CHAPTER 2
In the Ricardian Model, international trade is based on di erences in technology. Comparative
advantage, in this model, is the result of technological di erences across countries. Let’s set up a simple
model to illustrate this.
We’ll take the following steps for every trade model that we discuss.
I.
We’ll first set up the economic model for a country, which we’ll refer to as the home country
(H.C.). This would entail defining the technology and the production process along with supply and
demand for this country.
II.
We will then introduce a foreign country (F.C.), which would have exactly the same
characteristics as the home country except for its technology.
III.
Given that these two countries di er only in terms of technology, would they want to trade with
each other? The answer to this would really depend on whether there are any gains from trade.
IV.
We will finally show patterns of trade and gains from trade for each country.
The Model
I. The Home Country (H.C.) - Story of a single country
In this very basic economic model of a country, which we refer to as the home country, the following
assumptions are made:
Labour is the only factor of production.
Only two goods (say Wheat and Cloth) are produced.
The supply of labour is fixed in each country.
Technology in each good is fixed.
Perfect competition prevails in all markets.
The assumption that there is only one factor of production (labour), which is used to produce both
goods, means that labour is homogeneous. This implies that a worker can easily move between
industries and no special training is required.
The labour supply is fixed in this country; thus, we assume that endowments/resources are fixed and
don’t change while we solve the model. The economy’s total labour supply is defined as L.
Let’s assume L = 120, meaning that the H.C. is endowed with 120 workers.
The technology used for the production of each good is fixed and this translates into fixed labour
productivity. The constant labor productivity is modeled here with ‘unit labour requirement’.
The unit labour requirement is defined as the amount of labour needed to
produce one unit of output.
Let’s denote the unit labour requirement for Wheat as aLW and the unit labour requirement for Cloth as
aLC.. We will also assume that:
aLW = 2. That is, 2 units of labour is needed to produce one kilo of Wheat.
aLC = 1. That is, 1 unit of labour is needed to produce a yard of Cloth.
Now that we know the home country’s endowments and technology, we can write down an equation for
the production possibility frontier. Recall that the production possibility frontier (PPF) of an economy
shows, given the resource constraints, the maximum amount of a good (say Wheat) that can be
produced for any given amount of another good (say Cloth), and vice versa. Just as the term implies, this
PPF line is a frontier of possible combinations of the two goods, given the country’s limited resources
(L=120) and its fixed technology (aLW, aLc).
Suppose we use LC amount of labour to produce Cloth and Lw amount of labour to produce wheat.
Then, given its labour productivity (aLC), how much Cloth can the country produce?
Quantity of Cloth (QC) would be:
i) QC = LC /aLC.
Similarly, Quantity of Wheat (Qw) would be:
ii) Qw = Lw/aLw.
Rearranging the above equations, we get:
iii) LC = aLCQC.
Similarly we'll have:
iv) LW= aLWQW.
We have assumed that there is a limited supply of resources (L=120). Hence, the amount of labour used
in the two sectors (Cloth and Wheat) cannot be more than the total supply of labour (L). This resource
constraint can be written as: LC + LW = L.
Writing LC and LW in terms of quantities as in iii and iv, we get: aLCQC + aLWQW = L.
This is nothing but the equation for Home’s production possibility frontier, given the resource constraint
and the maximum amount you can produce of the two goods.We will rearrange the equation for the PPF
in terms of QW where QW = L/aLW - (aLC /aLW )QC.
Can you draw this graph with QC on the x-axis and QW on the y-axis?
Here, the intercept is L/aLW and the slope is (aLC /aLW).
Given that we have L=120, aLC = 1 and aLW = 2, we get QW = 120/aLW - (aLC /aLW )QC
Re-arranging the equation in terms of QW , we get: QW = 120/2 - (1/2 )QC.
This equation is represented in Figure 2.1 with Cloth on the x-axis and Wheat on the y-axis where the
slope of the PPF is the opportunity cost of producing Cloth - aLC /aLW.
Home Economy - Prices and wages
We will now denote PC as the dollar price of Cloth, PW as the dollar price of Wheat, wW as the dollar wage
in the Wheat industry, and wC as the dollar wage in the Cloth industry.
Then, under perfect competition, the non-negative profit condition implies that:
·
The value of the marginal productivity of labour (vmpL) = wages, in a sector.
·
VMPL=W.
·
Marginal productivity: the amount of goods that a labourer can produce in an hour = 1/ aLW.
·
Value of marginal productivity = price of Wheat * how much one unit of labour (person-hour) can
produce (PW / aLW).
This further implies certain conditions for production in the two sectors:
Wheat: if PW / aLW < wW, then there is no production of QW however, if PW / aLW = wW,
then there is production of QW.
Cloth: if PC / aLC < wC, then there is no production of QC however, if PC / aLC = wC, then
there is production of QC.
Cloth and Wheat: In the absence of trade, both goods are produced, and therefore, PC /
PW = aLC /aLW.
The above relations imply that if the relative price of Cloth (PC / PW) exceeds its opportunity cost (aLC /
aLW), then the economy will specialize in the production of Cloth. We know that PC / PW = aLC /aLW. So,
the price line is the same as the slope of the PPF.
Although we know the relative price of Cloth in the H.C., we still don’t know the combination of the two
goods produced in the home country. To nail down its output, we must introduce the demand side.
The demand is modeled by a country’s preferences for the 2 goods, which is represented by a map of
indi erence curves for the country. Recall that an indi erence curve (IC) represents all combinations of
the 2 goods that result in the same welfare for a person, or in this case, for the country. As the country
moves towards higher indi erence curves, lying further away from the origin, welfare increases. So, in
Figure 2.2, being on the indi erence curve 4 (IC4) leads to higher welfare than IC3, being on IC3 leads to
higher welfare than IC2, and being on IC2 leads to higher welfare than IC1.
For the country, the consumption point is at B where the Indi erence curve IC2 is tangent to the price
line Pc/Pw, which, in our model, lies on the PPF line (Fig 2.2). Thus, Point B is not only the point of
consumption but also the point of production in the home country.
This concludes the economic model for the home country.
II- Introducing the Foreign Country
The same assumptions hold for the F.C. as the H.C.:
Labour is the only factor of production.
Only two goods (say Wheat and Cloth) are produced.
The supply of labour is fixed in each country.
Technology in each good is fixed.
Perfect competition prevails in all markets.
The foreign country (F.C.) di ers from the home country in terms of its technology where a*LC = 6 and
a*LW = 3.
Absolute and comparative advantage
A country has an absolute advantage in the production of a good if it has a lower unit labour
requirement than the foreign country in this good.
aLC < a*LC and aLW < a*LW
a. Home is more productive in the production of both goods than Foreign.
b. Therefore, Home has an absolute advantage in both goods.
Even if Home has an absolute advantage in both goods, beneficial trade is
possible in this case. The pattern of trade will be determined by country’s
comparative advantage.
Given the unit labour requirement in the home and foreign country (Table 2.3) let’s now calculate the
opportunity cost (O.C.). From its definition, the opportunity cost of producing Cloth is the amount of
Wheat forfeited with the same amount of labour.
The opportunity cost of producing Cloth is lower in the home country. So, the home country has a
comparative advantage in producing Cloth. Likewise, the foreign country has a comparative advantage
in producing Wheat.
Home has an absolute advantage in producing both goods since it has lower unit labour costs for
producing both goods.
Comparative Advantage: aLC /aLW < a*LC /a*LW.
The opportunity cost of Cloth in terms of Wheat is lower in Home than it is in Foreign. In other words, in
the absence of trade, the relative price of Cloth at Home is lower than the relative price of Cloth in
Foreign. Home has a comparative advantage in Cloth and will export it to Foreign in exchange for Wheat
where Wheat is cheaper in the foreign country. The PPF for the foreign country would be drawn similar to
that of the PPF for the home country and is shown in Figure 2.3.
III - Trade Between The Two Countries
What determines the relative price (e.g., PC / PW) a er trade?
To answer this question, we must define the relative supply and relative demand for Cloth in the world as
a whole. The relative supply of Cloth equals the total quantity of Cloth supplied by both countries at
each given relative price divided by the total quantity of Wheat supplied,
(QC + Q*C )/(QW + Q*W).
First let’s recall the autarky prices for the two countries
Under the assumption of perfect competition, price is equal to marginal cost, which is unit labour cost
times wage.
If labour is perfectly mobile across sectors, then we must have equalized wages. Dividing the equations,
we get
Therefore, the autarky price of Cloth relative to Wheat is
The patterns of trade are determined by price di erences that result from technological di erences.
World relative supply curve under free trade
Let’s draw the supply function on a graph with relative price on the y-axis and relative quantity on the xaxis.
The world relative supply curve is derived as follows (refer to table 2.5)
- Video Tutorial: Drawing the relative world supply function -
The world relative supply graph (Figure 2.4) is shaped like a step where it is horizontal at relative price ½,
vertical between relative price ½ and 2, and horizontal again at relative price 2.
In order to determine an equilibrium for the world, we will need its relative demand curve. Here, we will
assume that the two countries have the same demand function. Recall that we allow the two countries
to di er only in terms of technology used for production.
In Figure 2.5, the negatively sloped word relative demand graph is represented by the curve ‘D’ with the
relative quantity of Cloth on the x-axis and the relative price of Cloth on the y-axis. In this case, the
equilibrium relative price of Cloth is found at the intersection of the relative demand and relative supply
curves, which is at point e in Figure 2.5. Our example shows that the equilibrium relative price of Cloth in
the world market, when both countries trade freely with each other, is 1 (point e in Fig. 2.5).
IV - The Gains from Trade
For the home country, the autarky (before trade) relative price of Cloth is ½ and when it opens up to
trade, it faces the world relative price of Cloth (WRPC), which is 1. Furthermore, as illustrated in Fig. 2.6,
we also know that the home country’s opportunity cost of producing Cloth is ½ (recall that aLC / aLW =
1/2), which is lower than the WRPC. Therefore, the home country would only produce Cloth and use all
its resources for its production, all while producing Wheat (represented by the point P in Fig. 2.6). This is
equivalent to saying that the opportunity cost of Wheat (= 2) is higher than the relative price of Wheat in
the world market (=1) and thus, the home country produces no Wheat while using all its resources to
produce only Cloth. In the end, the home country completely specializes in the production of Cloth.
What about the foreign country? For the foreign country, the autarky (before trade) relative price of Cloth
is 2, and when it opens up to trade, it faces the WRPC of 1 (Fig 2.7). Given that the opportunity cost of
producing Cloth in the foreign country (a*LC / a*LW = 2) is higher than the WRPC, the foreign country
would produce no Cloth and use all its resources to produce Wheat (shown at point P* in Fig 2.7).
Consequently, the foreign country completely specializes in the production of Wheat.
Recall that in our example, the home country has a comparative advantage in the production of Cloth
and the foreign country has a comparative advantage in the production of Wheat. We can thus conclude
that in the simple case of the Ricardian model, countries specialize in the production of the good in
which they have comparative advantage when they trade with each other.
If countries specialize according to their comparative advantage, they all gain from trade and
specialization. We will demonstrate this with the help of the consumption possibility frontier and
indi erence curves. Before we get into the details, let’s briefly summarize these two concepts.
The consumption possibility frontier and indi erence curves:
The consumption possibility frontier is a similar concept to the production possibility frontier. It is the
maximum amount of consumption of a good that a country can obtain for any given amount of the
other commodity. Under autarky, when there is no trade, the consumption possibility curve for a country
is the same as the production possibility curve. A country cannot consume beyond its production
possibility frontier.
NOTE: An autarkic (closed economy) can only consume what it can produce. Since production is
constrained by the PPF, consumption is as well.
Home Country: Gains from Trade
When both countries open and trade with each other, the world relative price of Cloth is 1. So, the home
country now faces the WRPC=1 instead of the autarkic price of ½. The WRPC is now the new consumption
possibility frontier for the country. Furthermore, the country is no longer restricted in its consumption by
the PPF because it can now trade with the foreign country at WRPC=1. Let’s see how trade enlarges the
consumption possibility frontier and takes the country to a higher indi erence curve.
Referring to Figure 2.8, for the home country, the autarky price is ½, which is the closed economy price in
the home country before trade. Point B is the pre-trade production and consumption point where the IC
is tangent to the PPF and the autarky price line. A er the home country opens and trades with the
foreign country, the WRP is 1, and the new production point a er trade is P. The new consumption point
is at point C, where the WRP is tangent to the indi erence curve IC. Let’s see what happens when Home
produces at point Pc. At that point, Home trades Cloth for Wheat at the new world price WRPc and
moves up the WRPc line to point C. Since Home can now consume more (at point C) than before (at
point B), there are gains from trading with the foreign country. Trade takes the home country from IC to a
higher indi erence curve IC, increasing the country’s utility and welfare.
Referring to Figure 2.8, for the home country, the autarky price is ½, which is the closed economy price in
the home country before trade. Point B is the pre-trade production and consumption point where the IC
is tangent to the PPF and the autarky price line. A er the home country opens and trades with the
foreign country, the WRPC is 1, and the new production point a er trade is Pc. The new consumption
point is at point C, where the WRPC is tangent to the indi erence curve IC4. Let’s see what happens when
Home produces at point Pc. At that point, Home trades Cloth for Wheat at the new world price WRPc and
moves up the WRPc line to point C. Since Home can now consume more (at point C) than before (at
point B), there are gains from trading with the foreign country. Trade takes the home country from IC2 to
a higher indi erence curve IC3, increasing the country’s utility and welfare.
Let’s consider this in more detail when the home country specializes in the production of Cloth (point
PC), trading Cloth for Wheat at the world price WRPC, as previously mentioned and moving to a higher
indi erence curve (from IC2 to IC3). The trade patterns for the home country are shown in Fig. 2.9.
The home country produces more Cloth than it consumes. Thus, Home produces Pc quantity of Cloth
and consumes Cc quantity while the rest (Pc - Cc) is exported to the foreign country. The home country
also imports Wheat from the foreign country for its consumption. Recall that Home produces 0 quantity
of Wheat and consumes Cw quantity of Wheat, which is imported from the foreign country.
In the Ricardian model, Home has a comparative advantage in the production of Cloth, specializes in
Cloth, and exports Cloth, moving to a higher indi erence curve. Trade unambiguously increases welfare
for the home country.
However, in the real world, we don’t see complete specialization of production, as explained by the
simplifying assumption we made in the Ricardian model. There are three main reasons why
specialization in the real international economy is not as extreme as predicted by our model:
The existence of more than one factor of production.
Countries sometimes protect industries from foreign competition by imposing tari s or
other restrictions.
It is costly to transport goods and services and the result of introducing transport costs
makes some goods nontraded
In some cases, transportation is virtually impossible. Example: Services such as
haircutting, bowling, going to the movies, etc. cannot be traded internationally.
Empirical Evidence
The Ricardian model continues to show its relevance today as demonstrated by an empirical study done
by Golub and Hsieh (2000), observing trade flows, productivity, and unit labour costs of manufacturing
sectors in several OECD countries while running cross-sectional regressions on these characteristics.
Their study is motivated by the fact that since the 1960s, very little empirical work has been done to
prove the e ectiveness of the model. Furthermore, claims of limitations have been made to state the
Ricardian model as being too simplistic for serious data analysis. Golub and Hsieh (2000), nonetheless,
assert the importance of observing relative labour productivities as a significant factor in global trade
patterns and point out that previous tests on the Ricardian model have been quite successful. They
proceed with the study by comparing the trade patterns of di erent countries in the dataset to the US.
The results find that the signs of coe icients that determine US bilateral trade patterns with other
countries are almost always correct and that statistical significance is maintained. In many cases of this
study, relative productivity and unit labour cost help explain how the US would trade with other
countries. Thus, these findings indicate that the insights of the Ricardian model o er the same results as
the regressions of Golub and Hsieh (2000)’s dataset while providing strong explanatory power on how
trade patterns will play out in practice. Even though the basic theory is quite simplistic and most of the
sectoral variation of trade remains unexplained, the Ricardian model has proven its success empirically.
Summary
We examined the Ricardian model in its simplest form. In this model, labour is the only factor of
production and countries di er only in their productivities of labour in di erent industries. We illustrated
how technological di erences between countries can give rise to trade that is beneficial. In the Ricardian
model, a country will export that commodity in which it has a comparative (as opposed to an absolute)
advantage. If we extend the two-goods model to include many commodities, we can also show that
transportation costs can give rise to the existence of non-traded goods.