International Economics at ICEF
Final exam
December 29 2022
Part II: Problems.
Marking scheme
Math problem. Answer all questions.
21. Assume the world has just two competitive economies, Home and Foreign, denoted
respectively by 𝑗=𝐻,F. There is just one homogeneous production factor, labor (𝐿), which is
immobile across countries, but perfectly mobile across sectors within a country. Country
labor forces are 𝐿H=40 and 𝐿F=60. There are two goods, denoted by 𝑖=1,2. Each country has
a representative consumer with identical Cobb-Douglas preferences over goods:
𝑢𝑗=(𝑐𝑗(1),𝑐𝑗(2))=𝑐𝑗(1)1/2𝑐𝑗(2)1/2.
Countries have different technologies to produce each good:
𝑦𝑗(𝑖)=𝐿𝑗(𝑖)𝑎𝑗(𝑖),
where 𝑎𝐻(1)=1, 𝑎H(2)=2, 𝑎F(1)=4, and 𝑎𝐹(2)=2.
(a) (15 pts) In which sector does each of the two countries have a comparative
advantage?
Country H can produce at most a(1)*LH=40*1=40 units of good 1 or a(2)*LH=40*2=80 units
of good 2. That said, the opportunity cost of producing 1 unit of good 1 in home country is
80/40=2 units of good 2. Similarly, county F can produce at most a(1)*LF=60*4=240 units of
good 1 or a(2)*LF=60*2=120 units of good 2. Thus, the opportunity cost of producing 1 unit of
good 1 in foreign country is 120/240=1/2 units of good 2. The opportunity cost of producing
good 2 is just the reciprocal of the opportunity cost of producing good 1 (for H: 1/2 units of
good 1 & for F: 2 units of good 1). Comparing the opportunity costs, clearly country H has a
comparative advantage in good 2 and country F - in good 1.
(b) (15 pts) Derive the relative prices p(1)/𝑝(2) in H and F under autarky. Which of the two
goods would each country export under free trade?
The profit maximization function of a firm in H is the pi=p1*Q1-wL. Similarly, for the other
industry.
Out of it we get that the autarky relative prices are p1/p2=a2/a1. That is, the autarky relative
prices are not surprisingly the opportunity costs. Thus, for H: P1/P2=2 units of good 2, for F:
p1/p2=1/2 units of good 1. [7 points for correct price ratio with the sketch of derivation].
Under free trade countries will export the good in which they have a comparative advantage as
it will be beneficial to exploit it. Note that the trade occurs only if the equilibrium world price is
at p1/p2€[1/2,2]. Thus, country H will export good 2, while country F will export good 1. [8
points for the correct free trade export pattern]
(c) (20 pts) Write the budget constraint of the representative consumer and solve the
maximization problem of the consumer. Show that the demand equation for the
household is: qj(𝑖)=1/2 𝑤𝑗𝐿𝑗/𝑝𝑗(𝑖), where 𝑤𝑗 is the wage rate.
We now deal with the representative consumer problem. The consumer will consume out of his
income. The only source of income in Ricardian model of trade is the wage income. Thus, the
budget constraint of a representative consumer is p1*c1+p2*c2<=w*L. Note that L might
represent the number of hours worked and not be measured in people. [5 points for correct
BC]
Thus, the problem of a consumer is max{U=sqrt(C1*C2)} s.t. p1*c1+p2*c2<=w*L. Note that
economically, the consumer will never consume less than all of his income. Thus, the BC is
binding. setting up Lagrangian and maximizing it wrt c1, c2 & the multiplier will yield exactly the
formula from the task. [15 points for the derivation and correct solution for formula].
(d) (15 pts) Derive consumption levels under autarky.
Using the formula from (c) we can plug in the values to calculate the consumption values in
Autarky.
: w=VMPL=MPL*P=a*P. Thus, the formula from (c) transforms to q=1/2*L*a. Applying it for a
given values of L & a we obtain the following consumption levels in autarkies:
For H: C1=20, C2=40; For F: C1=120, C2=60.
[2.5 points for each correct consumption level, 5 points for the general approach]
General comment:
The shortcut was to use the formula from (c). It would yield a very quick solution. Some students
tried to derive the demand out of the utility maximization problem, which sometimes led to the
numerical mistakes or the partial answers. Answers with numerical mistakes received discounts
of up to 3 points depending on the severity of mistakes.
(e) (20pts) Suppose the two countries open up to trade. Show that the relative price that
equates world relative demand and world relative supply is p(1)/p(2)=3/4. Are the
two countries going to fully specialize at the given world price?
For the first part we need to derive the equilibrium relative price. RD=(q1+q1*)/(q2+q2*). We
can plug the formula from (c) to derive RD value in equilibrium. If you do this, you shall get that
the RD=p2/p1. [ 5 points]
Relative supply is as follows: zero if p1/p2<1/2; infinity if p1/p2>2.
if p1/p2 belongs to (1/2,2), H fully specializes in 2, producing 40×2=80 units; F specializes in 1,
producing 60×4=240 units; thus RS=240/80=3. If p1/p2=1/2, RS is anywhere between 0 and 3,
meaning incomplete specialization of F. If p1/p2=2, RS is anywhere between 3 and infinity,
meaning incomplete specialization of H. [5 points]
Equilibrium: p1/p2=1/2 (contradicting the claim of the problem set!) RD=RS=2 [ Bonus of 5
points to those students who proved this.] If ¾ is used correctly, no penalty.
H fully specializes; F allocates 50 units of labor to good 1, and 10 units of labor to good 2.
At the price of ¾: both countries fully specialize. [10 points]
(f) (15pts) Compute equilibrium production and consumption levels in the two countries
under trade.
at price ½: Home produces 0 of good 1 and 40×2=80 of good 2; consumes 80 of good 1 and 40
of good 2. Foreign produces 50×4=200 of good 1 and 10×2=20 of good 2; consumes 120 units of
good 1 and 60 of good 2.
At price ¾: Home produces 0 of good 1 and 40×2=80 of good 2; consumes 53.3 of good 1 and
40 of good 2. Foreign produces 60×4=240 of good 1 and 0 of good 2; consumes 120 units of
good 1 and 90 of good 2.
Both variants bring equal number of points
True, false, or uncertain? Answer and comment any two questions below (40 points each)
22. Under free trade every product will be made in the country which can produce it most
efficiently. (Where 'most efficiently' means requiring the least amount of factor input).
FALSE Countries specialize under free trade in accordance with comparative but not absolute
advantage.
Requiring least input of the factor implies higher productivity in this sector at Home in
comparison to Foreign (absolute advantage concept). But the country that is less productive in
everything than the other country can be engaged in free trade and receive gains from trade if
it specializes in accordance with the comparative advantage. (20 points)
Example from the Ricardian model (15 points) graph free trade equilibrium (5 points)
23. Economists do not necessarily think Customs Unions are a good idea.
TRUE
Define Customs Unions (10 points), Trade Creation vs Trade diversion (10 points). Cooper–
Massell argument (10 points). Political but not economic reasons often explain formation of CU
(10 points) (No graph – 5 points )
If UNCERTAIN answer was given (Kemp-Wan theorem was added to all of the arguments
mentioned above) 100% of grade
24. The Russian oil export tax is reducing aggregate Russian welfare by introducing distortions
into the market.
FALSE/UNCERTAIN
As Russia can influence the price of oil at the world market, the large country case is
considered.
Russian oil export tax decreases the relative supply of the export good and increases the
Relative demand (since domestic price of the good falls). The shifts of the RS and RD curves lead
to the increase of the relative world price of the export good (Terms of trade-TOT). (10points)
Graph-RS-RD (5 points)
At the same time producers suffer loss from the decrease of the domestic price which is not
compensated by the gains to the consumers. (10 points)
Under partial equilibrium analysis we can show the net effect on the domestic welfare. The
change of welfare is ambiguous. If the TOT gain is higher than the loss from domestic market
distortions, the total welfare increases. (10 points)
Graph partial equilibrium (5 points)
Essay-style problems. Answer any two of the following questions. (60 points each)
25. Economists generally support a policy of free trade. Why is free trade hardly ever
observed in practice?
Free trade benefits the world but different groups can suffer (import -competing industry
(any model) (20 points)
Benefit consumers but producers are better organized (collective action problem) (10
points)
There are a lot of justifications for protectionists policy:
1)TOT argument for the large country–optimum tariff increases welfare. But it’s only for this
country with the expense of the trading partner. It’s mostly the theoretical possibility. In
practice can lead to trade war. Diagrams (5 points)
2)Market failure argument. Example (5 points)
3) Infant industry argument. Discuss problems: difficult to choose the industry, industry may
never mature. (5 points)
4)Policy intervention in non-competitive markets. Problem with this kind of model appears
to be that changes in assumptions about the underlying competitive situation lead to quite
different strategic policy (BS vs EG) (10 points)
Protectionism is a second-best policy. Domestic problems should be solved by domestic
policy measures (less distortions than under trade measures) (5 points)
26. “Arguments for or against free trade should not be based on comparing wage and income
levels in one country with those in another.” Discuss.
Compare wage and income levels in the same country: before and after trade liberalization;
Even a lower wage country can gain from trade if it specializes on goods in which it has a
comparative advantage (10 points)
Ricardian model example+ diagram) (15 points).
Misconceptions about comparative advantage/cheap labor argument (any of the following
arguments: Productivity and competitiveness, the Pauper labor argument; exploitation) (5
points)
Arguments against free trade can be based on the distributional effects from trade inside
one country. Country gains as a whole, identify losers and winners from trade (H-O, specific
factors model, including graphs) (30 points)
27. What factors give rise to foreign direct investment (FDI)? How would you assess the gains
and costs of FDI for the sending and host countries?
Firms decide to make FDI (vertical or horizontal) and produce abroad or just export. With
horizontal FDI they evaluate Proximity-concentration trade-off: High trade costs associated with
exporting create an incentive to locate production near customers. Increasing returns to scale
in production create an incentive to concentrate production in fewer locations.(15 points)
With vertical FDI They compare production costs differentials and fixed costs of operating
foreign affiliate. (10 points) Other factors mentioned in the OLI (theory) Ownership,
Internalization (Location is already explained) matter as well (5 points)
Foreign direct investment should benefit the countries involved for reasons similar to why
international trade generates gains.
(5 points) gains for sending (advantage of cost savings, overall gains from trade)
(5 points) costs for sending (similar to trade costs – allocation of net gains is different for
different groups of interest /HO; labor market effects – from outward FDI of high-labor cost
countries; flight of the capital problems
(5 points) gains for host (FDI is similar to industry reallocation when opening to free trade –
efficient use of resources, overall gains from trade)
(5 points) costs for host (similar to trade costs – allocation of net gains is different for different
groups of interest /HO; political pressure from multinationals)
10 points for examples