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(Solved) EC 440 Sample Exam Questions The following questions appeared on exams that I have given over the last several semesters. You can be sure that I will...



Can you help me solve these problems in the file?  These questions are about international trade.

EC 440
Sample Exam Questions
The following questions appeared on exams that I have given over the last several semesters. You
can be sure that I will not re-use any of these exact questions. But you can see that there are many
common themes in the questions. For example, questions about the Ricardian model frequently
involve the derivation of relative supply and/or relative demand. Questions frequently require you
to understand how to derive a demand curve based on underlying preferences. Questions often use
words such as “prove,” “show,” “solve,” “draw,” or “compare.”
These questions complement those in the workbooks, the in-class problem sets, and the end-ofchapter questions in the textbook. I encourage you to work out the answers for these questions and
discuss your solutions with others in the class. Of course, you are also welcome to discuss your
solutions with my assistant or me. However, “knowing” the answers to these questions is of no use
(because I will not repeat these exact questions) unless you work out the answer for yourself. For
example, the answers to question (14.b) is 5; and the answer to question (14.d) is 0.25. But it is not
at all helpful to “memorize” these numbers, since you are highly unlikely to ever see the same
numeric question. Rather, it is important to know how to derive the answers.
For some questions, there is only one correct way of showing something (for example, find the
solution to (14.d) by differentiating the production function with respect to labor, then substitute
the values of and into the result). For other questions, there are multiple ways of finding the
correct solution. For example, one way to find the solution to (14.b) is to use the function provided,
invert it to write price as a function of quantity � = −1⁄2 �, multiply by quantity
� = × −1⁄2 = 1⁄2 �, differentiate with respect to quantity � = 1 −1⁄2 �,
2 1
2 then recognize that −1⁄2 = , so that = . Alternatively, take a more generic approach and show that marginal revenue equals �1 − 1
�× , then know that the price elasticity of demand in this case has a value of 2. Substitution then results in the
correct answer. If you show a correct approach for finding an answer, you will likely earn most of
the points possible, even if you make a computational error so that your numeric answer is wrong.
On the other hand, an incorrect numeric answer without any explanation (or with an incorrect
explanation) would earn no credit. 1. There are two countries (Home and Foreign) and two goods (X and Y). Labor is the only input and all
individuals have the same preferences. The production possibilities frontiers and utility function are
given below.
1 3 ( , ) = ( )4 ( )4 a. Draw and label the world relative supply and relative demand curves, including as much numeric
information as possible.
b. Draw and label the free-trade consumption possibilities curves for both countries.
c. Explain the impact on your answers to parts (a) and (b) if the Foreign labor force were to double
in size (holding productivity constant).
2. Consider a Ricardian model where the two goods are and and the two countries are Home and
Foreign. Home has the comparative advantage in . All consumers spend ¾ of their income on and ¼ of their income on . The world relative supply curve is shown below.
a. Derive an equation relating the relative demand for in
terms of to the price of in terms of . b. Prove that the free-trade equilibrium relative price is
1 � = .
2 c. Which country(ies) (if either) continues to produce both and in the free-trade equilibrium? 3. Consider a Ricardian model where the two goods are and and
the two countries are Home and Foreign. Home has the
comparative advantage in . All consumers in the world have the
same preferences. The graph of world relative supply is shown to
the right. Relative demand can be represented by the following
equation:
1 = ( ⁄ ) Solve for the equilibrium price of X in terms of Y.
4. Consider a world with two goods (X and Y) and three countries (North, West, and South). Each of
the three countries is characterized as a Ricardian economy and the three production possibilities
frontiers are illustrated below. Draw the world relative supply curve.
5. A firm produces a unique variety of a product. The foreign demand for the firm’s product can be
written as = 100−2 . The marginal cost of exporting (including production, transportation, and
tariff) is = 1.
a. What price will the firm charge for its product in the foreign market if it exports? b. How much profit would the firm earn from exporting?
c. Suppose that the firm could undertake foreign direct investment creating a fixed cost of 30 but
reducing marginal cost to = 12. Would the firm prefer to export or would it prefer FDI? 6. A firm produces a product at a marginal cost of 2. It is considering exporting this product to a
variety of different countries. None of the countries impose import tariffs, and the marginal
transportation cost is 0.5 in all instances. In addition to a marginal transportation cost, there is a
fixed cost of entering each market (perhaps due to the need to establish separate distribution
networks), with that fixed cost equal to 15. The country-specific markets differ from each other
according to their demand for the product, with the individual demands given in the table below.
a. To which countries (if any) will this firm export? Show your work.
b. How much profit will the firm earn from exporting? Show your work.
c. How would your answer to part (a) change if the marginal transportation cost doubled while the
fixed cost of entering a market fell to zero? Explain your answer.
COUNTRY
A
B
C
D DEMAND = 180−2 = 160−2 = 140−2 = 120−2 7. A firm is trying to decide between exporting a product to a foreign market (therefore incurring
transportation costs and paying a per-unit tariff) or establishing a new factory in the foreign country
(therefore incurring a fixed cost, but avoiding transportation costs and tariffs). Sketch two diagrams.
In one diagram, show how the profits from exporting or FDI depend on the tariff; in the other show
how the profits from exporting or FDI depend on the fixed cost of establishing a new factory. You
need not derive the profit functions. Just explain the intuition of the diagrams and discuss what the
two diagrams show. 8. There are only two firms in the world (one in the Home country and one in the Foreign country) that
produce a drug used to treat the common cold. The inverse-demand curve is the same in both
markets:
1 = 100 − 2 There are no fixed costs and both firms have the same marginal cost of production: = $20.
Transporting each dose from one country to the other costs $10.
a. Solve for the monopolists profit-maximizing quantity of output and price. Show your work.
b. Assume Cournot competition. Derive each firm’s reaction function for selling in Home country’s
market if trade is permitted
c. Solve for each country’s profit maximizing quantity and the equilibrium price in the Home
country’s market if trade is permitted
d. Given the assumptions of this problem, compare the Home firm’s profit in autarky to its profit
with trade (recognizing that it will export the drug). Show your work.
9. Consider a U.S. firm that produces a unique variety of a product. It sells the product in the U.S. and
might also choose to sell the product in India. Sales to India might be by way of exports or foreign
direct investment. The U.S. demand for its product is = 100 × ( )−3 . The Indian demand for
its product is = 500 × ( )−3 . The marginal cost of production in the U.S. is $100. If it were to
open a factory in India, the marginal cost of production would be $50. Moreover, if the firm chose
to export to India, it would cost an additional $20 of transportation. There are no tariffs.
Assuming that it was trying to maximize profit, how much would the firm charge for its product in
the United States and in India if it exports the product to India? What price would it charge in India
if it were to undertake FDI and produce in India?
10. There are only two producers of a particular product. Firm A is located in America, firm E is located in Europe. The American inverse demand curve for this product can be written as = 1,000 − ,
2
where = + , and represents firm A’s sales in the American market, and represents
firm E’s sales in the American market. Both firms have the same marginal cost of production
( = 200). It costs 100 to ship each unit of the product from Europe to America.
Prove that with trade, the American firm will sell 600 units, America will import 400 units from
Europe, and the equilibrium price will be 500. 11. There are two countries (Home and Foreign) and two firms
selling an identical product. In the absence of trade, each firm
is a monopolist in its own market. The marginal cost of
production is constant and equal to 40. There are no fixed
costs. Demand is linear. There are no transportation costs or
tariffs. If trade is permitted, both firms compete as Cournot
rivals in both markets. The figure to the right shows the Home
country’s demand curve (which looks just like the Foreign
country’s demand curve.)
I have solved for the autarky and trading equilibrium and this is
what I’ve found:
Price
Total sales in Home
Home exports to Foreign
Foreign exports to Home Autarky Trade
70
60
30
40
0
20
0
20 Solve for Home country social welfare in autarky and with trade. Explain the intuition of why
welfare increased, decreased, or stayed the same.
12. Farmers and tailors are the only two factors of production in a pure specific factors model. Each
farmer can grow 1 ton of food, each tailor can make 2 shirts. In autarky, the price of 1 shirt is $10
and the price of 1 ton of food is $20. If trade is permitted, the economy can import shirts for $5
each. It exports food for $20 per ton.
a. Draw budget lines for farmers and tailors in autarky and compare them with free trade budget
lines.
b. How would your analysis of the problem change if all workers were alike, with each being able
to move between sectors to produce either 1 ton of food or 2 shirts? 13. An economy produces computers using capital and labor, and it produces food using only labor. The
marginal product of labor in food production is 10, regardless of how many workers produce food.
The marginal product of labor in computer production is 27 − . The total supply of labor is =
100. The world price of food is $1 and the world price of computers is $5.
a. Draw a diagram illustrating equilibrium in this economy, solving for the wage and distribution of
labor between sectors. b. Suppose that this economy is an importer of computers and the government implements a
100% import tariff, show how the tariff affects the diagram that you drew in answer to the first
part of the question.
c. Draw two budget lines for a typical worker: one that applies to free trade and the other that
applies once the tariff is implemented. What is the effect of the tariff on the worker’s welfare?
Hint: treat this as a mixed specific-factors model where the only modification is the absence
of a factor that is specific to agricultural production.
14. Answer each of the following. You need not show your work unless you think it will help me better
understand your answer.
a. Given the utility function (, ) = 0.25 0.75, how much money would a utility-maximizing
consumer spend on each good if he had $100 to spend?
b. Given the demand function = −2 , what is the value of marginal revenue when = 10? c. There are two countries (Home and Foreign) and two firms selling an identical product. In the
absence of trade, each firm is a monopolist in its own market. The marginal cost of production
is constant and equal to 40. There are no fixed costs. Demand is linear. There are no
transportation costs or tariffs. Suppose that the two firms are Bertrand rivals. What would be
the equilibrium price in each market with trade?
d. Suppose that output is produced using capital and labor according to the production function = √ × . Calculate the marginal product of labor when the firm employs 25 units of capital
and 100 workers. 15. Answer each of the following. You need not show your work unless you think it will help me better
understand your answer.
a. Suppose consumers spend ¼ of their income on X and ¾ of their income on Y. Write down the
Cobb-Douglas utility function that corresponds to these preferences.
b. Suppose that output is produced according to the production function = 1⁄3 2⁄3, where is
output, is capital and is labor. Write down an equation representing the marginal product
of labor.
c. Suppose that a monopolist faces an inverse market demand curve = 50 − 3, where is
price and is quantity. Write down an equation representing the marginal revenue curve. d. Suppose that Kodak and Fuji are the only two firms selling film in the United States and that the
market demand curve is = 50 − 3, where is price and is the combined quantity of sales
from both firms. Suppose that Fuji sells a quantity of 10 rolls of film. Write down an equation
representing the residual demand curve faced by Kodak.
e. What is the Lerner symmetry theorem?
f. What is the Melitz effect?

 


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