Review of Microeconomics
Before studying Global Economics, there is the need to be familiar with the consumer and
producer theory from Microeconomics. For the purpose of this course, some new
microeconomic concepts are also going to be introduced.
 Consumer Theory
One of the most basic things is that any consumer will maximize its utility,
constrained by its income.
M=Income
Max U(X,Y)
s.t: Px X+Py Y=M
Px
Py
⟺
Px X+Py Y=M
MRSx,y =
By solving this problem, we get always the demand functions for good X and good Y.
However, by using only the first of the two equations, MRSx,y =
Px
Py
, we are able to
draw the Relative Demand curve (RD), which give us the proportion of goods that
X
P
Y
Py
are demanded in the economy ( ), given the relative price of the goods ( x).
For example, on a simple CobbDouglas utility function like
𝑋, 𝑌 = 𝑋 0,5 𝑌 0,5 , we derive the
following Relative Demand (RD):
𝑀𝑅𝑆𝑥,𝑦 =
⇔
⇔
⇔
𝜕𝑈
𝜕𝑥
𝜕𝑈
𝜕𝑦
=
𝑃𝑥
𝑃𝑦
𝑃𝑥
𝑃𝑦
0,5 𝑋 −0,5 𝑌 0,5
0,5 𝑋 0,5 𝑌 −0,5
=
𝑃𝑥
𝑃𝑦
𝑷𝒙
𝟏
=
→ Relative Demand
𝑿
𝑷𝒚
𝒀
NOTE: As you will probably notice
throughout the course, we will use Social
Utility Functions (SUF), which give us the
preferences of a country as a whole. In
fact, this means that the (relative)
demand functions derived are relative to
an economy as a whole and not a single
consumer. Nevertheless, computations
are similar.

Producer Theory
In the producer theory, each firm decides which quantity of capital (K) and Labor (L)
to use to produce a certain quantity of output (Q), minimizing its
costs. Let ℚ be the quantity the firm wants to produce.
The production function is given by 𝑄 𝐿, 𝐾
𝑀𝑖𝑛 𝑇𝐶 = 𝑤. 𝐿 + 𝑟. 𝐾
𝑠. 𝑡: 𝑄(𝐿, 𝐾) = ℚ
⟺
𝑤
𝑟
𝑄(𝐿, 𝐾) = ℚ
𝑀𝑅𝑇𝑆𝐿,𝐾 =
The relevant equation here is the first one which tells us the Relative Demand for
inputs (K and L) in the factor market.
Nevertheless, we also want to derive the Relative Supply curve (RS) in order to
𝑃
compute the equilibrium relative prices ( 𝑥 ), if we also know the Relative Demand (RD).
𝑃𝑦
To do so, we’re going to assume that each firm is a price-taker, and so faces the
following maximization problem:
Max 𝜋 = 𝑃. 𝑄 − 𝑇𝐶(𝑄)
{𝑄}
And so, we immediately say that P = MC; and that’s not wrong! However in this course
we’re going to see things in a different perspective: It is known that firms can choose
the capital and labor to use, being exactly equivalent of choosing the quantity to
produce, since the production function give us the relation between Q and K, L.
So, each firm faces the following maximization problem:
Max Π𝑥 = 𝑃𝑥 . 𝑄 𝐾𝑥 , 𝐿𝑥 − 𝑇𝐶 𝐾𝑥 , 𝐿𝑥 = 𝑃𝑥 . 𝑄 𝐾𝑥 , 𝐿𝑥 − 𝑤. 𝐿𝑥 − 𝑟. 𝐾𝑥
{𝐾𝑥 ,𝐿𝑥 }
𝜕𝜋
F.O.C :
𝜕𝐿𝑥
𝜕𝜋
𝜕𝐾𝑥
= 0 ⇔ 𝑃𝑥 . 𝑀𝑃𝐿𝑥 − 𝑤 = 0 ⇔
= 0 ⇔ 𝑃𝑥 . 𝑀𝑃𝑘𝑥 − 𝑟 = 0 ⇔
𝑤
𝑃𝑥
𝑟
𝑃𝑥
= 𝑀𝑃𝐿𝑥
= 𝑀𝑃𝑘𝑥
We are assuming that a firm from sector X is maximizing its profit.
However, firms from sector Y do it as well. So, doing the same for sector Y we get that:
𝑤
𝑃𝑦
𝑦
= 𝑀𝑃𝐿 ;
𝑟
𝑃𝑦
𝑦
= 𝑀𝑃𝑘 .
By solving the following equation we get the RS:
𝑤
𝑦
𝑦
= 𝑀𝑃𝐿 ⇔ 𝑤 = 𝑀𝑃𝐿 . 𝑃𝑦
𝑃𝑦
𝑦
⟺ 𝑀𝑃𝐿𝑥 . 𝑃𝑥 = 𝑀𝑃𝐿 . 𝑃𝑦 ⟺
𝑤
= 𝑀𝑃𝐿𝑥 ⇔ 𝑤 = 𝑀𝑃𝐿𝑥 . 𝑃𝑥
𝑃𝑥
𝒚
𝑷𝒙
𝑴𝑷𝑳
=
𝑷𝒚
𝑴𝑷𝒙𝑳
Knowing the RD and RS, we are now able to compute the relative equilibrium prices.
However, the RS derived here will only be used on the H-O Model.
In the 2x2 model it’s not relevant to solve the firm's maximization problem since it
does not consider any production at all.
2x2 model
In this model, we have two countries (𝐻 and 𝐹) changing two goods (X and Y),
where those goods have no production, that is, the quantity of each good that an
economy has in autarky (closed economy, with no trade) is given and fixed. That is,
there is an endowment of goods (𝑋 , 𝑌) in autarky. Hence, the Relative Supply has to
be a vertical straight line.
Knowing the RD and the RS, we
can compute the relative autarky
prices in equilibrium.
Although RS-RD analysis is important, there is the need to plot other graphs in order to
understand better what's going on.
Consumers will maximize their utility, given the endowment of the economy.
If you remember consumer theory from
microeconomics, it is known that:
∗
𝑃𝑥
𝑀𝑅𝑆𝑥,𝑦 =
𝑃𝑦 𝑎𝑢𝑡 .
Meaning that the relative autarky prices,
in equilibrium, will be the slope of the
line tangent to 𝑈3 at point E (line 𝑟).
Formalizing the consumer problem, we have that:
𝑀𝑎𝑥 𝑈(𝑋, 𝑌)
𝑠. 𝑡: 𝑃𝑥 𝑋 + 𝑃𝑦 𝑌 = 𝑀 , 𝑤𝑕𝑒𝑟𝑒 𝑡𝑕𝑒 𝑖𝑛𝑐𝑜𝑚𝑒 𝑀 𝑖𝑠 𝑔𝑖𝑣𝑒𝑛 𝑏𝑦 𝑀 = 𝑃𝑥 𝑋 + 𝑃𝑦 𝑌 .
The idea here that 𝑀 = 𝑃𝑥 𝑋 + 𝑃𝑦 𝑌 is fairly easy to understand. First, we have to take into
account that we’re in an economy that has only 2 goods (X,Y) and those cannot be
produced. Hence, the “income” in this model is given by the total value of the goods that
are endowed.
 FT Equilibrium
Until know, we have only seen the autarky equilibrium and not the free trade
equilibrium between countries. Assume now that there are 2 countries ( 𝐻 and 𝐹 ), that
have different endowments and/or different preferences. The following graphs
represent each one of the economies:
𝐻 − 𝐻𝑜𝑚𝑒 𝐶𝑜𝑢𝑛𝑡𝑟𝑦
𝐹 − 𝐹𝑜𝑟𝑒𝑖𝑔𝑛 𝐶𝑜𝑢𝑛𝑡𝑟𝑦
Will they trade? If they do so, what is the pattern of trade?
As we can see, given this example,
𝑃𝑥
𝑃𝑦
𝐻
<
𝑎𝑢𝑡 .
𝑃𝑥
𝑃𝑦
𝐹
, meaning that, in country H, Y is
𝑎𝑢𝑡 .
relatively more expensive than in country F ⇒ H wants to trade X for Y, that is, export X
and import Y. On the other side, in country F, X is relatively more expensive ⇒ F wants to
trade Y for X, that is, export Y and import X. So, there would be trade between these
countries because they have incentives to do so, and the pattern of trade is going to be the
one described above.
Despite the conclusions reached so far, there is the need to examine more specifically
what’s happening. In order to do that, we want to “draw this problem” in an Edgeworth
Box - Try to rotate the graph from Foreign country (F) represented above by 180˚, such
that it forms a square similar to this:
(Note that the E represents both countries’ endowments). We’ve already seen that
country H wants to trade X in exchange for Y, and that F wants to trade Y in exchange for X,
and this fact is verified in the Edgeworth box. Actually, any point in the area with dashed
lines would be better than point E (Why? Because both countries, H and F, can consume at
higher utility curves).
These countries will trade until there is no more incentive to trade, i.e until
𝑃𝑥
𝑃𝑦
𝐻
=
𝑃𝑥
𝑃𝑦
𝐹
⇔ 𝑀𝑅𝑆𝑥,𝑦 𝐻 = 𝑀𝑅𝑆𝑥,𝑦 𝐹 ⟶ Contract Curve
Here, the contract curve does not have a specific shape. However, that is not a relevant
feature. What is important is to understand that the contract curve give us all the possible
equilibrium points. ( Note that 𝑝 =
𝑃𝑥
𝑃𝑦
. )
𝜃 is the competitive equilibrium, for this given endowment. A competitive equilibrium is
reached when countries change goods until no one can improve its utility, given the
relative prices prevailing in the market.
Formally speaking, point 𝜃 is given by the following conditions:
𝑀𝑅𝑆𝑥,𝑦 𝐻 = 𝑀𝑅𝑆𝑥,𝑦 𝐹 → 𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝐶𝑢𝑟𝑣𝑒
𝑃𝑥 ∗ 𝑋𝐻 + 𝑃𝑦 ∗ 𝑌𝐻 = 𝑃𝑥 ∗ 𝑋𝐻 + 𝑃𝑦 ∗ 𝑌𝐻
𝑃𝑥 ∗ 𝑋𝐹 + 𝑃𝑦 ∗ 𝑌𝐹 = 𝑃𝑥 ∗ 𝑋𝐹 + 𝑃𝑦 ∗ 𝑌𝐹
The last 2 conditions mean that, for each country, the value of consumption is equal to the
value of the endowments. In a more intuitive way, we can say for example that country H
has an income (M) = 𝑃𝑥 ∗ 𝑋𝐻 + 𝑃𝑦 ∗ 𝑌𝐻 , and so like what we saw in the consumer theory
from Microeconomics, it cannot consume a bundle of goods more expensive than that. So,
in a competitive equilibrium, each country consumption’ expenditure must be equal to its
“income”. This is what makes the equilibrium competitive. However, we can obtain non-
competitive equilibriums; if, for example, country H forces country F to consume less than
its “income” would allow for.
Furthermore, if H is exporting X and importing Y, under free trade, it’s natural that
𝑃𝑥
𝑃𝑦
𝐻
starts to increase because X starts to be more scarce and Y more abundant in
𝑎𝑢𝑡 .
country H. The opposite happens in country F. So, the conclusion drawn is that
𝑃𝑥
𝑃𝑦
𝐻
<
𝑎𝑢 𝑡.
𝑃𝑥
𝑃𝑦
∗
<
𝐹𝑇
𝑃𝑥
𝑃𝑦
𝐹
.
𝑎𝑢𝑡 .
There are further ways to represent the free trade equilibrium:
 Aggregate Supply and Aggregate Demand
One of the easiest ways to compute the relative prices under FT equilibrium is by
aggregating the demand from country H with the one from country F. Here we will not
aggregate relative demands but the demand for good X.
Two things should be noticed here.
𝐹
The first one is that 𝐸𝑥𝑝.𝐻
𝑥 = 𝐼𝑚𝑝.𝑥 , since there are only two countries trading, what one
exports the other has to import. If we do the same for market Y, we have that 𝐸𝑥𝑝.𝐹𝑦 =
𝐼𝑚𝑝.𝐻
𝑦 .
The second one is that, by Walra’s law (proved later on), we can say for sure that when the
market for good X is in equilibrium, the market for good Y has to be in equilibrium as well,
and vice-versa. This means that, given that the relative equilibrium price for market X is
𝑃𝑥
𝑃𝑦
∗
, then the relative equilibrium price for market Y is
𝑃𝑥
𝑃𝑦
∗
as well.
 Offer Curves
An Offer Curve gives us how much it is willing to “offer” of one good (export) in exchange
for the other good (import).
But, before doing it, we have first to realize that relative prices are what define the
“budget constraint” for a country to consume.
Take country H as an example. If the
equilibrium prices are the autarky
prices, then country H will consume
at 𝐶0 = 𝑋𝐻 , 𝑌𝐻 ,that is, it will not
trade and just consume its
endowments (why?).
If the international prices are higher
than the autarky prices, then the
“budget constraint” changes from
line 𝑟 to line 𝑠. At these new prices,
the economy wants to consume at 𝐶1
, and for that it needs to import 𝛼
units of good Y and 𝛽 units of good X.
If we try to do this with several different relative prices, we can draw the offer curve of
country H :
We can do the same for country F and derive both countries’ offer curves. The equilibrium
would be when the offer curves cross each other.
 Excess Supply Functions
There is one more way to find out the equilibrium price, but I’m not going to
discuss it in great detail, so I’ll just leave here the graphical representation:
Equilibrium: 𝐸𝑥𝑐𝑒𝑠𝑠 𝑆𝑢𝑝𝑝𝑙𝑦 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝐻+𝐹 = 0
H-O Model / 2x2x2 model
Before studying the H-O Model and its assumptions, it is very important to know the
producer theory in order to better understand this model! (See again the chapter on
Reviews of Microeconomics)
The crucial assumption in this model is that technologies/ production functions are
Constant Return to Scale (CRS). If we consider that X = F(K, L) is a production function,
CRS, where X is the quantity produced and K and L are the inputs used, we obtain that:
𝐹 𝜃𝐾, 𝜃𝐿 = 𝜃. 𝐹 𝐾, 𝐿 = 𝜃. 𝑋
For example, if 𝜃 = 2, that means that when we are doubling the inputs, the output also
doubles --> 𝐹 2𝐾, 2𝐿 = 2. 𝐹 𝐾, 𝐿 = 2. 𝑋
There are some implications derived from this assumption.
1
1) If 𝜃 = , then :
𝐹
𝐿
𝐾 𝐿
,
𝐿 𝐿
=
𝑋
𝐿
⟺𝑓 𝜅 =
𝑋
𝐿
, 𝑤𝑕𝑒𝑟𝑒 𝑘 =
𝐾
𝐿
𝑋
This means that the average productivity of labor, , is a function of the capital
𝐿
intensity (𝜅). The same can be proved for the average productivity of capital,
𝑋
𝐾
2) If F(K, L) is a CRS function, meaning it is homogeneous of degree 1, then the
derivatives of F (
𝜕𝐹
𝜕𝐾
𝑎𝑛𝑑
𝜕𝐹
𝜕𝐿
) have to be homogeneous of degree 0, meaning that
the marginal productivity of capital (𝑀𝑃𝐾 ) and the marginal productivity of labor
( 𝑀𝑃𝐿 )are homogeneous of degree 0 ⇒
𝑀𝑃 𝐾 = 𝐺 𝐾,𝐿 = 𝐺 𝜃𝐾 ,𝜃𝐿
𝑀𝑃 𝐿 = 𝐻 𝐾,𝐿 = 𝐻 𝜃𝐾 ,𝜃𝐿
, for any θ.
For example, if 𝜃 = 2, that means that when we are doubling the inputs, the output will
remain constant.
So, for 𝜃 =
1
𝐿
, we have that the 𝑀𝑃𝐾 𝑎𝑛𝑑 𝑀𝑃𝐿 𝑎𝑟𝑒 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑘 (capital intensity)
3) The Euler Theorem says that
𝜕𝐹
𝐹 𝐾, 𝐿 = 𝐾.
𝜕𝐾
+ 𝐿.
𝜕𝐹
𝜕𝐿
⟺ 𝑋 = 𝐾. 𝑀𝑃𝐾 + 𝐿. 𝑀𝑃𝐿
By the producer's maximization problem, we know that (See chapter on review of
microeconomics) :
𝑟
𝑃𝑥
𝑤
𝑀𝑃𝐿 =
𝑃𝑥
𝑀𝑃𝐾 =
So, we have that:
𝑋 = 𝐾. 𝑀𝑃𝐾 + 𝐿. 𝑀𝑃𝐿 ⟺ 𝑋 = 𝐾.
𝑟
𝑃𝑥
+ 𝐿.
𝑤
𝑃𝑥
⟺ 𝑃𝑥 . 𝑋 = 𝑟. 𝐾 + 𝑤. 𝐿
The last equation means that the value of production (𝑃𝑥 . 𝑋) must be equal to the cost
of production (𝑟. 𝐾 + 𝑤. 𝐿) , implying that the firm has zero profits. This result makes
sense, given the assumption of the model that firms are price-takers.
4) Another important result is that, for the same capital intensity (𝑘), the 𝑀𝑅𝑇𝑆𝐿,𝐾 is
constant (= 𝛼):
Another relevant
feature here is that,
when the capital
intensity decreases,
the 𝑀𝑅𝑇𝑆𝐿,𝐾
decreases as well.
Because
𝑀𝑅𝑇𝑆𝐿,𝐾 =
𝑤
𝑟
,
then we can say also that
𝑤
𝑟
decreases with the capital intensity.
5) The contract curve is given by 𝑀𝑅𝑇𝑆𝐿,𝐾 𝑥 = 𝑀𝑅𝑇𝑆𝐿,𝐾 𝑦 , and it can have only one out
of these three shapes:
1) 𝑘𝑥 > 𝑘𝑦 --> X is the capital
intensive good.
2) 𝑘𝑥 = 𝑘𝑦
3) 𝑘𝑥 < 𝑘𝑦 --> X is the labor
intensive good.
Furthermore, cases 1 and 3 imply that the P.P.F of an economy has to be concave. Case
2 implies that the P.P.F has to be linear.
6) CRS is compatible with Factor Intensity Reversals (FIR)
This is a property that is not going to be used intensively in this course, because along
the course we always assume no FIRs, for simplicity.
Basically this property says that two sectors may invert their relative factor intensity for
different factor prices. For example, for a certain factor price sector X is the capital
intensive sector, and for other factor price it is the labor intensive sector.
Now that we've seen some properties of this model, we need to summarize some
important relationships:
Take into account that throughout this model we will always assume that X is the
capital intensive good ( 𝑘𝑥 > 𝑘𝑦 ) :
(i) Relationship between
𝑤
𝑟
and 𝑘𝑥 , 𝑘𝑦
If X is the capital intensive
good, then we have a
concave contract curve.
By picking two points
along the contract curve,
points A and 𝐵1 , we
observe that :

𝑘𝐴 is higher than 𝑘𝐵 ,
that is, the capital
intensity at point A is
higher than at point B. This applies for both goods, X and Y.

𝑤
𝑟 𝐴
>
𝑤
𝑟 𝐵
. First we have to realize that MRTS =
𝑤
𝑟
in equilibrium , which is the
slope of the tangent. In order to compare point A with 𝐵1 , we have to use point 𝐵2
knowing that the slope of a tangent to 𝐵1 is the same as the slope of the tangent to 𝐵2 .
As we can see clearly, 𝑀𝑅𝑇𝑆𝐿,𝐾 𝐴 > 𝑀𝑅𝑇𝑆𝐿,𝐾 𝐵2 .´
 From point A to point B, the capital intensity decreased
and
𝑤
𝑟
𝐖𝐡𝐞𝐧
decreased as well. In other words,
𝐰
𝐝𝐞𝐜𝐫𝐞𝐚𝐬𝐞 , 𝐤 𝐱 𝐚𝐧𝐝 𝐤 𝐲 𝐝𝐞𝐜𝐫𝐞𝐚𝐬𝐞 𝐭𝐨𝐨.
𝐫
(ii) Relationship between
w
r
and
𝑃𝑥
𝑃𝑦
If we continue to assume that X is the capital intensive good, we know that the
contract curve is concave as well as the PPF.
The contract curve will be similar to the one represented above. When we move
from point A to 𝐵1 ,
w
r
decreases and more is produced of X and less of Y -
𝐾𝑥 𝑎𝑛𝑑 𝐿𝑥 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑤𝑕𝑖𝑙𝑒 𝐾𝑦 𝑎𝑛𝑑 𝐿𝑦 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒. By looking at the PPF, we
realize that
𝑃𝑥
𝑃𝑦
increases when we move from A to 𝐵1 .
Do not forget that, by
definition,
𝑃𝑥
𝑃𝑦
= 𝑀𝑅𝑇𝑥,𝑦
, that is, the slope of the
line tangent to a certain
point. At 𝐵1 the slope is
higher than at A.
 From point A to point 𝐵1 ,
𝑤
𝑟
decreased while
𝐖𝐡𝐞𝐧
𝑃𝑥
𝑃𝑦
𝐰
𝐫
increased. In other words,
𝐝𝐞𝐜𝐫𝐞𝐚𝐬𝐞 ,
𝑷𝒙
𝑷𝒚
𝐢𝐧𝐜𝐫𝐞𝐚𝐬𝐞𝐝 .
In order to summarize all these relationships together, we draw the Samuelson
Note that this graphs are only for the
case where X is capital intensive and
there are no Factor Intensity Reversals.
Diagram.
After deriving some important relationships and the Samuelson diagram, it is
also important to know some theorems on this model.
 Rybczynski Theorem
At constant relative commodity prices,
𝑃𝑥
𝑃𝑦
, an relative increase in one
factor increases the supply of the good that uses intensively that factor, and
an absolute contraction on the supply of the other good.
In other words:
𝑁𝑜 𝐹𝐼𝑅𝑠
𝑃𝑥
If
𝑃𝑦
=
𝑃𝑥
𝑃𝑦
0
𝑋 𝑖𝑠 𝐾 − 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑣𝑒
Δ𝐾 > 0 ; Δ𝐿 = 0
⇒
𝑋𝑠 ↑
𝑌𝑠 ↓
Proof: Assuming that there is an increase in capital endowment (𝐾 )
First we need to understand that for relative commodity prices to maintain
constant it is necessary that 𝑘𝑥 and 𝑘𝑦 maintain constant as well. We can
easily observe that in the Samuelson Diagram:
When there is an increase in the capital endowment, the edgeworth box
"expands vertically". Hence, for the relative prices to remain constant, the
capital intensities need to be constant, i.e the slope of the line 𝛼𝐴 needs to
be maintained in order for 𝑘𝑥 to be constant, and the slope of the line 𝛽𝐴
needs to be maintained in order for 𝑘𝑦 to be constant. Following this, we get
to a new point, out of the old contract curve, point B. Note that this point
belongs to the new contract curve (the contract curve changes when the
endowments change).
Furthermore:
𝛼𝐴 < 𝛼𝐵 ⇒ 𝑋 𝑠 ↑
𝛽𝐴 < 𝜑𝐵 ⟹ 𝑌 𝑠 ↓
Prooving the Ryb. Theorem!
Note that point B is obtained by maintaining
𝑃𝑥
𝑃𝑦
𝑃𝑥
=
0
𝑃𝑦
. If we do this for
all the relative prices, we would be able to plot the new contract curve and
the new PPF, as it is represented above. Intuitively, we know that the
expansion of the PPF is biased towards X since there is an increase on the
factor that is used intensively by this good (K). If Y was the K-intensive good
for example, the expansion would be biased towards Y.
 Stolper Samuelson Theorem
An increase in relative commodity prices
𝑃𝑥
, everything else constant, will
𝑃𝑦
increase the real return on the factor used intensively by good X and a
decrease in the real return on the factor used intensively by good Y.
In other words:
𝑁𝑜 𝐹𝐼𝑅𝑠
𝑃𝑥
If
𝑃𝑦
↑
⇒
𝑋 𝑖𝑠 𝐾 − 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑣𝑒
Δ𝐾 = 0 ; Δ𝐿 = 0
𝑟
𝑃𝑥
↑;
𝑟
𝑃𝑦
↑;
𝑤
𝑃𝑥
↓;
𝑤
𝑃𝑦
↓
Proof:
Assuming that initially
to
𝑃𝑥
𝑃𝑦
1
𝑃𝑥
𝑃𝑦
, we have that :
=
𝑃𝑥
𝑃𝑦
0
, and then the relative prices increased
When the relative prices increase, the capital intensities for both goods
decrease.
As we've seen in Microeconomics,
𝑟
𝑃𝑖
= 𝑀𝑃𝐾𝑖 and
𝑤
𝑃𝑖
= 𝑀𝑃𝐿𝑖 , for good 𝑖.
It is also known from Microeconomics that 𝑀𝑃𝐾 depends negatively on
capital intensity (k) and that 𝑀𝑃𝐿 depends positively on capital intensity (k).
So, we can immediately say that
𝑟
𝑃𝑥
↑;
𝑟
𝑃𝑦
↑;
𝑤
𝑃𝑥
↓;
𝑤
𝑃𝑦
↓.
There are still two more theorems, but we're going to talk about them later
on.
 Autarky equilibrium
The autarky equilibrium is fairly easy to derive:
(a) Demand side is given by a social utility function
(b) Supply side is given by a PPF
Then, the closed economy equilibrium is:
We can also represent this equilibrium by plotting the RS and RD :
 Shock in closed economy
Starting in a closed economy equilibrium, what happens if 𝚫𝑲 > 0 ? (Note that this is
not the same as in the Ryb. Theorem' proof , since we're not fixing relative prices)
Assuming that X is the capital intensive good, technologies are CRS and preferences are
homothetic, as we always assume, we have:
(i) On the Supply Side
By the Ryb. Theorem, for the same relative prices, an increase in capital endowment
will increase the supply of the food that uses capital intensively (good X), and decrease
the supply of the other good (Y). So, for the same
𝑃𝑥
𝑃𝑦
the RS expands.
(ii) On the Demand Side
When the capital endowment increases, consumer's
budget constraint increase as well. However, because
preferences are homothetic, for the same relative
prices, the relative consumption is the same. That is,
for the same
𝑃𝑥
𝑃𝑦
,
𝑋
𝑌
remains constant.
,
𝑋
𝑌
increases. This means that
(iii) We conclude that
𝑃𝑥
𝑃𝑦
decreases and
𝑋
𝑌
increases, in equilibrium. We conclude
also that :
By the Samuelson diagram :
𝑃𝑥
𝑃𝑦
↓ ⇒
By the Stolper Samuelson Theorem:
𝑤
𝑟
𝑃𝑥
𝑃𝑦
 International Trade
i.
↑ ; 𝑘𝑥 ↑ ; 𝑘𝑦 ↑
↓ ⇒
𝑟
𝑃𝑥
↓;
𝑟
𝑃𝑦
↓;
𝑤
𝑃𝑥
𝑤
↑;
𝑃𝑦
↑.
𝑃
To simplify : 𝑝 = 𝑃𝑥
𝑦
Small Country Case
In this case, we assume that the country is so small that it cannot influence
international prices. As so, the international prices (𝑝∗ ) are given, and the
country is a price-taker.
Here, we assume that relative autarky prices are lower than relative
international prices (𝑝𝑎𝑢𝑡 . < 𝑝∗ ).
The first conclusion is that the small country is going to export X, the good
where it has relative advantage, and it's going to import Y.
0 - Autarky
1 - Free Trade
When the small country is under free trade, it will produce at 𝑃1 . Under free
trade, the economy can consume at any point in the CPF (Consumption
Possibility Frontier). By maximizing utility, it will consume at 𝐶1 , a bundle out of
the PPF.
Another obvious conclusion is that the economy will be better off under free
trade, since 𝑢1 > 𝑢0 .
ii.
Large Country Case
In the large country case, both countries influence international prices. That means
international prices are an endogeneous variable.
Suppose there are two countries, the Home country (H) and the Foreign country (F),
𝐻
𝐹
where 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . . Given this, we can compute the offer curves of each country
and calculate the equilibrium international prices (To draw the offer curves, please
recall what we've done in the 2x2 model)
Another way to compute the equilibrium is by aggregating supply and demand.
However we're not going to compute it here, since it's similar to what we've
done in the 2x2 chapter.
 Determinants of Trade
𝐻
𝐹
We already know that , for example, if 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . , then Home will export X and
import Y, while the Foreign Country will export Y and import X. However, it's also
𝐻
𝐹
important to figure out why 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . and what determines it. In this course,
we're going to see the following features:
a)
b)
c)
d)
e)
Size
Preferences
Factor Endowments
Technology
Market Structure
NOTE: Throughout these demonstrations it
is assumed that technologies are CRS ,
preferences are homothetic, there are no
FIRs and X is the capital-intensive good
First of all we have to realize that, in this model, if both countries are absolutely
𝐻
𝐹
identical they will have no incentive to trade since 𝑝𝑎𝑢𝑡
. = 𝑝𝑎𝑢𝑡 .
a) Assume that there are two countries (H and F) which are absolutely identical, except
that F is twice as H . This means that 2. 𝐾𝐻 = 𝐾𝐹 and 2. 𝐿𝐻 = 𝐿𝐹 . An equivalent thing
to do is to see what happens to the Home country when its endowments are doubled,
for a fixed relative price:
As we've seen when proving the Ryb. Theorem, in order to maintain the same relative
prices it is also necessary to keep the capital intensities constant.
So, we conclude that, for the same relative prices, both countries supply the same
relative amount
𝑋
𝑌
. That is, 𝑅𝑆𝐻 = 𝑅𝑆𝐹 .
For the demand side, we know that consumers from country F have twice the income
of consumers from country H (𝐼𝑛𝑐𝑜𝑚𝑒𝐹 = 𝑤. 2𝐿𝐻 + 𝑟. 2𝐾𝐻 ) . However, because
preferences are equal and homothetic, F consumer's optimal relative consumption is
the same as H consumer, for the same relative prices. This means that 𝑅𝐷𝐻 = 𝑅𝐷𝐹 .
𝐻
𝐹
Since both countries have the same RS and RD, it's easy to conclude that 𝑝𝑎𝑢𝑡
. = 𝑝𝑎𝑢𝑡 . ,
hence they will not have any incentive to trade.
We just proved that, in the context of this model, size does not matter for trade!
b) Assume again there are two countries (H and F) absolutely identical, except that H'
preferences are biased towards Y and F' preferences are biased towards X , as shown
below:
Given this, we conclude that, for the same relative prices
𝑋 𝐷
𝑌 𝐻
<
𝑋 𝐷
𝑌 𝐹
.
Please be aware that if the axis are changed, i.e the vertical axis is X instead of Y and
the horizontal axis is Y instead of X , we would have obtained that
𝑋 𝐷
𝑌 𝐻
>
𝑋 𝐷
𝑌 𝐹
from
the graph represented above. It all depends on the way you choose to draw it.
On the supply side, since we assumed that endowments* and technologies are
constant, among other things, we know that
𝑋 𝑆
𝑌 𝐻
=
𝑋 𝑆
𝑌 𝐹
, for the same relative
prices.
* We can assumed that F is twice as H and still we will obtain the same result, since size does
not matter for trade.
The autarky equilibrium for both countries would be:
𝐻
𝐹
Because 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . , there will be trade where the Home country exports X and
imports Y while the Foreign country exports Y and imports X.
So, preferences matter for trade!
c) Here, factor endowments are seen in relative terms
𝐾
𝐿
. That's why this parameter
for trade is different from "size", where relative factor endowments are equal.
So, let's assume that 𝐿𝐻 = 𝐿𝐹 and that 𝐾𝐻 = 2. 𝐾𝐹 , without lost of generality (since
size does not matter).
Due to the Ryb. Theorem, we know that, for the same relative prices,
𝑋 𝑆
𝑌 𝐻
>
As seen before, because preferences are equal and homothetic, we have that
𝑋 𝐷
𝑌 𝐹
, for the same relative prices.
𝑋 𝑆
𝑌 𝐹
𝑋 𝐷
𝑌 𝐻
.
=
𝐻
𝐹
Because 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . , there will be trade where the Home country exports X and
imports Y while the Foreign country exports Y and imports X.
So, relative factor endowments matter for trade!
With respect to factor endowments, there is a theorem about it : H-O Theorem
The theorem says that a capital abundant country tends to export the capital intensive
good, while the labor abundant country tends to export the other good.
However, there are 2 different definitions of abundance.
1. Physical definition - This is what we've seen above. If
𝐾
𝐿 𝐻
>
𝐾
𝐿 𝐹
and preferences
are equal, then H exports the capital intensive good (X) and F exports the labor
intensive good (Y).
2. Price definition - Here, the definition of capital abundance is not who has more
𝐾
𝐿
,
but rather the price of those factors. That is, knowing that capital costs 𝑟 and that labor
costs 𝑤, if
𝑤
𝑟 𝐻
>
𝑤
𝑟 𝐹
, then in the Home country labor is relatively more costly than
in the Foreign country, hence H is capital abundant while F is labor abundant. This
means that H is going to export X while F is going to export Y. For this to be compatible
𝐻
𝐹
with this model, it is mandatory that 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . , which is proven below:
(Note that, in this version, same preferences assumption does not need to hold. So, we
can say that the "physical version" is a particular case of the "price version")
iv) A better model to see differences in technologies is the Ricardian Model.
Nevertheless, in the H-O Model, technology is also a determinant of trade. But we will
not prove it.
v) The H-O model assumes that all the markets are in perfect competition, where all
firms are price-takers for all sectors. However, this might not be true. For example, we
can have a monopolist producing in one sector.
 Consequences of Free Trade
The consequences of trade are summarized in the Factor Price Equalization Theorem
This theorem says that factor prices will be equalized under free trade, if there are no
transportation costs and there is incomplete specialization for both countries. By other
words, if country H and F have the same technologies, CRS, there are no FIRs and no
transportation costs, then they will trade until 𝑝𝐻 = 𝑝𝐹 = 𝑝∗ .
The concept of incomplete specialization was not specified until here for simplicity
reasons. However that concept must be explained, in order to fully understand the FPE
Theorem.It happens that until now the Samuelson Diagram was not rigorously drawn.
Take the example of this country, with an endowment of 𝑘 .
If the international prices are below 𝑝1 , the country will produce only good Y - it will
fully specialize in good Y. To do so, it will allocate all its inputs in sector Y , and so the
relative prices of inputs
𝑊
𝑟
will be 𝛼. However, it doesn't matter how "low"
commodity prices (𝑝) are, because the country is already allocating all its inputs in
sector Y, hence
𝑊
𝑟
will always be 𝛼 for any 𝑝 < 𝑝1 . Furthermore, at
𝑊
𝑟
= 𝛼 , the
capital intensity of good X is 𝑘1 . Note that this is the maximum capital intensity that
sector X can have. The minimum is, naturally, 𝑘 .
If the international prices are above 𝑝2 , the country wants to produce only good X - it
will fully specialize in good X. To do so, it will allocate all its inputs in sector X , and so
the relative prices of inputs
𝑊
𝑟
will be 𝛽. And the same happens as before : it doesn't
matter how "high" commodity prices(𝑝) are, because the country is already allocating
all its inputs in sector X, hence
𝑊
𝑟
will always be 𝛽 . Moreover, at
𝑊
𝑟
= 𝛽 , the
capital intensity of good Y is 𝑘2 . It should also be noticed that this is the minimum
capital intensity that sector Y can have. The maximum is, naturally, 𝑘 .
Having said this, the complete Samuelson Diagram looks like this:
So, when we say "incomplete specialization" it means that 𝑝1 < 𝑝∗ < 𝑝2 . Additionally,
keep in mind that samuelson diagram can be different for two identical countries with
different endowments.
Going back to the FPE Theorem, let's assume two countries, H and F, with a relative
endowment of 𝑘𝐻 and 𝑘𝐹 , respectively.
If international prices are 𝑝𝐴 , the real return on factors will be the same under free
trade for both countries. That happens because at that price both countries will have
the same capital intensities under free trade, hence the same 𝑀𝑃𝐿 and 𝑀𝑃𝐾 . This
applies for both goods, so the return on factors has to be the same in both countries.
But, if 𝑝 = 𝑝𝐵 , country F will fully specialize in the production of good X and the H
country will not. In equlibrium, the capital intensities in each country will be different,
thus the return on factors cannot be the same.
Another important feature on this chapter is that free trade is a good substitute for
factor mobility. The main idea here is that when countries "trade" factors (labor and
capital), that is, workers and machines moving from one country to another, it's always
𝑤
𝑟
𝑃𝑖
𝑃𝑖
with the aim of increasing the real return on labor and capital ( and ). That is,
workers have an incentive to move to the country where they can achieve a higher
utility level and capital owners invest where they can have a higher return. However, if
FPE Theorem prevails, that incentive disappears given that real return on factors will be
equalized under free trade.
Ricardian Model
The Ricardian Model is a model focused mainly on differences in technologies
among countries. Ricardo proved that what matter for trade is not absolute
advantage but rather comparative advantage.
In this model there are two countries, the Home country and the Foreign country,
two goods, X and Y, and only one factor, labor. There is still a factor endowment (for
labor only).
In this model it's assumed that the production function are like this:
1
𝑋=
. 𝐿𝑥
𝑎𝑥
where 𝑎𝑥 is the technological coefficient or unit labor requirement, that is, the
amount of labor required to produce 1 unit of X.
Considering only the Home Country for now, to build the model we only need 3
equations:
𝑋=
1
𝑎𝑥 𝐻
𝑌=
. 𝐿𝑥
1
𝑎𝑦 𝐻
. 𝐿𝑦
𝐿𝑥 + 𝐿𝑦 = 𝐿𝐻
Note that
𝐻
𝑝𝑎𝑢𝑡
. =
𝑎𝑥 𝐻
𝑎𝑦 𝐻
.
⇔
𝑎𝑥 𝐻 . 𝑋 + 𝑎𝑦 𝐻 . 𝑌 = 𝐿𝐻 ⟺ 𝑌 =
𝐿𝐻
𝑎𝑦 𝐻
−
𝑎𝑥 𝐻
𝑎𝑦 𝐻
. 𝑋 --> PPF
𝐻
𝐹
 Free trade - Assume that 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . ⇔
𝑎𝑥 𝐻
𝑎𝑦 𝐻
<
𝑎𝑥 𝐹
𝑎𝑦 𝐹
First of all, it is important to figure out what will be the international price (𝑝∗ ) when
country H and F start trading. To do so we're going to use the supply and demand
model.
The world RS would be like this
:
𝐻
𝐹
--> If 𝑝∗ < 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . , then
both countries would fully
specialize in producing Y
⟹
𝑋
𝑌
=0
𝐻
∗
𝐹
-->If 𝑝𝑎𝑢𝑡
. < 𝑝 < 𝑝𝑎𝑢𝑡 . , then
H will fully specialize in X and F
will fully specialize in Y
𝐻
𝐹
∗
--> If 𝑝𝑎𝑢𝑡
. < 𝑝𝑎𝑢𝑡 . < 𝑝 , then
both countries would fully specialize in procucing X
Depending on the demand curve, we can obtain different equilibriums:
1. Country H is considered a large country and F a small country
Here, the international
𝐻
prices are equal to 𝑝𝑎𝑢𝑡
.
, so country H does not
have any incentive to
trade. However,
country F gains from
trade since 𝑢1 > 𝑢0
Here, F fully specialize
in producing good Y.
2. Both countries are considered large countries
𝐻
∗
𝐹
Here both countries fully specialize because 𝑝𝑎𝑢𝑡
. < 𝑝 < 𝑝𝑎𝑢𝑡 . . Country H fully
specialize in X while country F fully specialize in Y.
3. Country F is considered a large country and H a small country
Here, the international
𝐹
prices are equal to 𝑝𝑎𝑢𝑡
. , so
country F does not have any
incentive to trade. However,
country H gains from trade
since 𝑢1 > 𝑢0
Here, H fully specialize in
producing good X.
 Gains from trade
Although we already know that there are gains from trade ( since at least one of the
countries sees its utility level increase when trading), we want to analyze those
gains by computing the changes in the real wage rates.
In this model,
𝑊
𝑝𝑖
= 𝑀𝑃𝐿𝑖 =
1
𝑎𝑖
but only if the country is producing good 𝒊.
So, assuming that both countries were producing both goods before trade, we have
that :
Specific Factors Model/ Ricardo-Viner Model
The Specific factors model is a short-run model of the H-O Model. The latter
assumes that K and L can move freely across sectors, which we know it's possible in
the long-run. The specific factors model assume that only labor can move freely
across sectors.
In this model there are two sectors, X and Y, where sector X uses land (T) and labor
(𝐿𝑥 ) while sector Y uses capital (K) and labor (𝐿𝑦 ). There is still endowments in the
economy.So, we have that:
(1) 𝑋 = 𝐹(𝑇, 𝐿𝑥 )
𝑌 = 𝐺(𝐾, 𝐿𝑦 )
(2) 𝑇 = 𝑇 ; 𝐾 = 𝐾 ; 𝐿𝑥 + 𝐿𝑦 = 𝐿
(3) Going back to the microeconomics review chapter,
𝑤
𝑃𝑦
𝑤
= 𝑀𝑃𝐿𝑥 and
𝑃𝑥
𝑦
= 𝑀𝑃𝐿 .
By manipulating the equations, we get that
𝑤
𝑃𝑦
=
𝑃𝑥
𝑤
𝑃𝑦
𝑃𝑥
𝑃𝑥
𝑀𝑃𝐿𝑥
𝑃𝑦
and so we can represent this model in the following graph:
𝑦
⇔ 𝑀𝑃𝐿 =
=
𝑃𝑥
𝑃𝑦
𝑀𝑃𝐿𝑥
 Free Trade Equilibrium ( Assuming that 𝑝𝑎𝑢𝑡 . < 𝑝∗ )
Before doing this analysis, it's necessary to understand that if
𝑇
𝐿𝑥
and
𝐾
𝐿𝑦
change
then the real return on factors change as well, as we've done in the H-O Model.
Because international prices are higher than autarky prices:
𝐿𝑥 ↑ and 𝐿𝑦 ↓ ⇒
𝑇
𝐿𝑥
↓ and
𝐾
𝐿𝑦
↑ ⇒
𝑟𝑇
𝑃𝑖
𝑟𝐾
𝑃𝑖
𝑤
𝑃𝑥
𝑤
𝑃𝑦
↑
(Real return on land increased)
↓ (Real return on capital decreased)
.
↓ (Real wage in terms of X decreased)
.
↑ (Real wage in terms of Y increased)
.
We conclude that, in this case (𝑝𝑎𝑢𝑡 . < 𝑝∗ ), when the country opens to trade, land
owners will gain while capital owners will lose. Workers will be devided since the
real wage increased in terms of one good but decreased in terms of the other good.
Economies of Scale
The conclusion from the H-O Model and the Ricardian Model is that identical
countries do not have any incentive to trade. However, in reality, what we see is
trade between very similar countries. For example, Germany and France trade a lot
- Germany exports volkswagens to France and imports Renaults from France, and
vice-versa. This model tries to explain why this happens, and the main argument is
that is due to the existence of economies of scale. However, there are two different
model regarding economies of scale:
(A) Economies of scale external to the firm (and intrinsic to the industry)
(B) Economies of scale internal to the firm
(A) The idea here is that, if a new firm goes into the sector (X or Y), it immediatly get
advantage of economies of scale.
Assume two goods, X and Y, two countries, H and F, and 1 factor, labor (L). Assume
also that sector X is the only one that get advantage of economies of scale. The
model is as follow:
𝑋=
𝑌=
1
𝐴𝑥
. 𝐿𝑥 , 𝑤𝑕𝑒𝑟𝑒 𝐴𝑥 𝑑𝑒𝑝𝑒𝑛𝑑𝑠 𝑜𝑛 𝑋
1
. 𝐿𝑦
𝑎𝑦
𝐿𝑥 + 𝐿𝑦 = 𝐿
Solving the model, we get the following PPF: 𝑌 =
𝐿
𝑎𝑦
−
𝐴𝑥
𝑎𝑦
. 𝑋 , where 𝐴𝑥 is
not fixed, as it was in the Ricardian Model. Drawing the PPF, we get :
Because the aim of this model is to show that 2 identical countries have incentive to
trade if there are economies of scale, let's assume that H and F have the same
preferences, the same technology and the same endowments. Assume also that X is
the sector that has economies of scale.
The first thing you should notice is that both countries have the same PPF (the one
drawn above). When opening to FT, if one country specialize in one good while the
other specialize in the other good, there are gains from trade due to economies of
scale (X becomes cheaper). Although this model explains why there can be trade
between identical countries, it does not predict the pattern of trade. There are
several possibilities (actually, there are 6 possible patterns of trade).
 Gains from trade
To measure if countries gain from trade, we have to look at the real wage rates in
both countries. Let's consider the pattern of trade where H fully specialize in X and F
fully specialize in Y , although there are other possible patterns of trade. Remember
that in this pattern of trade 𝑝𝐻 < 𝑝∗ < 𝑝𝐹
Before trade :
𝑤
𝑃𝑥 𝐻
𝑤
𝑃𝑦
After trade: ↑
↑
=
𝐻
𝑤
𝑃𝑥 𝐻
𝑤
𝑃𝑦
=
=
1
𝑃𝑥 𝐹
𝑤
1
𝑎𝑦
𝑃𝑦
1
𝐹
=
=
1
𝐴 1𝑥
1
𝑎𝑦
↑
𝐴 2𝑥 ↓
= ↑
𝐻
𝑤
𝐴 1𝑥
𝑤
𝑃𝑥 𝐻
. ↑ 𝑝∗
When trading both countries gain from trade!
𝑤
𝑃𝑥 𝐹
𝑤
𝑃𝑦
=
𝐹
=
1
𝑎𝑦
𝑤
𝑃𝑦
.
𝐹
1
↓ 𝑝∗
(B) In this model, each firm has economies of scale instrinsic to its own production, thus a
natural monopolist will appear in the production of each good. So, the number of goods is
endogeneous and equal to the number of firms, since each firm produces one good.
Unlike the models we've seen before, there is only one sector here (ex: cars), but each firm
produces a differentiated good in that sector (ex: volkswagen, renault, fiat, etc.). This type
of competition is called monopolistic competition.
Building the model:
i.
The demand faced by each firm is given by: 𝑞𝑖 = 𝑄
1
𝑛
− 𝑏(𝑝𝑖 − 𝑝) , where Q is the
total amount of output (ex: total amount of cars) and 𝑝 the average price in the
market. Furthermore, we assume that each firm is so small that it cannot influence
the total market output (and price 𝑝 ) --> Q is given and fixed.
𝑄
= 𝑛 . Every firm has the same cost structure : 𝑇𝐶 = 𝐹 + 𝑐. 𝑞𝑖
ii.
In equilibrium,
iii.
Each firm acts as a monopolist for the demand it faces: 𝑀𝑅 = 𝑀𝐶
𝑞𝑖
In order to calculate the MR we have to manipulate the demand expression
𝑞𝑖 = 𝑄
1
𝑛
− 𝑏(𝑝𝑖 − 𝑝)
⇔ 𝑝𝑖 =
1
𝑛.𝑏
+𝑝 −
1
𝑏.𝑄
. 𝑞𝑖 ⇔ 𝑝𝑖 = 𝛼 − 𝛽. 𝑞𝑖
Solving the monopolist problem:
𝑀𝑅 = 𝑀𝐶 ⇔
⇔
𝑛
1
𝑏. 𝑄
𝑀𝐶 = 𝑐
1
𝑝𝑖 =
.𝑞 + 𝑐
𝑏. 𝑄 𝑖
𝑄
1
+𝑝
𝑛. 𝑏
𝛽=
𝛼 − 2. 𝛽. 𝑞𝑖 = 𝑐 ⇔ 𝛼 − 𝛽. 𝑞𝑖 − 𝛽. 𝑞𝑖 = 𝑐 ⇔ 𝑝𝑖 − 𝛽. 𝑞𝑖 = 𝑐
knowing that 𝑞𝑖 =
𝛼=
, we have that: 𝑝𝑖 = 𝑐 +
1
𝑛.𝑏
→ 𝑷𝑷 𝑳𝒊𝒏𝒆
iv. There is free entry and exit in the long-run -> 𝑝𝑖 = 𝐴𝐶
𝑝𝑖 = 𝐴𝐶 ⇔ 𝑝𝑖 = 𝑐 +
knowing that 𝑞𝑖 =
𝑄
𝑛
, we have that: 𝑝𝑖 = 𝑐 +
𝐹
𝑄
𝐹
𝑞𝑖
. 𝑛 → 𝑪𝑪 𝑳𝒊𝒏𝒆
v. Because every firm has the same cost structure and face the same demand, we conclude
intuitively that 𝑝𝑖 = 𝑝.
It's important to note that, in this model, if we assume the same cost structure and the
same demand for both countries, the only thing that changes from country to country is
the size of the market (Q).
By plotting both lines, CC and
PP, we're able to compute
the equilibrium price in the
sector as well as the number
of firms operating in that
sector.
 Population Growth
If there is a population
growth in a country,
meaning that the size of
the market (Q) increases, it
results in a price decrease
and an increase in the
number of firms.
A price decrease implies a real wage
𝑤
𝑃
increase
An increase in the number of firms represent an increase in the variety of products
Overall, consumer's utility increases due to an increase in the real wages and an increase in
the variety of products (in this model, consumers value variety).
 Free Trade
When two countries (H and F) start trading, what happens is that both markets start
representing a single market, that is 𝑄𝐹𝑇 = 𝑄𝐻 + 𝑄𝐹 . Graphically, we have that:
(Assume that 𝑄𝐻 > 𝑄𝐹 )
As we can see,
price decreases
and the number of
varieties increase
for both countries.
So, we conclude
that both
countries are
better off with
trade than without
trade.
Note that we don't know where each firm is located under free trade, meaning that
a firm can be in country H or country F.
 Migration
Let's assume now that there is no free trade of goods but people can freely move
from one country to another. Note that for migration to be possible we have to
assume no free trade, otherwise both countries would be equal in terms of welfare,
hence there would be no incentive to migrate.
(A) Country H and F are equal, except that 𝑄𝐻 > 𝑄𝐹 .
d
Under this context, 𝑝𝐹 > 𝑝𝐻 and 𝑁𝐹 < 𝑁𝐻
, meaning that 𝑢𝐹 < 𝑢𝐻 .
Faced with this fact, people would start
moving from country F to country H.
In the end, the foreign country would
disappear due to a total migration.
(B) Country H and F are equal, except that 𝑄𝐻 > 𝑄𝐹 and 𝐹𝐹 < 𝐹𝐻 (in country F firms
have a lower fixed cost than in country H).
These differences are such that
𝐹𝐻
𝑄𝐻
<
𝐹𝐹
𝑄𝐹
- Recall CC line equation: 𝑝 = 𝑐 +
𝐹
𝑄
.𝑛
What we will obtain is a picture similar to the one above , in (A) , thus people would start
to move from country F to H , that is, people would start migrating from the more efficient
country (F) to the less efficient country (H), and so the more efficient country would
disappear.
Optimal policies and Non-economic Objectives(NEO)
Now, we're going back to the H-O Model in order to study government
interventions in the economy. Along this chapter we will always assume that there
are Social Utility Functions (SUF). Furthermore, we are only going to consider the
small country case, where 𝒑𝒂𝒖𝒕. > 𝒑∗ (The small country exports Y and imports X).
But, before studying the optimal policies and NEO for a country, it is important to
know first what are the instruments available for the government to use. The
government can use the following instruments:
 Tariff(𝑇)
 Tax on production (𝑡𝑝 )
 Tax on consumption (𝑡𝑐 )
 Tax on factors (𝑡𝑓 )
Tariff(𝑻) - Assuming a tariff on imports (good X)
First of all, I advise you to always keep in mind that if in the vertical axis is "X" instead of
"Y" and in the horizontal axis is "Y" instead of "X", the graph will be completely different.
However, the final conclusions must be identical.
Secondly, note that the autarky equilibrium is no longer represented. Only the Free trade
& Laissez Faire equilibrium (0) and the Tariff equilibrium (1). Laissez Faire equilibrium is the
equilibrium without any type of government intervention.
Analysis
When there is no Tariff, the small country will produce at 𝑃0 and consume at 𝐶0 , achieving
a utility level of 𝑢0 .
When the Tariff is imposed we have to keep in mind two things :
On the supply side, firms will face a higher price domestically (𝑝𝑇 ∗ > 𝑝∗ ) , although the
interational prices remain the same (𝑝∗ ) . Faced by this new domestic price, the economy
will produce at 𝑃1 .
On the demand side, consumer will also face this new domestic price , 𝑝𝑇 ∗ . This means
that the new consumption point is tangent to a utility curve, with slope 𝑝𝑇 ∗ . Furthermore,
we have to keep in mind that the international prices did not change, hence the economy
will consume in a point along the CPF (consumption possibility frontier). This line
correspond to the national production at international prices. Faced with these
restrictions, the only possible point of consumption is 𝐶1 .
Concluding, when a Tariff is imposed, the small country will produce at 𝑃1 and consume at
𝐶1 , achieving a utility level of 𝒖𝟏 which is lower than 𝒖𝟎 . This means that, in the small
country case, FT is the optimal policy.
Tax on production (𝒕𝒑 ) - Assuming a tax on the production of the imported good (X)
Analysis
A tax on production will induce producers to move away from the Free Trade
equilibrium(𝑃0 → 𝑃1 ). However, consumers will not be affected directly meaning that they
will still face 𝑝 = 𝑝∗ .
The CPF will be similar to before (Tariff equilibrium) for the same reason. However the new
consumption point is not equal as before because now consumers face a price 𝑝 = 𝑝 ∗ .
This means that the new consumption point is a point tangent to a utility curve, with slope
𝑝 ∗ ,which is the slope of the CPF. Basically, we can say that the new consumption point is
located where the utility curve is tangent to the CPF.
Furthermore, the economy is worse off with the imposition of a tax on production
(𝑢1 < 𝑢0 )
Tax on consumption (𝒕𝒄 ) - Assuming a tax on the consumption of the imported good (X)
On the supply side, a tax on consumption will not affect producers since they face the
same price as in the free trade equilibrium. That's why 𝑃0 = 𝑃1 .
On the demand side, we have to keep in mind the reasoning made before:
The CPF will be the one drawn above, since the international prices does not change (do
not forget that we're in the small country case)
Consumers face a domestic price different from the international prices (𝑝𝑡∗𝑐 > 𝑝∗ ) , and
so their utility is maximized when the utility curve is tangent to a point such that the slope
is 𝑝𝑡∗𝑐 .
The economy is worse off with the imposition of a tax on consumption (𝑢1 < 𝑢0 ).
Tax on factors (𝒕𝒇 ) - Assuming a tax on 𝐿𝑥 and X is K-intensive
A tax on factors, mathematically speaking, is a little confusing. So, here we're only going to
use intuition to explain it.
Going back to the edgeworth box and the PPF:
When a tax is imposed on 𝐿𝑥 , sector X wants to use more capital. That's why the
contract curve changes.
Furthermore, the imposition of a tax created a distortion on the factor markets,
resulting in a contraction of the PPF. For the same price, the economy wants to
produce less of X.
On the demand side, it's equivalent to the tax on production.
In the end, the economy lies on lower utility level.
NOTE : To compute 𝑷𝟏 , there is the need to make a few demonstrations that are not
going to be shown here. The only thing we know is that, at 𝑷𝟏 , the economy is
producing less of X than initially.
Equivalences
There are some equivalences important for international trade, however they will not
be proved here.
1. A subsidy is equivalent to a negative tax
2. A tariff is equivalent to tax consumption and production simultaneously
(𝑇 = 𝑡𝑝 + 𝑡𝑐 )
3. A uniform tax on factors (taxing capital and labor simultaneously) is equivalent
to a tax of production.
4. A tax on imports is equvalent to a tax on exports
NEO
It might be the case that the government want to intervene in the economy,
although knowing that the best policy is free trade. The government might have
some non-economic objectives (NEO) :
i.
ii.
iii.
iv.
Level of production (Ex: 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑋 ≥ 𝑋 )
Level of consumption ( Ex: 𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑋 ≤ 𝑋 )
Level of trade ( Ex: 𝐼𝑚𝑝𝑋 ≤ 𝐼 )
Level of employment ( Ex: 𝐿𝑋 ≤ 𝐿)
Note: The restrictions will always
be active (for example,
𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑋 = 𝑋).
This happens because the more
you tax the less welfare you
attain, and here we're evaluating
the less costly options.
What we want to do here is to evaluate what is the less costly measure (in terms of
welfare) for each of these NEO. (Still assume that 𝑝𝑎𝑢𝑡 . > 𝑝∗ )
i.
(A) By using a tax on consumption
As we've seen earlier, a tax on consumption will not change the production point on
the PPF (𝑃0 = 𝑃1 ). So, in the context of this NEO, the value of a tax on consumption
is zero.
(B) Tax on production
A tax on production will attain the NEO!
(C) Tariff
By the equivalence that 𝑇 = 𝑡𝑝 + 𝑡𝑐 , and knowing that a tax on consumption has
zero value for this NEO --> Tariff is worse than a tax on production but better than a
tax on consumption. With the Tariff we can also attain the NEO, however it's more
costly than 𝑡𝑝 .
So, until now we know that : 𝑡𝑝 ≻ 𝑇 ≻ 𝑡𝑐
(D) Tax on factors
By subsidizing 𝐿𝑥 ( or a negative tax on 𝐿𝑥 ) for example, we induce the economy to
produce more of X , attaining the NEO. However, it is more costly than the tax on
production, as shown in the graph below:
As we can see 𝑢2 < 𝑢1 ⇒ 𝑡𝑝 ≻ 𝑡𝑓
 For a NEO on production, the best option is a tax on production!
ii.
On this NEO the objective is to make the economy to consume at 𝑋 = 𝑋 .
(A) Tax on consumption
A tax on consumption will be able to attain the objective, as we can see in the
picture above.
(A) Tax on production
Intuitively we know that a tax on production is more costly than a tax on
consumption for this NEO. However, it is also able to attain the NEO, since changes
in production will affect consumers.
In the picture below it is demonstrated why a 𝑡𝑝 is more costly than 𝑡𝑐 ( it is because
𝑢2 < 𝑢1 )
(C) Tariff
By the equivalence that 𝑇 = 𝑡𝑝 + 𝑡𝑐 , and knowing that a tax on consumption is
better than a tax on production, we conclude that the Tariff can also attain the NEO,
however 𝑡𝑐 ≻ 𝑇 ≻ 𝑡𝑝
(D) Tax on factors
We've seen in the NEO on production that 𝑡𝑓 is more costly than a 𝑡𝑝 . However, if
we try to compare 𝑡𝑓 and 𝑡𝑝 ,by drawing them on the same graph, we reach the
concluisonn than a tax on production is equivalent than a tax on factor,that is
𝑡𝑝 ≈ 𝑡𝑓 .
 We can rank the measures analized above ( 𝑡𝑐 ≻ 𝑇 ≻ 𝑡𝑝 ≈ 𝑡𝑓 ) and conclude
that, for a NEO on consumption, the best option is a tax on consumption!
iii.
On this NEO we're not going to make any demonstration like we've done on the
NEO above because it's difficult to compare them.
However, intutitively, it is not difficult to reach the conclusion that a Tariff is the
best policy for this NEO. First we have to realize what is this objective about: We
want to decrease the imports of X. Knowing that 𝐼𝑚𝑝𝑥 = 𝐶𝑥 − 𝑃𝑥 , what we want is
to decrease the consumption of X, or increase the production of X, or do both
simultaneously. So, knowing that a tax on consumption decreases 𝐶𝑥 , a tax on
production increases 𝑃𝑥 ( as well as a tax on factors) and that a tariff do both
simultaneously, it's obvious that the most efficient way to decrease imports is by
imposing a Tariff!
Below is the graph representing the imposition of a Tariff
 For a NEO on the level of imports, the best option is a Tariff!
iv.
On this NEO the objective is to make 𝐿𝑥 = 𝐿. Before analyzing the effect of any
type of taxation , there is the need to understand what means, graphically, that
𝐿𝑥 = 𝐿. (Always assuming that X is K-intensive)
Is is important to understand that any point of production that lies on the line above
𝐿 will attain the NEO.
(A) Tax on consumption
Again, a tax on consumption will not change 𝐿𝑥 since it does not affect production.
So, in the context of this NEO, the value of a tax on consumption is zero.
(B) Tax on production
A tax on production will attain the NEO on the level of employment.
(C) Tariff
By the equivalence that 𝑇 = 𝑡𝑝 + 𝑡𝑐 , and knowing that a tax on consumption has
zero value for this NEO --> Tariff is worse than a tax on production but better than a
tax on consumption. With the Tariff we can also attain the NEO, however it's more
costly than 𝑡𝑝 .
(D) Tax on factors --> Note that here we need to subsidize 𝑳𝒙
Intuitively, we know that a tax on factors is capable of satisfying the NEO. However, we
don't know if it's better or worse than a tax on production. We need to plot both
solutions in the same graph and conclude which one is better:
 Because 𝑢2 > 𝑢1 , we conclude that 𝒕𝒇 is the best instrument for a NEO on
the level of employment!
Summarizing all what we said before, the best instrument is always the one
that directly affects the NEO!
Immiserizing Growth (I.G)
This chapter if all about what might happen if optimal policies are not
followed. Here, we're only going to analyze the small country case.
We know that the optimal policy in this case is Free trade, with no
intervention of the government. However, let's see what might happen when
a Tariff is imposed on imports (X) and an investment is made in sector X, with
the idea of making the country grow, in terms of welfare (What we will see is
that, actually, the welfare decreases). Assume that X is capital intensive and
Δ𝐾 > 0 ( Investment on sector X).
Due to the Ryb. Theorem and because X is capital intensive, an increase in
the capital endowment caused an expansion of the PPF biased towards X.
How we can see 𝑢2 < 𝑢1 , that is, the utility level decreased when the
investment was made. This is what we call immizerizing growth. However, it
may not happen as well, as we're going to see next
NOTE: The Rybczynski Line for capital tell us where the new production point
is, when the PPF expands due to an increase in capital endowment. Note also
that the line is negatively sloped. This happens because 𝑋 𝑆 must increase and
𝑌 𝑆 must decrease for the same relative prices, according to the Ryb.Theorem
In the following example we can see that there is actually growth (𝑢2 > 𝑢1 )
and a non-optimal policy is being followed: