NAME:
STUDENT #:
SIGNATURE:
Department of Economics and Finance
College of Business and Economics
University of Guelph
ECON*3620 - International Trade
midterm KEY
Problem 1. Suppose there are two countries, Australia and Canada for example, that are
capable of producing two goods, say Wheat and Potatoes. The amount of labour in
Canada is 600 and the amount of labour in Australia is 360. The amount of labour needed to
produce a metric ton of each commodity is given in the table below. (37 pts)
Type of good
Wheat
Potatoes
Canada
5
6
Australia
6
4
Country
a) Which country has a comparative advantage in the production of Wheat? Circle
AUSTRALIA, CANADA, or NEITHER. (2pts)
Canada gives up 5/6 units of Potatoes when producing Wheat compared to Australia’s 6/4
units of Potatoes. Hence Australia has the comparative advantage in Potatoes
b) What is the autarky price ratio PP /PW in each country assuming both goods are consumed?
(4 pts)
PP/PW is just equal to the ratio of unit labour requirement given perfect competition (price
equals marginal cost, no economic profits) and competitive labour markets. Notice the relative
price is just the opportunity cost (in terms of forgone Wheat) of producing Potatoes.
So PW /PP = 6/4 or 3/2 in Australia and 5/6 in Canada
Autarky price ratio in AUSTRALIA 4/6 or 2/3 Autarky price ratio in CANADA 6/5
c) Assume that preferences (the same for all individuals in both countries) are given by the utility
function U = QP3/4Q W1/4 . The marginal utility of Potatoes is (3/4)(QW /QP)1/4 while the marginal
utility of Wheat is (1/4)(QP /QW)3/4. Derive the relative demand curve. Show your work. (3 pts)
MRSPW = MUP/MUW = PP /PW (1pt)
MRSPW = (3/4)(QW /QP)3/4/(1/4)(QP /QW)1/4= 3QW /QP = PP /PW (2pts)
Or MRSWP = (1/4)(QP /QW)1/4/(3/4)(QW /QP)3/4= (1/3)QP/QW= PW /PP
So that
Relative demand curve equation (PP/PW)(QP/QW) = 3 or (PW/PP)(QW/QP) = 1/3
d) On the graph below determine the intercepts of the RS curve on the vertical and horizontal
axis and record your answers on the three lines. What is the equilibrium world price ratio and
relative supply? Show your calculation for the horizontal intercept. (I will give full credit to your
answer below for whatever RD curve you found in part (c) if used correctly.) (6pts)
PP/PW
6/5
RS
2/3
RD
3/4
2.5
(QP + QP*)/(QW + QW*)
The vertical part of the RS curve is found by dividing the output of Potatoes that Australia
produces if specializing (360/4) (as they have the comparative advantage in Potato production)
by the amount of Wheat that Canada produces (600/5) or 90/120=3/4 (.75). The equilibrium
world price is PP /PW = 6/5.
With PW /PP on the vertical axis and QW/QP on the horizontal axis the vertical intercepts are
3/2 and 5/6 and the horizontal intercept is 4/3. The world equilibrium price is 5/6
Relative demand curve (the actual equation) drawn above (PP/PW)(QP/QW) = 3 or
(PW/PP)(QW/QP) = 1/3
World relative supply (QP + QP*)/(QW + QW*) = 5/2 or 2.5
Equilibrium world price PP /PW = 6/5
e) Based on your answer for the world price ratio in part (d) determine relative wages between
Australia and Canada, wA/wC. Show your work. (2 pts)
Wages are equal to the price of the good times the marginal product of labour (the marginal
product of labour is the reciprocal of the unit labour requirement). Since the world price ratio
is PP / PW = 6/5 it is the autarky price of Canada. Australia specializes in Potato production
while Canada produces both goods.
Relative wages are then wA /wC = (PP /aA P) / (PW /aCLW)= (PP/PW)( aCLW/aA P) = (6/5)(5/4) = 3/2.
L
L
Or, as Canada produces both goods, wA /wC = (PP /aALP) / (PP /aC LP)= aCLP/aALP) = 6/4) = 3/2.
Relative wage wA /wC = 3/2 or 1.5 (wC /wA = 2/3)
f) What share of world production does Canada consume? Explain or show your work (I’m not
asking for the amount consumed just the share or percentage - an easier calculation) (2 pts)
From part (e) each Australian worker consumes 3/2 times that of a Canadian worker. We can
determine consumption shares (see class notes) by noting that for every 2 units of
consumption by a Canadian worker a Australian worker consumes 3 units. Multiplying units
consumed by population yields 2 x 600 + 3 x 360 = 1200 + 1080 = 2280 consumption shares.
Canada has 1200/2280 of the total consumption shares, or about 52.6% of world production .
Australia consumes 1080/2280 or 47.4% of world production.
Share of world production consumed by Canada 1200/2280 or about 52.6%
g) Suppose that Canada sees its productivity in Potatoes increase so that it only takes 3 workers
to produce one unit of Potatoes. (Assume Canada has its original labour force of 600) (Circle
one of the three capitalized words in each of the statements below.) (6pts)
The opportunity cost of producing Potatoes in Canada falls to 3/5 unit of Wheat and that in
Australia remains at 2/3 units of Wheat, so that Canada now has the comparative advantage
in Potato production. The relative supply curve shifts as a result of the change in the unit
labour requirement. The intercept of the lower horizontal portion of the RS curve in (d)
changes as Canada’s autarky price ratio PP/PW falls to 3/5 from 6/5. Assuming the same
relative demand curve the equilibrium price, PP / PW, is now 2/3 (show this) and the relative
supply remains is 9/2 or 4.5. Canada specializes in Potato production while Australia
produces both goods (The new RS curve is shown in part (h) that follows (Equilibrium world
price PW/PP = 3/2 then equilibrium world supply QW/QP = 2/9.)
Canada has a comparative advantage producing POTATOES, WHEAT, NEITHER GOOD
The equilibrium world price PP /PW FALLS, INCREASES, REMAINS THE SAME
Canada produces ONLY POTATOES, ONLY WHEAT, BOTH GOODS
In parts (h) and (i) below preferences are such that Potatoes and Wheat are always consumed in
the ratio 4 to 1 (4 unit of Potatoes for each 1 unit of Wheat). Given the NEW unit labour
requirement for potatoes in Canada (bolded below)
Canada
Wheat
5
Potatoes
3
Country
Australia
6
4
h) Label the graph below and draw the NEW RD curve – label it RD. Find the new equilibrium
relative price and supply. Think before you draw your RD curve (6pts)
PP/PW
RD
2/3
RS
Red RS curve and intercept part (i)
3/5
10/3
4
20/3
(QP + QP*)/(QW + QW*)
The vertical axis has the new autarky prices reflecting Canada having the comparative
advantage in potato production. The vertical part of the RS curve is now where Canada
produces 200 units or potatoes and Australia produces 60 units of Wheat so QP/QW = 10/3.
The relative demand curve is vertical at QP/QW = 4 since the two goods are consumed in a
fixed proportion (U = min[QP, 4QW])
World relative supply (QP + QP*)/(QW + QW*) = 4
Equilibrium world price PP /PW = 2/3
i) Suppose that in Canada population doubles to 1200 (as in part (h) above assume the NEW per
unit labour requirements from part g). Circle one of the three capitalized words in each of the
statements below. (6pts)
Comparative advantage and autarky price are unchanged. The horizontal intercept of the
vertical portion of the RS curves doubles to 4 (400 units of Potatoes are produced rather than
200 – Australia still produces 60 units of Wheat. As a result, the RS curve now intercepts the
RD curve at the Canadian autarky price or 3/5. Canada produces both goods and Australia
specializes. As the relative price of Potatoes falls (relative price of Wheat rises) Australian
relative wage increases.
Australian workers’ relative wage FALLS, INCREASES, REMAINS THE SAME
The equilibrium world price PP/PW FALLS, INCREASES, REMAINS THE SAME
The autarky price ratio in Canada FALLS, INCREASES, REMAINS THE SAME
Problem 2 – Specific Factor Model.
On the graph below (similar to those presented in class) the value of the marginal product of
A
labour (price times marginal product) in manufacturing, PMMP M
L , and agriculture, PAMP L , is
shown on the left and right vertical axes respectively and the labour force is shown on the
horizontal axis. Let land be used with labour to produce the agricultural good and let capital be
used with labour to produce the manufacturing good. (26 pts)
105
90
45
Labour
Suppose that
a)
PMMP LM
= 90 – (3/4)LM and PAMPLA =105 – (1/2)LA and the labour force is 120.
Calculate the number of workers in the agricultural sector and the manufacturing sector
Show your work (8 pts)
In equilibrium, wages in each sector, which are equal to the value of the MPL, are equated.
2 pts for equating VMP equations. 2 pts for using labour constraint. 2pts for determining 1st
labour force and 2pts for 2nd labour force. (Other exam answers 2/3 of those here)
That is wA = PAMP LA = PMMPLM = wM. Using the labour constraint, LA + LM = 120, we find
90 – (3/4)LM = 105 – (1/2)LA = 105 – (1/2)(120 – LM ) = 45 + (1/2)LM, so 45 = (5/4)LM
Solving we find that LM = 36 and so LA= (L – LM) = 120 – 36 = 84.
Workers in manufacturing = 36 (Other exam 24) Workers in agriculture = 84 (Other exam 56)
b)
Calculate the equilibrium wage. Show your work (4 pts) (1 or 2 lines of work needed)
As wM = PMMP LM = PAMPLA = wA we can use either labour force to find the equilibrium wage.
wM = PMMPLM =90 –(3/4)LM = 90 - 27= 63; wA = PAMPLA =105 –(1/2) LA = 105 – (1/2)84 = 63;
Equilibrium wage = 63 (Other exam 42)
c)
Calculate GDP and GDP per capita. Show your work. (If you want you can leave your
answer unreduced) (6 pts)
Area below two value of marginal product (VMP) curves is GDP = income to capitalists,
workers, and landowners
= (105-63)(84)(1/2)(income to landowners)
+(63)(120) (income to workers)
+(90-63)(36)(1/2) (income to capitalists) = GDP = 1764 + 7560 + 486 = 9810
GDP/capita = 9810/120= 81.75 (other exam 4360/80 = 54.5)
Full credit as well if GDP = (105-63)x84/2+63x120+(90-63)x36/2 = 42x84/2+63x120+27x36/2
(other exam GDP = (70-42)x56/2+42x80+(60-42)x24/2 = 28x56/2+42x80+18x24/2 =
784+3360+216 = 4360)
GDP = 9810 (other exam 4360) (4pts);
GDP/capita = 9810/120 or 81.75 (other exam 4360/80 or 54.5) (2pts)
Multiple choice – 2 pts each.
d)
If the marginal product of labour in agricultural sector decreases.
A) workers move from agriculture to manufacturing. Agriculture wages fall people move
B) the nominal wage declines and landowner’s income increase. Landowner income falls
C) both capitalist’s income and landowner’s income decrease. Capitalist income rises
D) the nominal wage increases and capitalist income falls. Capitalist income rises
E) GDP increases. Productivity falls – not a chance
e)
If the price of the manufacturing good increases because of trade
A) both capital and landowner income rise. Landowner income falls
B) individual workers real wage may have fallen. Tricky – depends on preferences
C) landowner income and nominal wages decline. Nominal wages increase
D) Both (B) and (C).
E). All of the above.
f)
If there are currently half the workers in manufacturing
A) GDP and manufacturing wages could be increased if workers move out of agriculture.
B) the nominal wage in manufacturing is less than that in agriculture.
C) capitalist’s income will increase given the free mobility of labour.
D) All of the above.
g)
If the labour force falls in the country
A) landowners and capitalist income rises. Nope falls
B) both manufacturing and agricultural production rises Also falls
C) GDP increases. No way
D) individual workers are better off – nominal and real wages rise
E) None of the above.
Problem 3. Assume a Heckscher Ohlin (H-O) model with “large” countries for this problem
(except in part (a)). Four problems test your knowledge of the main results of the H-O model.
In each problem state which of the four main trade theorems (0 points off for spelling errors) of
the H-O model of trade best pertains to the problem. Work/Discussion/Graphs are not required
(but are required for any partial credit.) (26 pts)
a) Our several decades Korea has experienced an increase in the number of workers with a
university education. Suppose ship production uses skilled labour more intensively than rice
production (which uses unskilled labour intensively). Assume Korea is a small country so that
the world prices of both goods are unchanged after the increase in university educated workers in
Korea. Circle one of the CAPITALIZED terms in the first two questions below. (6 pts)
The Rybczynski theorem tells us about the change in production in both sectors, given the
change in a factor, if prices are unchanged. It is the appropriate theorem to use here. If prices
are unchanged factor intensities are unchanged as well – a result known as the Stolper
Samuelson theorem. If a factor increases(falls) the production of the good using that factor
relatively intensively increases (falls). In this case production of rice in Korea falls as skilled
workers have increased and production of ships increase
Production of rice in Korea should DECREASE, REMAIN UNCHANGED, INCREASE
The skilled worker to unskilled labour ratio in the Korean ship building industry should
DECREASE, REMAIN UNCHANGED, INCREASE.
Relevant trade theorem used in answering problem Rybczynski and Stolper Samuelson
b) Smaller countries (such as Iceland) often stand to greatly benefit from trade as the equilibrium
world relative price is often much closer to their trading partner’s autarky price ratio. Suppose
Iceland is relatively well endowed with fishermen (used intensively in fish production) compared
to land (used intensively in producing wool from sheep) compared to their trading partner.
(Circle one of the capitalized terms in the statements below.) (6 pts)
Iceland will export fish as it is relatively well endowed with fishermen by the H.O. Theorem.
In Iceland, the world relative price of fish will go up and that of wool will go down compared
to autarky. Landowners suffer in Iceland while fishermen see an increase in wages – by the
Stolper Samuelson Theorem. Fishermen are used less intensively in producing both goods in
Iceland as theirwages have increased.
Trade results in an DECLINE, NO CHANGE, INCREASE in land rents in Iceland.
Fish production uses fishermen LESS, AT THE SAME, MORE intensively after trade.
Relevant trade theorem used in answering problem Stolper Samuelson and Heckscher Ohlin
c) Russia has one of the world’s largest oil deposits as well as vast forestlands. Mexico has large
oil deposits as well but little of its land is covered by forest, and so Mexico would be considered
as being relatively well endowed with oil. Assume that two goods are produced using the two
factors in each country, paper and gasoline. If gasoline production uses oil relatively intensively
which commodity will Russia export and which country will have the higher relative rental rate
of forestland. (8 pts)
The HO theorem states that countries export the good which uses its relatively abundant
factor intensively – hence Russia exports paper and Mexico exports gasoline. The factor price
equalization theorem states that factor rewards are the SAME in both countries.
Exported Commodity from Russia Paper
Relevant trade theorem used in answering problem Heckscher Ohlin
Country with higher relative forestland rental rates Neither
Relevant trade theorem used in answering problem Factor Price Equalization
d) Determine the equilibrium price of labour and capital if it takes 3 units of capital and 8 units
of labour to produce 1 unit of pork in Canada. Assume it takes 6 units of capital and 2 units of
labour to produce 1 unit of a fish in Spain, and Canada and Spain trade with one another. Let the
equilibrium world price of the pork be 72 and the price of fish be 60. Determine factor prices
assuming competitive markets. Show your work (6 pts)
(you need to show your work to receive any extra credit here – if an error in math but problem
set up correctly you should get around 2 points off for the price of labour and capital.) In
competitive markets the cost of producing the good is equal to its price. Since we have factor
price equalization in the H-O model and good prices equalize through trade as well we have
60 = 6r + 2w (price of fish = cost to produce good)); and
72 = 3r + 8w (price of lamb = cost to produce good)
Solving for r and w
Price of labour _6; Price of capital _8
(In other version price of pork 36 and that of fish 30 so Price of labour 3; Price of capital 4)
Relevant trade theorem used in answering problem Factor Price Equalization
Problem 4.
Suppose two countries each produce a capital intensive good, automobiles and a labour intensive
good, shirts. Let the foreign country be relatively well endowed with capital. Describe the
impact of the situations below in parts (c) - (f) on the terms of trade and the welfare of the home
and foreign country by filling the blanks below with either INCREASE, DECREASE, or
AMBIGUOUS. Assume that comparative advantage is not changed in any of the situations
((c) - (f) below). The Standard Model of chapter 6 with 2 ‘large’ countries is assumed. Work
or Discussion is not required but are helpful if you want any partial credit (28 pts)
a) Which country exports shirts? Circle either FOREIGN or HOME (2 pts)
By the HO theorem
b) With trade which country sees a fall in the relative price of cars compared to autarky?
Circle either FOREIGN or HOME (2 pts)
Home since they have the comparative advantage in shirts. Price of automobiles fall relative
to shirts in Home compared to autarky and the price of shirts rise compared to autarky.
c) A export subsidy is placed by the foreign country on their exports. (6 pts)
Export subsidies, not surprisingly, increase production of the export good in the foreign
country at any given terms of trade (there is a divergence between world and domestic prices).
Consumers in the foreign country increase consumption of the imported good relative to the
exported good at any given world relative price, and shifts the RD curve. These two shifts
result in a reduction in the terms of trade for the foreign country and hence a reduction in
welfare because of the distortion caused to consumers and producers by the subsidy. In the
home country the terms of trade rise and they see an increase in welfare
Terms of trade: Foreign DECREASE Home INCREASE
Welfare:
Foreign DECREASE Home INCREASE
d) There is a fall in productivity in the import sector of the home country (6 pts)
Here the PPF in Home contracts disproportionately affecting production of cars. The terms of
trade decrease in the home country given the fall in production of the imported good at any
world price. The effect on welfare in the home country is negative as the PPF contracts as
productivity falls. In the foreign country terms of trade and hence welfare increase.
Terms of trade: Foreign INCREASE Home DECREASE
Welfare:
Foreign INCREASE Home DECREASE
e) An import tariff is placed on foreign country imports. (6 pts)
The Foreign country is putting a tariff on their imports here. Tariffs on imported goods
usually increase the internal relative price of the imported good when compared to the initial
terms of trade (but not so if the terms of trade increase enough - the Metzler paradox). The
country always sees an increase in its terms of trade if it uses an import tariff, but the effect on
welfare is ambiguous (tariffs cause consumption and production distortions). The tariff will
decrease the terms of trade in the Home country as well as welfare.
Terms of trade: Foreign INCREASE Home DECREASE
Welfare:
Foreign AMBIGUOUS Home DECREASE
f) The amount of labour in the home country increases (6 pts)
This is export biased growth in the home country as they have a comparative advantage in
producing shirts, which uses labour relatively intensively. The terms of trade decrease in the
home country (relatively more shifts and fewer cars are produced at any given relative price
than before the increase in labour). The effect on welfare in the home country is ambiguous
as there is a decrease in the terms of trade but the PPF expands. In the foreign country terms
of trade and hence welfare increase.
Terms of trade: Foreign INCREASE Home DECREASE
Welfare:
Foreign INCREASE Home AMBIGUOUS
Problem 5 - Assume the Standard (Chpt. 6) trade model. Assume two “large” countries. Read
these carefully so you get the axes right. No work necessary just well labeled graphs (23 pts)
a) Use relative demand and relative supply curves to show the impact of introducing an export
subsidy on the terms of trade of the trading partner of the country using a subsidy. Use arrows
to show shifts in curves. PE and QE, and PI and QI, refer to the price and quantity of the exported
and imported good, of the trading partner of the country using a subsidy. Label the old terms of
trade - superscripted with a 1, and the new terms of trade - superscripted with a 2 (6 pts)
RD1
RD2
RS2
RS1
PE / PI
(PE/PI)2
(PE/PI)1
QE / QI
An export leads to increased production of the exported good in the foreign country and an
increase in relative supply of that good for a given relative price of exports so the RS curve
shifts left – as shown – since the trading partners terms of trade are referenced. Consumers in
the country using the export subsidy demand less of the exported good at any given relative
price –so the worldwide RD curve shift right as the PI refers to the price of the exported goods
in the country using the tariff. As a result PE/PI falls (the terms of trade of the trading partner
of the country using the tariff rise. In the other exam the terms of trade of the country using
the tariff are on the vertical axis so shifts are all in the opposite direction).
Circle either True or False in the three statements below. (2pts each) (Note that these are
unrelated to the graph above)
TRUE FALSE
Un-tied aid (an income transfer for the donor to recipient country) increases
the terms of trade of the donor country.
TRUE FALSE
The Metzler paradox can refer to the situation where an import tariff results
in the terms of trade falling so much that the factor used intensively in the
production of the good sees its factor reward rise.
TRUE FALSE
Increasing an import tariff increases welfare in the tariff increasing country’s
trading partner.
b) Using relative demand and relative supply curves show on the graph below the impact of
import biased growth in a country. Use arrows to show any shifts in curves. PE and QE refer to
the price and quantity of the exported good of the the country experiencing growth and PI and
QI refer to the price and quantity of the imported good of that country. Label both the old terms
of trade (superscripted 1) and the new terms of trade (superscripted 2). (5 pts)
RS2
RD
RS1
PE / PI
(PE/PI)2
(PE/PI)1
QE / QI
Import biased growth results in increased production of the imported good at a given terms of
trade in the country experiencing growth. Hence the relative supply curve shifts to the left
increasing the terms of trade. Then relative demand curve doesn’t shift. (On the other exam
the terms of trade of the country not experiencing growth were on the vertical axis so the
relative supply curve shifted to the right and the terms of trade of the trading partner fell.
Circle one of the terms in the 4 sets of bolded capitalized terms in the following two statements.
(1 ½ points each – 6 points in total)
Immiserizing growth occurs when IMPORT, EXPORT, biased growth causes the terms of
trade to INCREASE, FALL in contrast to the CONTRACTION, EXPANSION of the
production possibility frontier (3 sets of capitalized terms in this statement)
Import biased growth MAY BE,
capitalized terms in this statement)
MUST BE,
CAN NEVER BE, immiserizing (1 set of