

A B

I When P W /P W → ∞, domestic would (want to) supply 100 apples

A B

I We can repeat a similar exercise for foreign’s import demand of apples (and the banana market)
 Week 1: The Ricardian Model (21/24)

W /P W :
I By collecting how much domestic would supply and foreign would demand at different PA B
 Week 1: The Ricardian Model (22/24)

I The last thing we will examine is the effect of trade on real wages (wage divided by price)

I Initially, real wages were αC = M P LC,A = wC wC

PC,A
apples and βC = M P LC,B = PC,B
bananas

I By specializing in apples, domestic real wages in terms of apples stayed the same. However:

wD
αD = W
(19)
PA

wD PW
= W
× B
W
(20)
PA PB

wD PW
W
= αD × A
W
(21)
PB PB
 Week 1: The Ricardian Model (23/24)

I Domestic real wages in terms of bananas was βD = 2 before trading

I After trading, domestic real wages in terms of bananas became:

wD PW
W
= αD × A
W
(22)
PB PB

2
=4× (23)
3

> βD (24)
 Week 1: The Ricardian Model (24/24)

I Altogether, the Ricardian model can explain why rich countries import from poor countries

I Mutually beneficial trade arises from differences in technology, and hence, comparative advantages

I All of our “old” trade theories will be driven by comparative advantage trade

I By specializing, countries reach indifference curves unambiguously higher than they could alone

I Moreover, real wages necessarily increase in both countries as a result of free trade

I As a segue for next week: one observation is that real wages do not always rise in every industry