Lecture 2. Ricardian Model

Things to do today:

Address the following issues:

Why do wages differ so much across the world?

Does economic growth in the “Third World” hurts the “First World” prosperity?

Should developed countries stop trading with developing countries?

Explain the basis for trade:

Countries trade with each other because they are different from each other.

Comparative advantage is an essential concept.

In Ricardian models comparative advantage is solely due to international differences in the

productivity of labor.

2

David Ricardo

Figure 3.1 David Ricardo (1772-1823)

Born in London as the third son of a Jewish family emigrated from Holland he married

the daughter of a Quaker and was disinherited by his parents. Ricardo nonetheless

accumulated a fortune as a stock-jobber and loan contractor. As Blaug (1986, p. 201) puts

it: "Ricardo may or may not be the greatest economist that ever lived, but he was certainly the

richest." His fame today rests mainly, of course, on his contributions to the theory of

comparative advantage.

3

David Ricardo and his principle of comparative advantage

Like in the case of Smith’s principle of the absolute advantage Ricardo’s concept of comparative advantage

applies both to nations and individuals. What if one party does not have an absolute advantage in anything?

Can people still cooperate with each other and benefit from their cooperation?

Example. Division of work between lawyer and secretary

Imagine a situation of a lawyer who has an absolute advantage in both typing (types twice as fast as a

secretary) and legal advice (has a law degree while a secretary does not), while a secretary has an absolute

disadvantage in both. According to the principle of comparative advantage the lawyer specializes in legal

advice and the secretary in typing. To understand this assume that lawyer earns $ 100 per hour practicing law

but must pay $ 10 per hour to the secretary. Assuming that the lawyer types twice as fast as the secretary the

lawyer would have lost $ 80 per hour if worked without sharing the work with the secretary (i.e. lost $ 100

per hour if was not giving legal advice and gained $ 20 if typed everything by himself).

In 1817 David Ricardo (1772-1823) published his famous book entitled “Principles of Political Economy

and Taxation” in which he presented the law of comparative advantage – one of the most important laws in

economics. According to the law of comparative advantage, even if one nation is less efficient than the other

nation in the production of all commodities, there is still a basis for a mutually beneficial trade. The nation

should specialize in the production of and export the commodity in which its absolute disadvantage is

smaller and import the commodity in which its absolute disadvantage is greater.

4

Numerical Example. Trade between England and Portugal in cloth and wine

England Portugal Total

Labor hours necessary to produce 1 unit of Cloth

(i.e. industrial good)

1 2

Labor hours necessary to produce 1 unit of Wine

(i.e. agricultural good)

2 8

Potential output of cloth given total labor

endowment – 24 hours

24 12 12

Potential output of wine given total labor

endowment – 24 hours

12 4 12

Actual preferences concerning allocation of time

to the production of cloth - 8 hours

8 4 12

Actual preferences concerning allocation of time

to the production of wine - 16 hours

8 2 10

Trade in cloth 8

(imported)

8

(exported)

No gains

Trade in wine 3

(exported)

3

(imported)

England gains 1,

Portugal gains 1

5

Simple Ricardian 2x2x1 model

Basic Assumptions:

Two countries: Home and Foreign (*)

Two goods (homogenous): 1 - agricultural (wine) and 2- industrial (cloth)

One factor of production: Labor

Technology: linearly homogenous production function (CRS), fixed labor input coefficients in both sectors

Production function in sector i can be written as:

i

ii

a

LQ

where:

Qi – output

Li – labor input

ai – unit labor requirement (i.e. the number of hours you need to work to obtain 1 unit of good i)

This production function implies that marginal and average products of labor are constant and equal:

iaMPLAPL

1

6

Labor supplies in both countries L and L* are inelastic (do not change with changing wage rates)

Perfect competition prevails in the economy in product and factor markets (no markup over the marginal

cost and wages equal to the marginal product of labor) in both countries

People want to consume both goods (decreasing marginal utility of consumption of each good)

All people are homogenous (only one group, same tastes, equally productive, supply the same amount of

labor)

Autarky Equilibrium (No trade)

SUPPLY SIDE:

Profit maximizing firms in sector i take as given both product prices (pi) and the wage rate (wi)

Profit = Sales revenue – labor costs

ii

i

iii

i

iiiiiii Lw

a

pLw

a

LpLwQp

7

Demand for labor in sector i can be obtained from the First Order Condition (F.O.C.)

0

i

i

i

i

i wa

p

L

i

i

i wa

p

(interpretation: LHS = the value of the marginal product of labor, RHS = nominal wage)

Alternatively,

i

i

i p

w

a

1

(interpretation: LHS = marginal product of labor, RHS = real wage in terms of i)

8

Demand for labor Li =

i

i

i

i

i

i

i

i

i

wa

pif

wa

pif

wa

pif

),0(

0

Output Qi =

i

i

i

i

i

i

i

i

i

wa

pif

wa

pif

wa

pif

),0(

0

Remember that the supply of labor is fixed, hence this limits the amount of output produced.

Full employment condition:

LLL 21

Alternatively, (using the production functions)

LQaQa 2211 (PPF)

9

Production possibility frontier (PPF) is derived from the full employment condition

Workers are mobile between sectors which implies the equalization of the nominal wage rate:

w1 = w2 = w

If both goods are to be produced in the economy then the values of marginal products of labor in both sectors

must be equalized:

2

2

1

1

a

pw

a

p

Case 1. If 2

2121

2

2

2

2

1

1 ,0,,0,a

LQQLLL

a

pw

a

p

a

p (everybody employed in sector 2)

Case 2. If 2

1

2

22

1

11

1

1

2

2

2

2

1

1 ,,a

LL

a

LQ

a

LQ

a

p

a

pw

a

p

a

p (positive employment in both sectors)

Case 3. If 0,,0,, 2

1

121

1

1

2

2

1

1 Qa

LQLLL

a

pw

a

p

a

p (everybody employed in sector 1)

10

The EQUILIBRIUM wage rate is equal to the maximum value of the marginal product of labor

(if both goods are produced then the values of marginal products will be equalized).

Assuming that both goods are produced, if you want to increase the output of one good you will have to

decrease the output of the other good. This can be illustrated using the TRANSFORMATION CURVE

called also the PRODUCTION POSSIBILITY FRONTIER (PPF). This curve shows you the maximum

output of one good, given the output of the other good.

11

Figure 1. Production Possibility Frontier

Q2

Q1

1a

L

2a

L

12

You can differentiate totally the full employment condition to obtain the slope of the PPF (transformation

curve):

22112211 QdaQdadQadQaLd

Knowing that 0Ld (total labor supply remains unchanged) and 021 dada (technology remains

unchanged) we get:

1

2

2

1

a

a

dQ

dQ

Recall that 1

2

2

1

a

a

dQ

dQMRT (marginal rate of product transformation – MRPT) is the opportunity cost of

good 2 expressed in terms of good 1.

The opportunity cost of good 2 is equal to the amount of output of good 1 our economy would have to give

up (to release resources needed) to produce an additional unit of good 2.

13

Example. England and Portugal

In our example in order to produce one unit of good 2 in Home country (England) you need 1 hour of work

a2 = 1 and in order to produce one unit of good 1 you need two hours of work a1 = 2. In this case the

opportunity cost of good 2 expressed in terms of good 1 equals ½. (i.e. in order to produce an additional unit

of good 2 in England you need to give up ½ of a unit of good 1.) In Foreign country (Portugal) you need 2

hours of work to produce one unit of good 2 and 8 hours of work to produce one unit of good 1. Hence the

opportunity cost of producing good 2 in terms of good 1 equals 1/4. Comparing opportunity costs in both

countries we can notice that the opportunity cost of producing good 2 (cloth) expressed in terms of good 1

(wine) is lower in Portugal than in England.

In our example, when the production possibility frontier (transformation curve) is linear, the opportunity cost

is constant. (However, it will not be constant in other, more complex models that we will discuss later in

class).

DEMAND SIDE:

GDP = Consumer Expenditure = Labor Income (No profit by assumption – perfect competition)

Consumer budget constraint:

22112211 QpQpLwCpCp

Consumer expenditure = labor income = sales revenue (firm income)

14

The slope of the budget constraint can be obtained by total differentiation:

LwdLdwCdpCdpdCpdCp 22112211

Knowing that 0Ld (total labor supply remains unchanged), dw = 0 (the wage rate remains unchanged) and

021 dpdp (product prices remain unchanged) we get:

1

2

2

1

P

P

dC

dC

Note that if both goods are produced the slope of the budget constraint equals the slope of the transformation

curve. Why? Because marginal products of labor will have to be equalized if labor moves between sectors!

2

2

1

1

a

p

a

p

Hence,

2

1

1

2

1

2

2

1

dQ

dQ

a

a

P

P

dC

dC

However, if the marginal product of labor in sector 1 is smaller than the marginal product of labor in sector 2

then the slope of the budget constraint is bigger and only good 2 is produced

1

2

1

2

2

2

1

1

a

a

p

p

a

p

a

p

15

Figure 2. Production possibility frontier and budget constraint (only good 2 is produced)

1a

L

2a

L

16

In order to assure that both goods are produced in the closed economy Inada conditions must be satisfied:

2

112

1

221

)0,()0,(

),0(),0(

C

CUCU

C

CUCU

17

Figure 3. Equilibrium in the closed economy

1a

L

2a

L C2

C1

C

18

Summary of conclusions (closed economy):

In autarky the price ratio is determined by the supply side only (unit labor requirements) and consumer

preferences do not matter for relative price determination. However, consumer preferences do matter for

allocation of labor across sectors (and the amounts of each good produced).

1

2

1

2

2

2

1

1

a

a

p

ppw

a

p

a

p A (the slope of PPF)

OPEN ECONOMY

Now imagine that there is FOREIGN country where the autarky price ratio (relative price) is lower than in

HOME country.

**

*

*

*

1

2

1

2

1

2

1

2 AA pp

p

a

a

a

a

p

pp

This implies that Home country has comparative advantage in production of good 1, and Foreign country has

comparative advantage in production of good 2.

How do we determine relative prices (p2/p1) in a trading equilibrium?

19

TOTAL WORLD SUPPLY = TOTAL WORLD DEMAND

WW

WW

CCCQQQ

CCCQQQ

222222

111111

**

**

Constructing the RELATIVE SUPPLY CURVE

CASE 1. Both countries are small

If the relative price of good 2 is below the opportunity cost in FOREIGN country (and also in HOME

country), no country produces good 2, both countries produce good 1.

1

2

1

2

1

2

*

*

a

a

a

a

p

p

Relative price range

*

*,0

1

2

a

a

Output *

**,0

11

1112a

L

a

LQQandQQ WW

Relative output 01

2 W

W

Q

Q

CASE 2. Home country (Country 1) is small, Foreign country (Country 2) is large

20

1

2

1

2

1

2

*

*

a

a

a

a

p

p

Relative price equal to the autarky price in Foreign country (2), hence country 2 produces both goods

(incomplete specialization in production), while Home country produces only good 1

Relative output range )/

*/*,0(

1

2

aL

aL

CASE 3. Both countries are large (complete specialization in production)

1

2

1

2

1

2

*

*

a

a

p

p

a

a

Foreign country produces good 2, Home country produces good 1.

Relative price range

1

2

1

2 ,*

*

a

a

a

a

Relative output 1

2

/

*/*

aL

aL

CASE 4. Home country is large, Foreign country is small

21

1

2

1

2

1

2

*

*

a

a

p

p

a

a

Relative price equals the autarky price in Home country, Home country produces both goods (incomplete

specialization in production), while Foreign country produces only good 2.

Relative output range ),/

*/*(

1

2 aL

aL

The RELATIVE DEMAND CURVE

Traditional, negatively sloped, the negative slope reflects the substitution effect, if the relative price of good

2 increases, its relative demand falls, the location of the relative demand curve depends on the relative

country size (which determines relative demand)

The equilibrium relative price is determined by the intersection of the relative demand and the relative

supply curves.

22

Figure 4. Relative demand and relative supply

1

2

/

*/*

aL

aL

W

W

Q

Q

1

2

1

2

p

p

*

*

1

2

a

a

1

2

a

a

23

GAINS FROM TRADE

Now we demonstrate that countries can gain from engaging in international trade.

Assume the complete specialization case.

When Home country (country 1) specializes in production of good 1 the world price of good 1 equals

wap 11

When Foreign country (country 2) specializes in production of good 2 the world price of good 2 equals

**22 wap

Hence, the relative price under complete specialization equals

w

w

a

a

p

p **

1

2

1

2

The ratio of unit labor requirements is fixed, hence it is the relative wage that adjusts to equilibrate the world

product markets!

24

Now look at behavior of real wages (expressed in terms of both goods = their purchasing power)

Real wage in Home country expressed in terms of good 1 after opening to trade remains unchanged (as it is

determined only by the Home country technology level)

11

1

ap

w

However, real wage expressed in terms of good 2 will change!

2

1

12

1

12

1

p

p

ap

p

p

w

p

w

After opening to trade the relative price of good 2 (expressed in terms of good 1) in Home country is lower

(compared to autarky). So our wage rate expressed in terms of good 2 is higher as we can consume more.

*ATA ppp

Similar results hold for Foreign country (i.e. real wage expressed in terms of good 2 remains unchanged

while increases in terms of good 1).

25

Figure 5. Graphical illustration of gains from trade

1a

L

2a

L C2

C1

C

B

A

TC2

TC1

26

Decomposition of the gains from trade:

I) Gains from exchange (move from C to B) that come from the change in relative prices

II) Gains from specialization (move from B to A) that come from adjusting the levels of output