AU International Economic Problem Set Worksheet
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Any combination of handwritten and computer-printed answers is acceptable, but they should be
combined into one file in .docx or .pdf format please. Answer all parts of both questions (1 and 2).
Food
F
C
B
A
E
M
U1
G
N
U0
O
J
H
K
Computers
1. Interpret the neoclassical trade diagram (above); use the letters as needed for line segments
(lengths = quantities), triangles, etc.
a. What is the meaning of the curve that goes through points F and G? What can we infer
from the fact that this curve gets steeper as the quantity of computers increases?
b. What is the meaning of the curves U0 and U1? the tangency points G, F, and E?
c. Assuming that the countrys resources are fully employed, what are the quantities produced in autarky? With free trade?
d. What are the quantities consumed in autarky? With free trade?
e. What are the volumes (quantities) of imports and exports with free trade? Where is the
trade triangle on this diagram?
f. What is the meaning of the slope of the line FE (in absolute value, i.e., ignoring the
minus sign)? In what units is this slope measured?
g. What would be the meaning of the slope of a line drawn tangent to the production possibility frontier at point G? Why would this line be steeper than line FE? (HINT: in which
good does this country have a comparative advantage? How do you know?)
h. How do we see the gains from trade on this diagram?
i. What if the country did not have full employment of its resourceswhere would production take place? How would this matter for policy? (Think outside the box!)
1
2. Consider the Specific Factors Model applied to the Foreign countrylets call it South
America in the 19th century. Agricultural goods are produced with land (T) and labor (LA);
manufactured goods are produced using capital (K) and labor (LM). Thus, land and capital are
the immobile (specific) factors while labor is the mobile factor. Suppose South America
opens up to trade and exports agricultural goods (A) and imports manufactures (M).
a. First, analyze what happens to the equilibrium nominal wage rate W as a result of trade,
using a diagram like the figure below, and assuming that the price of the export good
rises (for convenience, you may assume that the price of the imported good stays constant
for this diagram). Label all
curves and axes completely and
explain your diagram carefully
(what shifts and why? how does
equilibrium employment
change?). Also compare the
change in the nominal wage
with the change in the value of
the MPL for the export good!
(Hint: think about which price
rises or falls.)
b. Draw a diagram with a production possibility frontier and indifference curves for South
America (similar to slide 15 in the PowerPoint for Topic 3A, but drawn for the Foreign
country.) Show the equilibrium points in autarky (no trade) and with free trade.
c. Analyze what happens to real wages in terms of each good, W/PA and W/PM, and explain
your answer. Do workers gain or lose from trade, or what does this depend on?
i. What general principle does your answer to this part illustrate, with regard to gains or
losses for the mobile factor?
d. Analyze whether the landlords (owners of land) and capitalists (owners of capital)
gain or lose from free trade. Focus on whether the real rental rates for land and capital
(RT/PA, RT/PM, RK/PA, and RK/PM) rise or fall (you do not have to analyze the percentage
changes in RT or RK).
i. Does it matter which good the landlords and capitalists consume more of, A or M?
Why or why not?
ii. What general principle does your answer to this part illustrate, with regard to gains or
losses for specific (immobile) factors of production?
e. Does South America get aggregate gains in consumer welfare from trade? If so, what
does this imply about magnitudes of the gains to the group(s) that gain from trade compared with the losses to the losers?
f. Assuming that the landlords were the richest group in South America in the 19th century,
capitalists were the middle class, and workers (labor) were the poorest, and also assuming
that workers consumed mostly food (agricultural products, A), did free trade make the
regions distribution of income more equal or more unequal according to this model? Do
you think that this pattern of trade (specializing in primary commodities) helped or hindered the long-run economic development of South America? Discuss briefly.
2
Topic 3A
Trade and Income Distribution:
The Specific Factors Model
Feenstra, chap. 3
Excluding Applications (some will be covered later)
ECON-371
International Economics: Trade
Prof. Robert A. Blecker
Spring 2021
Introduction
2
? The Ricardian model (chap. 2) showed the aggregate
national gains from trade according to comparative
advantage
?
?
Everyone gains in each country because everyone is an equivalent
worker and labor is the only factor of production
This was helpful for understanding comparative vs. absolute
advantage and international differences in wages
? But in reality, opening a country to trade may generate
winners and losers within each country.
?
?
Determining who gains and who loses explains a lot about trade
politics (support for trade liberalization or protection).
To see this, we need theories with more than one factor of
production (primary input) in each country
Quick Guide to Models in Chapters 2-4
3
? Chapter 2 Classical/Ricardian Model:
?
One factor input (labor), mobile between industries within a country
?
?
Constant marginal products, constant opportunity costs
All workers gain equally from trade within each country
? Chapters 3 & 4 Neoclassical Models:
?
?
All have more than one factor input with diminishing marginal
products and increasing opportunity costs
Owners of some factors gain and owners of other factors lose from
trade
? Chapter 3 Specific Factors:
?
One mobile factor, two immobile or specific factors
? Chapter 4 Heckscher-Ohlin:
?
Two (or more) mobile factors (can be employed in any industry)
The Specific-Factors Model (SFM)
4
? This is one effort to explain who gains and who loses.
?
This model assumes that some factors of production are immobile
between industries (specific factors)
?
In chapter 4 well study the Heckscher-Ohlin model, which assumes
that all factors of production are mobile between industries
? In any standard trade model, free trade leads to:
?
?
An increased relative price of the exported good
A decreased relative price of the imported good
? In the SFM, we study how these changing relative prices
affect the real earnings of two kinds of factors:
?
?
Factors that are mobile between industries
Factors that are immobile in or specific to particular industries
Preview: Effects of Relative Price Changes
5
?
The earnings of specific (or immobile) factors go up or down
the most with changes in relative prices because they are
stuck in a sector and cannot be employed elsewhere.
?
?
?
We will assume capital is specific to manufactures and land is
specific to agriculture
The specific factor in the export sector gains and the specific factor in
the import-competing sector loses
Mobile factors can avoid these extreme effects by seeking
employment in other sectors.
?
?
We will assume labor is the mobile factor
In the SFM, mobile factor owners may either gain or lose, depending
on which good they consume relatively more of
?
They gain in terms of imported goods but lose in terms of exported goods
Assumptions: Countries, Goods, and Factors
6
? Assume two countries: Home and Foreign
?
Following Feenstra & Taylor, we will focus mainly on Home
?
Problem Set 2 asks you to analyze what happens in Foreign
? Two goods (industries) and three factors of production:
?
?
Manufacturing (M) uses labor (L) and capital (K).
Agriculture (A) uses labor (L) and land (T = terra).
?
Both sectors exhibit diminishing marginal productivity of labor:
decreasing MPLM and MPLA (holding supplies of K and T constant)
? So L is the mobile factor, while K is specific to Mfrs. and T
is specific to Agr. (K and T are immobile)
?These are just examples; other cases of mobile and
immobile factors are also possible!
Relevance of the Specific Factors Model
7
? SFM is often presented as a short-run model:
?
Because in the long run all factors could move to other industries or
sectors or could have alternative uses (even land)
? But the example we cover can also be thought of as a
common North-South or center-periphery pattern of
trade
?
The Center (industrialized/advanced countries) exports
manufactures, using a lot of capital
?
The Periphery (developing countries) exports primary products
(agricultural/mineral), using land/natural resources
?
?
Example: European countries and overseas colonies (19th early 20th C.)
But this pattern of trade is still relevant today (e.g. China-Africa)
Total and marginal product curves
(for manufacturing)
8
Total product
Diminishing
MPL in Mfrs.
Note this holds the supply of capital, the other factor used
in manufacturing, constant. There are also similar curves
for the agricultural industry (holding land constant).
Mathematics for SFM (for those who like math)
9
QM = F ( LM , K )
M
Production
functions:
Marginal
products of labor
(holding K or T
constant):
Q A = F ( LA , T )
A
?QM
M
MPL
=
= FLM
M
?LM
?QA
A
MPL
=
= FLA
A
?LA
Resource constraint:
LA + LM =
L
These are
positive
but
diminishing
Production Possibilities Frontier with fixed
supplies of K and T and diminishing MPL
Production Possibilities Frontier
Badly
drawn;
the line
should be
tangent
to the
PPF at a
single
point!
The slope (in absolute
value) is the opportunity
Note the slope is
cost of manufactures, or
increasing as labor
moves from Agriculture the marginal rate of
transformation for
to Manufacturing
manufactures (measured
in units of QA /QM )
10
Note: Review and comparison
11
? The classical (Ricardian) trade model
assumes constant opportunity cost
(marginal rate of transformation = MRT)
?
The PPF is a straight line so its slope is constant
?
?
This is a later interpretations of Ricardo; its not
necessarily faithful to the original!
Assumes constant marginal productivity
? Neoclassical trade theory assumes
increasing opportunity cost (MRT)
?
QY
QY
QX
The PPF is curved away from the axis; its slope
increases moving from left to right
?
This is assumed in both the Specific Factors and
Heckscher-Ohlin (factor proportions) models
[chapters 3 and 4], both of which have diminishing
marginal productivity
Note: X and Y are any two goods.
QX
Wages, Prices, and Marginal Products
12
? Suppose one unit of L moves from Agr. to Mfrg:
agricultural output falls by MPLA and manufacturing
output rises by MPLM.
? In each sector, the wage must equal the value of the
marginal product, which is the price of each good times
its MPL:
W = PM ? MPLM
W = PA ? MPLA
? Assuming labor is mobile, wages in the two sectors must
be equal. This implies P ? MPL = P ? PML
M
M
A
A
PM MPLA
or
=
PA MPLM
Autarky (no trade) equilibrium
13
In general equilibrium:
Agriculture
Output, QA
Note: MRT means
marginal rate of
transformation
and is the same as
the opportunity
cost of producing
Manufactures.
MRS means
marginal rate of
substitution and
is the slope of the
indifference
curve.
? PM/PA = ?(slope of PPF) =
?(slope of indifference
curve)
? or, PM/PA = MRT = MRS
? The indifference curve is
tangent to the PPF
A
U1
Slope = (PM/PA)
B
PPF
Manufacturing
Output, QM
The foreign country and comparative advantages
14
? The Foreign Country (*) has a similar structure to Home:
?
?
Mfrs. are produced with K and L
Agr. goods are produced with T and L
?
But the technology, factor supplies, and consumers tastes may differ
? F&T assume that the autarky price of manufactures in the
Home Country is less than in the foreign country :
(PM/PA) < (PM/PA)*
?
?
Home has comparative advantage in manufacturing (it can produce
manufactures at lower opportunity cost than Foreign).
Home will export Mfrs. and Foreign will export Agr. at a world (W)
relative price of Mfrs. that is higher for Home but lower for Foreign:
W
PM ? PM ?
PM*
?? < *
< ??
PA ? PA ?
PA
? Key to all results!!!
Home Country with Free Trade vs. Autarky
Autarky production = A
Free trade production = B
Autarky consumption = A
Free trade consumption = C
Trade
triangle
(point A is
not on it!)
Note there is
incomplete
specialization at
point B (some of
the imported
good is produced
with free trade)
15
Employment and wages of labor
16
? The quantity of labor employed in each industry has to
add up to the total labor supply (assuming full employment):
LM + LA = L
? Therefore we can show the allocation of labor to the two
sectors on one graph
?
?
Labor used in manufacturing is measured from the left origin (left to
right).
Labor used in agriculture is measured from the right origin (right to
left).
? Labor demand is determined by the marginal products so
that W = P × MPL.
16
Recall the diminishing MPL curves:
17
Fixed supply
of capital (K)
Fixed supply
of land (T)
Now we will take the MPLA curve for agriculture, flip it over
horizontally (rotate 180° to the left), and superimpose it on top of the
MPLM curve on a single diagram (next slide ?)
Putting the two MPL curves together, we get:
The allocation of Labor between
Manufacturing and Agriculture
PM?MPLM
is drawn
normally
from left to
right
PA?MPLA is drawn from
right to left (so it slopes up
instead of down)
Labor Market
Equilibrium occurs
where the two
MPL curves cross
This determines
how many
workers are
employed in each
sector.
18
Effects of Trade: Modeled by an increase in the
price of the exported good (M for Home)
This amount of labor
moves from A to M
19
Note: for
convenience
we assume
that PM rises
and PA stays
constant; then
PM?MPLM shifts
up and the
equilibrium
shifts from
point A to B.
Workers who
lose jobs in
agriculture
(supposedly)
all get jobs in
manufactures.
Earnings of Labor (the mobile factor)
20
? It looks like the wage has increased, but this is only the
nominal (money) wage
? Effect on Real Wages (compare wage change with price
changes)
?
?
From the Graph, you can see that ?W < ?PM·MPLM
If we divide both sides by W = PM·MPLM we get:
?W ?PM ? MPLM ?PM
=
<
W
PM ? MPLM
PM
?
?
?
The real wage in terms of manufactured goods has decreased.
The real wage in terms of agricultural goods has increased.
So the net effect on workers (labor = the mobile factor) depends on
how much of their income they spend on M vs. A
20
Earnings of Capital and Land (the
Specific Factors)
? Determining the Payments to Capital and Land
? If QM is the output in manufacturing and QA is the
output in agriculture, the revenue earned in each
industry is PM QM and PA QA, and the payments
to capital and to land are:
Payment to capital = ???????? ? ???????? ? ???? ? ????????
Payments to land = ???????? ? ???????? ? ???? ? ????????
© 2021 Worth Publishers
International Economics, 5e | Feenstra/Taylor
21
21
Earnings of Capital and Land
(continued)
?
The earnings of one unit of capital (a machine, for
instance), which we call RK, and the earnings of an acre
of land, which we call RT, are calculated as:
Payments to capital ???????? ? ???????? ? ???? ? ????????
???????? =
=
????
????
Payments to land ???????? ? ???????? ? ???? ? ????????
???????? =
=
????
????
We call RK the rental on capital and RT the rental on
land
?
?
?
Note these are measured in nominal or money units (similar to W)
More broadly the two rental rates and the wage are factor prices
© 2021 Worth Publishers
International Economics, 5e | Feenstra/Taylor
22
22
Rental rates = value of marginal products
23
? The rental rates on capital and land must equal the value of their
marginal products:
RK = PM ? MPK M
RT = PA ? MPTA
MPKM and MPTA
are positive but
diminishing
? An increase (decrease) in the quantity of labor used in an industry will
raise (lower) the marginal product of the factor specific to that industry.
?
?
?
The increase in the price of manufactured goods leads to more labor used in
manufacturing and less in agriculture in Home
As more labor is used in manufacturing, the marginal product of capital will rise.
As more labor leaves agriculture, the marginal product of land will fall.
? Thus capitalists gain and landlords lose in the manufactures-
exporting Home country
?
The opposite occurs in Foreign, which exports agricultural goods
Real Earnings of Capital Owners (Capitalists)
24
? This implies that:
? MPKM = RK/PM
?
?
RK must be increasing by more than PM is increasing, in
percentage terms. The real return to capital is increasing in terms
manufactured goods.
Also remember RK/PA is amount of food that can be purchased
by capital owners.
RK increased, PA fixed, so RK/PA increases.
? Real return to capital in terms of the amount of food that can be
consumed has also increased.
?
Real Earnings of Land Owners (Landlords)
25
? This implies that:
? MPTA = RT/PA
?
?
RT must be falling. The real return to land is falling in terms of
agricultural goods.
Also remember RT/PM is amount of manufactured goods that
can be purchased by land owners.
RT fell, PM increased, so RT/PM falls.
? Real return to land in terms of the amount of manufactured goods
that can be consumed has also fallen.
?
Note
26
? Here we skip the Numerical Example on pages 82
(bottom) 84 (top) of Feenstra-Taylor
? You are not responsible for that, but you are
responsible for the rest of the theory in chapter 3.
? We will continue with the General Equation... on
page 84 (middle)
Equation for the Change in Factor Prices
(Home Country)
27
? Assuming PM increases and PA does not change, then:
?RT
?W ?PM ?RK
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International Economics Problem Set
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