International Economics. Li Yumei Economics & Management School of Southwest University. International Economics. Chapter 3 The Standard Theory of International Trade. Organization. 3.1 Introduction 3.2 The Production Frontier with Increasing Costs 3.3 Community Indifference Curves
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Economics & Management School
of Southwest University
The Standard Theory of International Trade
The following three questions are examined
in the more realistic case of increasing costs (which is
different from Chapter 2 constant costs).
Increasing opportunity costs mean that the nation must
give up more and more of one commodity to release
enough resources to produce each additional unit of
Constant Opportunity Costs: It means that the nation
must give up the fixed amount of one commodity to
release enough resources to produce each additional unit
of another commodity.
Decreasing Opportunity Costs: ?
With increasing costs, each nation’s PPF (production
possibility frontier) is concave (凹的) from the origin
(rather than a straight line with constant costs).
How to show the PPF in each nation with increasing
FIGURE 2-1 The Production Possibility Frontiers of the United States and the
United Kingdom with constant costs
FIGURE 3-1 Production Frontiers of Nation 1 and Nation 2 with Increasing Costs.
MRT is the opportunity cost of one commodity relative to
The slope of production frontier gives the marginal rate of
See Figure 3-1 Nation 1(page 61)
(1) MRT at point A ( ¼): It means that Nation 1 must give up ¼ of a unit of Y to release just enough resources to produce one additional unit of X at this point.
(2) MRT at point B (1): It means that Nation 1 must give up one unit of Y to release just enough resources to produce one additional unit of X at this point. Reflecting the increasing opportunity costs.
1. Resources or factors of production are not homogeneous (e.g. all units of the same factor are not identical or of the same quality);
2. Resources or factors of production are not used in the same fixed proportion or intensity in the production of all commodities. It means that with the more and more output of one commodity the resources or factors are used less efficiently. Such as wheat land for milk production. (page 62)
1. Due to the fact that the two nations have different factor
endowments or resources at their disposal (details in
Chapter 5) and / or use different technologies in
2. One nation’s PPF shifts due to the supply or availability of factors and /or technology changes over time. And the type and extent of these shifts depend on the type and extent of the changes that take place (details in Chapter 7)
Increasing opportunity costs meant that the nation must give
up more and more of one commodity to release just enough
resources to produce each additional unit of another
commodity. This is reflected in a production frontier that is
concave from the origin. The slope of the production frontier
gives the marginal rate of transformation (MRT). Increasing
opportunity costs arise because resources are not
homogeneous and are not used in the same fixed proportion
in the production of all commodities. Production frontiers
differ because of different factor endowments and /or
technology in different nations.
1. They reflect the demand preferences or the tastes in a
2. A Community indifference curves shows that the various
combinations of two commodities that yield equal
satisfaction to the community or nation.
3. Higher curves refer to greater satisfaction, lower curves
to less satisfaction.
4. Community indifference curves are negatively sloped
and convex from the origin.
FIGURE 3-2 Community Indifference Curves for Nation 1 and Nation 2.
1. Higher indifference curves higher satisfaction
Points N and A give equal satisfaction to Nation 1, since they are both
on indifference curve Ⅰ. Points T and H refer to a higher level of
satisfaction, since they are on a higher indifference curve Ⅱ. Point E
refers to greater satisfaction, since it is on the indifference curve Ⅲ.
( N=A ﹤T,H ﹤E) . In Nation 2, A’=R’ ﹤H’﹤E’.
2. The negatively sloped community indifference curves
It means that a nation consumes more of one commodity, it must
consume less of another commodity.
1. MRS of one commodity for another commodity in consumption refers to the amount of another commodity that a nation could give up for one extra unit of one commodity and still remain on the same indifference curve.
2. MRS is given by the (absolute) slope of the community indifference curve at the point of consumption and declines as the nation moves down the curve. (See page 63 Figure 3.2: in Nation 1 MRS of X at point N is greater than point A; in Nation 2 MRS of X of point A’ is greater than point R’)
3. The decline in MRS or absolute slope of an indifference curve is a reflection of the fact that the more of X and the less of Y a nation consumes, the more valuable to the nation is a unit of Y at the margin compared with a unit of X. Therefore, the nation can give up less and less of Y for each additional unit of X it wants.
4. Declining MRS means that community indifference curves are convex from the origin. Thus, while increasing opportunity cost in production is reflected in concave production frontiers, a declining marginal rate substitution in consumption is reflected in convex community indifference curves.
1. Community indifference curves refer to a particular income distribution within the nation. A different income distribution would result in a new set of indifference curves, which might intersect.
2. Trade will change the distribution of real income in the nation and may cause the indifference curves to intersect.
1. Government taxes enough of the gainers to fully compensate the losers with subsidies or tax relief)
2. Restriction assumptions about tastes, incomes and patterns of consumption to preclude intersecting community indifference curves
Here the compensation principle or restrictive
assumptions do not completely eliminate all the
conceptual difficulties inherent in using community
indifference curves. We still draw them as
The demand factor is introduced into the simple trade model,
and it makes the model more realistic.
Community indifference curves are assumed that they don’t
insect each other. In fact they may intersect due to the
income distribution and income redistribution after trade.
A community indifference curve shows the various combinations of two
commodities that yield equal satisfaction to the community or nation.
Higher curves refer to a greater level of satisfaction. Community
indifference curves are negatively sloped and convex from the origin. And
to be useful, they must not cross. The slope of an indifference curve gives
the marginal rate of substitution (MRS) in consumption, or the amount of
commodity Y that a nation could give up for each extra unit of commodity X
and still remain on the same indifference curve. Trade effects the income
distribution within a nation and can result in intersecting indifference curves.
This difficulty can be overcome by the compensation principle, which
states that the nation gains from trade if the gainers would retain some of
their gain even after fully compensating losers for their losses. Alternatively,
some restrictive assumptions could be made.
In section 3.2 the production or supply conditions (production possibility
frontier) are discussed in a nation; In section 3.3 the tastes or demand
preference conditions (community indifference curves) are
discussed in a nation.
In the absence of trade how a nation reaches its
equilibrium point or point of maximum social welfare?
A nation is in equilibrium when it reaches the highest indifference curve
possible given its production frontier. That is to say, the point where its
production frontier is tangent to indifference curve is the equilibrium point
in a nation.
FIGURE 3-3 Equilibrium in Isolation.
It is given by the slope of the common tangent to the
nation’s production frontier and indifference curve at the
autarky (in the absence of trade) point of production and
Consumption. (see Figure 3.3 page 66)
The equilibrium-relative price of X in isolation is
PA=PX/PY=1/4 in Nation 1 and PA’=PX/PY=4 in Nation 2.
Since PA﹤PA’, Nation 1 has a comparative advantage in
commodity X and Nation 2 in commodity Y.
Due to their different production possibility frontiers (or
supply conditions) and community indifference curves
The forces of supply (as given by the nation’s PPF) and the
forces of demand (as summarized by the nation’s
indifference curves or maps) together determine the
equilibrium-relative commodity prices in each nation in
It refers to the excess in the percentage of total exports over the
percentage of total imports in each major commodity group for
each country or region.
See page 67 table 3.1
In the absence of trade, a nation is in equilibrium when
it reaches the highest indifference curve possible with
its production frontier. This occurs at the point where a
community indifference curve is tangent to the nation’s
production frontier. The common slope of the two
curves at the tangency point gives the internal
equilibrium-relative commodity price in the nation and
reflects the nation’s comparative advantage.
A difference in relative commodity prices between two nations
is a reflection of their comparative advantage and form the
basis for mutually beneficial trade. Lower relative commodity
prices mean the comparative advantage while higher relative
commodity prices mean the comparative disadvantage.
Each nation should then specialize in the production of the
commodity of its comparative advantage and exchange par of
its output with the other nation for the commodity of its
FIGURE 3-4 The Gains from Trade with Increasing Costs.
1. With increasing costs, the specialization will continue until relative
commodity prices in the two nations become equal at the level at which
trade is in equilibrium. PX/PY=1. By then trading with each other, both
nations can benefit from the trade. Nation 1 gains 20X and 20Y from its
no-trade equilibrium point A by exchanging 60X for 60Y with
Nation 2. Nation 2 gains 20 X and 20Y from its no-trade equilibrium
point A’ by exchanging 60Y for 60X with Nation 1.
2. With specialization in production and trade, each nation can consume
outside its production frontier (which also represents no-trade
It is the common relative price in both nations at which
trade is balanced.
E.G. Figure 3.4
PB=PB’=1. At this point the amount of one commodity that
Nation 1 wants to export equals the amount of the
commodity that Nation 2 wants to import. Or the amount of
one commodity that one nation wants to import equals the
amount of the commodity that the other nation wants to
This is the basic difference between the trade model under
increasing costs and the constant costs.
Due to the increasing costs, no nation specializes
completely in the production of only one product in the real
The increasing costs mean that the production costs of
given-up product decline until they are identical in both
nations. Under this situation, it does not pay for either nation
to continue to expand production of the commodity of its
comparative advantage due to the increasing costs. (Case
study 3-2 page 71)
1. Under constant cost, the complete specialization
happens in a small country while a large country
continue to produce both commodities even with trade
due to the dissatisfaction demand for the imports from a
2. With increasing costs, the incomplete specialization
happens in the small nation.
The gains from trade can be broken down into two components: the
gains from exchange and the gains from specialization.
FIGURE 3-5 The Gains from Exchange and from Specialization.
1. Gains from exchange: from A to T, Nation 1 exports 20X
for 20Y at the prevailing world market price of PW=1 and
end up consuming at point T.
2. Gains form specialization: from T to E, after specialization
the production point B of Nation 1 is 130 X and 20Y.
Nation 1 exchange 60X for 60Y and consumes at point E.
The higher indifference curve, the increase in
consumption from T to E would represents the gains from
(Case study 3.3 and 3.4 page from 74 to 75)
With trade, each nation specializes in producing the
commodity of its comparative advantage and faces increasing
opportunity costs. Specialization in production proceeds until
relative commodity prices in the two nations are equalized at
the level at which trade is in equilibrium. By the trading, each
nation ends up consuming on a higher indifference curve than
in the absence of trade. With increasing costs, specialization
in production is incomplete, even in a small nation. The gains
from trade can be broken down into gains from exchange and
gains from specialization in production.
1. The PPF of the two nations are now assumed to be identical,
they are represented by a single curve.
2. The pretrade-relative price of X is lower in Nation 1 than in
Nation 2. X is the comparative advantage of Nation 1 while
Nation 2 is Y.
3. With the opening of trade, Nation 1 specializes in the
production of X (and moves down its production frontier) while
Nation 2 specializes in the production of Y (and moves up its
own production frontier). Specialization continues until PX/PY
is the same in both nations and trade is balanced.
With increasing costs, even if two nations have
identical production frontiers, there is still a basis for
mutually beneficial trade if tastes, or demand or
preferences, differ in the two nations. The nation with the
relatively smaller demand or preference for a commodity will
have a lower autarky-relative price for, and a comparative
advantage in, that commodity. This will set the stage of
specialization in production and mutually beneficial trade, as
To introduce demand preferences or tastes (demand
conditions given by community indifference curves)
to extend the simple trade model (only supply
conditions given by production possibility frontier)
with increasing opportunity costs:
For an exposition of the gains from trade, see:
The changing pattern of comparative advantage in the United
States and other industrial nations is examined in: