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