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Economics 140: Practice Midterm Exam

Part I: Analytical Problem

Note: No credit will be given for unsupported answers.

1. Consider a small open economy that produces clocks and food (clocks with capital (K)
and labor (LC); food with land (T ) and labor (LF )). Capital and land are fixed factors
while labor can move between sectors (LC + LF = L). The production technology in
each sector demonstrates constant returns to scale with diminishing returns of marginal
product of each factor and factor complementarity. Consumers in this economy exhibit
homothetic preferences. W , R, RT denote worker wages, rental rate of capital, and
rental rate of land respectively.

(a) Graphically represent the autarky equilibrium with quantity of production in
clocks QC on the x-axis and quantity of production in food QF on the y-axis.

[Solution]

QF

QC

PPF

U

QC = DC

QF = DF

(b) The economy opens up to free trade and observes a relative world price (PC/PF )
T .

Let us further assume that the relative world price is higher than in the autarky
relative price, (PC/PF )

T > (PC/PF )
A. How does the equilibrium production and

consumption change with trade? Show on a separate graph how openness to trade
affects consumers’ welfare. Again, put quantity of production in clocks QC on the
x-axis and quantity of production in food QF on the y-axis.

[Solution]
When the economy opens up to free trade and observes that the relative world
price is higher than in the autarky relative price, the equilibrium production
in clock increases from QAC to Q

T
C with trade, and the equilibrium consumption

decreases from DAC (= Q
A
C) to D

T
C. On the other hand, the equilibrium production

in food decreases from QAF to Q
T
F , and the equilibrium consumption increases from

DAF (= Q
A
F ) to Q

T
F with trade. Consumers gain from trade as their utility grows

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from UA to UT with trade.
QF

QC

PPF
UA

QAC

QAF

UT

DTC

DTF

QTC

QTF

(c) Examine the changes in real income of each factor owners.

i. Show changes in the real wage for the workers in each sector W/PC, W/PF .

[Solution]
From the producers’ profit maximization problem, we can derive the following
first- conditions: W = PC ×MPLC = PF ×MPLF . Then,

W

PC
= MPLC and

W

PF
= MPLF .

Since the quantity of production in clock increases, and the production of
food decreases with trade, labor reallocates from the food sector to the clock
sector, i.e., LC increases and LF decreases. Because of the assumption of di-
minishing returns of marginal product of labor, MPLC decreases and MPLF
increases. Therefore, the real wage for the workers in the clock sector falls,
and the real wage in the food sector rises.

ii. Show changes in the real rental rate of the capital owners in the clocks sector
R/PC, R/PF .

[Solution]
As the clock firm maximizes its profit, we can derive the following equation:
R = PC ×MPKC. Then,

R

PC
= MPKC and

R

PF
=

PC ×MPKC
PF

=
PC
PF
×MPKC.

Due to the assumption of factor complementarity, MPKC increases as LC
grows. Thus, the real rental rate of the capital owners increases.

iii. Show changes in the real rental rate of land in the food sector RT /PC, R
T /PF .

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[Solution]
As the food producer maximizes its profit, we can derive the following equa-
tion: RT = PF ×MPTF . Then,

RT

PF
= MPTF and

RT

PC
=

PF ×MPTF
PC

=
PF
PC
×MPTF .

Due to the assumption of factor complementarity, MPTF decreases as LF
declines. Thus, the real rental rate of the land owners decreases.

iv. What are the key assumptions on the production technology that drive the
change in each result?

[Solution]
Each sector use labor and a specific factor. Labor can move freely across
sectors. And the production technology in each sector demonstrates constant
returns to scale with diminishing returns of marginal product of each factor
and factor complementarity.

2. Consider two countries, England (Home) and India (Foreign∗), that produce cloth
and trains with capital (K) and labor (L). Both factors freely move across sectors.
The production technology in each sector demonstrates constant returns to scale with
diminishing returns of marginal product of each factor and factor complementarity.
Consumers in this economy exhibit homothetic preferences. W , R denote worker wages
and rental rate of capital respectively. The production of clothing is labor intensive
while train production is capital intensive. England is relatively capital abundant, and
India is relatively labor abundant.

(a) What is the relationship between autarky relative prices in the two countries
(PC/PT )?

[Solution]
Since England is relatively capital abundant and train production is the capital-
intensive good, England will produce a higher ratio of train to clothing than India.
That is, England has a larger relative supply of train and India has a larger rel-
ative supply of clothing. Because consumers in both countries exhibit the same
homothetic preferences, the relative demand curve is the same for both countries.
Therefore, the autarky relative price of clothing is lower in India than in England((

P ∗
C

P ∗
T

)A
< ( PC PT )A) . (b) What is the pattern of trade that results from free trade between these two coun- tries? [Solution] When Home and Foreign trade with each other, their relative prices converge,(( PC PT )A >

(
PC
PT

)W
>

(
P ∗
C

P ∗
T

)A)
. The relative price of cloth declines in England

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and rises in India. The economy exports the good whose relative price increases.
Thus, England will export train and import cloth, while India will export cloth
and import train.

(c) Show how wages and the rental price of capital change in each country with free
trade. Will English capitalists (i.e. the owners of capital) be in favor of free trade
with India? Will Indian capitalists (i.e. the owners of capital) be in favor of free
trade with England?

[Solution]

The relative price of cloth
(

PC
PT

)
falls in Home country with trade. England will

produce more trains. Therefore, more labor and capital are allocated to the train
sector. Since the train is a capital intensive good, the relative demand of labor(

LT
KT

)
decreases and the relative factor price ( W

R
) falls in England. Thus, capital

owners in England gain.

In the foreign country, the relative price
(

PC
PT

)
increases with trade. India produces

more cloth and allocate more labor and capital toward the clothing sector. Since

cloth is a labor intensive good, the relative demand of labor
(

L∗
C

K∗
C

)
increases and

the relative factor price ( W
R

) increases in India. Thus, Indian workers gain.

W
R

PC
PT

SS

(
P ∗
C

P ∗
T

)A

(
W ∗

R∗

)A
(

PC
PT

)W

W
R

(
PC
PT

)A

(
W
R

)A

(d) What will happen to the capital labor ratio (K/L) in the cloth and train sectors
England after opening to trade? What about India?

[Solution]
Since the ratio of wage to rental rate

(
W
R

)
falls in England, the producers in both

sectors will increase the relative input of labor
(

LC
KC

and LT
KT

)
. That is, the capital

labor ratio
(
K
L

)
decreases in both sectors in England.

On the other hand, the relative input of labor
(

L∗
C

K∗
C

and
L∗
T

K∗
T

)
decreases in India

because the wage-rental rate ratio
(
W
R

)
rises in India. That is, the capital labor

ratio increases in both sectors in India.

The following figure is an exmaple of the change in the relative factor market in

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Home country.

W
R

L
K

RDT

RDC

RDfactors

L̄
K̄

RS

(W/R)

RDtradefactors

(W/R)trade

→ →

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Part II: True / False / Uncertain

Determine whether each of the following statements is true, false or uncertain, and briefly
justify your answer (2-3 sentences). No credit will be given for unsupported answers.

1. Two countries will only trade with each other if they have different endowments and/or
different technologies.

False: The two countries will always trade with each other if their autarky relative
prices are different. Even with identical endowments and technology, consumers in the
two countries may have different preferences which will lead to different autarky prices
and the countries will still gain from trade. (In fact, as we will see in the trade models
with increasing returns to scale, product differentiation will allow even countries with
identical endowments, technology and preferences to trade with each other.)

2. The U.S. imports relatively more from Germany (abundant in skilled labor) than from
Bangladesh (abundant in unskilled labor) in sectors intensive in skilled labor. This
empirical evidence is consistent with the predictions of the Heckscher-Ohlin model.

True: This is the Heckscher-Ohlin effect of trade where a country has a compar-
ative advantage (and therefore exports) the good that is intensive in the country’s
relatively abundant factor. Germany is relatively abundant in skilled labor compared
to Bangladesh and therefore has comparative advantage in skill-intensive goods while
Bangladesh is relatively abundant in unskilled labor compared to Germany and there-
fore has comparative advantage in skill-intensive goods. This is why U.S. imports
more of the skill-intensive goods from Germany and the less skill-intensive goods from
Bangladesh.

3. One of the key predictions of the specific factors model is such that winners and losers
from trade depend on which factor they own.

False: The specific factor model predicts that winners & losers from trade are defined
by their current industries, rather than by which factor they own. This is because fac-
tors are “stuck” in their current industries regardless of the changes in relative goods
prices with trade which benefit factors in industry whose relative price increases and
hurt factors “stuck” in industry whose relative price falls.

4. Suppose that Home and Foreign can produce two goods (C and F) using two factors
of production (K and L) with a bowed-out production possibilities frontier (PPF),
and suppose that production of C is K-intensive. If Home has a relative abundance
of L compared with Foreign, then K owners in Home should support free trade policies.

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False: With free trade, the abundant factor gains while the scare factor loses (Stolper-
Samuelson effect). Therefore, the capital owners in the Home economy, the scarce
factor, would be against free trade.

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