HW2 Solution Key



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HW2 Solution Key

UCDavis, 160a, Fall 2011 Prof. Farshid Mojaver



Ricardian Model

Problem 1

You are given the information shown in the table about the production relationship between Wonderland and the rest of the world and use the standard Ricardian assumptions:






Labor Hours per Bottle of Wine

Labor Hours per Pound of Cheese

Wonderland

10

5

Rest of the World

6

2

Wonderland has 40 million labor hours in total and the rest of the world has 30 million labor hours in total per year.

  1. Which country has absolute advantage in wine? In cheese?

  2. Which country has comparative advantage in wine? In cheese?

  3. Graph each country’s PPF. Use indifference curve to show the no-trade equilibrium (label as point A) for each country. (Suppose Wonderland consumes 4 million pounds of cheese and the rest of the world consumes 6 pounds of cheese).

  4. When trade is opened between Wonderland and the rest of the world, what the pattern of trade is? If the world price ratio is 0.4 bottle of wine per pound of cheese (Be careful this is not Pw/Pc but Pc/Pw), what happens to production in each country? (Label the new production point in each country as point P)

  5. Suppose that 2 million bottles of wine and 5 million pounds of cheese are traded. Show the consumption of each good in each country graphically using indifference curve (label the consumption point C)?







Labor Requirement

Opportunity Costs

Labor

Endowment






aLW

aLC

PW/PC

PC/PW




Wonderland

10

5

2

1/2

40m

ROW

6

2

3

1/3

30m

  1. ROW has absolute advantage on producing both wine and cheese because its labor requirements are lower.

  2. Comparative advantage means lower opportunity costs. Therefore, wonderland has comparative advantage in producing wine and ROW has comparative advantage in producing cheese.

  3. Wonderland: 10QW + 5QC = 40; ROW: 6 QW + 2QC = 30





  1. 15



Cheese

Cheese

P


8

C

10



5


A

C

4

A

6

P


Wine

Wine



4

2

2

3

5

Wonderland



ROW


  1. When the world price ratio is .4 bottle wine per pound of cheese, PC/PW = .4 and therefore, PW/PC = 2.5. In this case, the world price ratio is between these two country’s opportunity costs, therefore, Wonderland will specialize in producing wine (4m bottles of wine) and ROW will specialize in producing cheese (15m pounds of cheese).


Problem 2

Assume that Home and Foreign produce two goods, televisions and cars, and use the following information to answer the questions.



a. What is the marginal product of labor for televisions and cars in the Home country?

What is the no-trade relative price of televisions at Home?


Answer: MPLC =3, MPLTV =2, and PTV/ P C = MPL C / MPLTV =3/2
b. What is the marginal product of labor for televisions and cars in Foreign? What is the no-trade relative price of televisions in Foreign?
Answer: MPL*C =3, MPL*TV =2, and P*TV/ P* C = MPL* C / MPL*TV =1/2
c. Suppose the world relative price of televisions in the trade equilibrium is PTV/ PC =1. Which good will each country export? Briefly explain why.
Answer: Home will export cars and Foreign will export televisions because Home has a comparative advantage in cars whereas Foreign has a comparative advantage in televisions.
d. In the trade equilibrium, what is the real wage at Home in terms of cars and in terms of televisions? How do these values compare with the real wage in terms of either good in the no-trade equilibrium?
Answer: Workers at Home are paid in terms of cars because Home exports cars.

Home is better off with trade because its real wage in terms of televisions has increased.






e. In the trade equilibrium, what is the real wage in Foreign in terms of televisions and in terms of cars? How do these values compare with the real wage in terms of either good in the no-trade equilibrium?
Answer: Foreign workers are paid in terms of televisions because Foreign exports televisions.



f. In the trade equilibrium, do Foreign workers earn more or less than those at Home, measured in terms of their ability to purchase goods? Explain why.

Answer: Foreign workers earn less than workers at Home in terms of cars because

Home has an absolute advantage in the production of cars. Home workers

also earn more than Foreign workers in terms of televisions.
Problem 3

a. Suppose that the number of workers doubles in Home. What happens to the

Home PPF and what happens to the no-trade relative price of wheat?


Answer: With the doubling of the number of workers in Home, it can now produce

200 = 4 x 50 bushels of wheat if it concentrates all resources in the production of wheat or it could product 100 = 2 x 50 yards of cloth by devoting all resources to the production of cloth. The PPF shifts out for both wheat and cloth. The no-trade relative price of wheat remains the same because both MPLW and MPLC are unchanged.




b. Instead of doubling the number of workers in Home, suppose that there is technological progress in the wheat industry, so that Home can produce more wheat with the same amount of labor. What happens to the Home PPF, and what happens to the relative price of wheat? Describe what would happen if a similar change occurred in the cloth industry.



Answer: Because the technological progress is only in the wheat industry, Home’s production of cloth remains the same if it devotes all of its resources to producing cloth. If instead Home produces only wheat, it is able to produce more wheat using the same amount of labor. Home’s PPF shifts out in the direction of wheat production. Recall that the relative price of wheat is given by PW / PC =MPLC / MPLW.

With the technological progress in wheat, the marginal product of labor in the wheat production increases. Thus, the relative price of wheat decreases. If instead, the technological progress is in the cloth industry, we would have the opposite results. Home’s PPF would shift out in the direction of cloth production and the relative price of wheat would increase.



Problem 4:Consider an economy that labor is not mobile between sectors in the short run.

  1. Show the effect of international trade on production and consumption in the short run

  2. Answer question in part a assuming the keeps its domestic production prices intact using appropriate tax and subsides.

Answer)

  1. Suppose the international price P*> domestic relative prices P


Production falls to point B as cloth production becomes unprofitable and its unemployed workers can not find employment in the wheat sector. Then part of that wheat is exported at P* and the country consumes at point Con an indifference curve below its pre-trade position.

b)

Question 5: Make an argument to show that a domestic firm may lose out in international competition even if it is the most productive producer in the world.

A domestic firm that has the highest productivity in the world may lose out in international trade because there might be firms with even higher productivity in that country that drive the average wages higher (i.e, US might have the most productive apparel industry in the world but even higher productivity in wheat production drives the wages high so that it is not cost effective produce apparel in US).

Question 6


Read the following excerpt from Adam Smith on division of labor and labor productivity to answer the subsequent questions


  1. What is the difference between specialization in the Ricardian model and the Smithian model?

With Ricardian specialization we mean shifting resources to sectors with comparative advantage so we produce more with the same level of productivity.

In the Smithian model specialization increases productivity so there is an additional source of gain from trade in his that model.




  1. What does the Smithian division of labor imply on the productivity of larger economies?

Larger economies with larger demand for everything imply more division of labor higher levels of specialization and higher productivity. Thus larger economies are more productive according to the Smithan model while in the Recardian model country size does not affect productivity.


  1. What is the source of gains from trade and increased productivity in the Ricardian model?

Allocation efficiency


  1. Consider a two good economy: grain and computer. They are both produced with labor only but grain is subject to constant return to scale technology while computer production is subject to increasing return to scale technology. Draw the Production Possibility Frontier for this economy.





Heckshcer-Ohlin Model

Jeopardy Answers

DIRECTIONS: As in the popular TV game show, you are given an answer to a question and you must respond with the question. For example, if the answer is, "a tax on imports", then the correct question is, "What is a tariff?"



  1. term used to describe Argentina if Argentina has more land per unit of capital than Brazil.

Land abundant country

  1. term used to describe aluminum production when aluminum production requires more energy per unit of capital than steel production.

Aluminum is an energy intensive industry

  1. general term used to describe the amount of a factor needed to produce one unit of a good.

Unit Factor Requirement

  1. the two key terms used in the Heckscher-Ohlin model; one to compare industries, the other to compare countries.

Labor (capital) intensive industry; labor (capital) abundant country

  1. term used to describe when the capital-labor ratio in an industry varies with changes in market wages and rents

Variable factor proportions

  1. term describing the ratio of the unit-capital requirement and the unit-labor requirement in production of a good.

Capital intensity

  1. the assumption in the Heckscher-Ohlin model about unemployment of capital and labor. Zero



  1. interpretation given for the slope of the production possibility frontier.

Opportunity cost of production (Y in terms of X)

  1. the H-O model theorem that would be applied to identify the effects of a tariff on the prices of goods and factors. Stolper-Samuelson Theorem

Multiple Choice Questions

1. In the 2-factor, 2 good Heckscher-Ohlin model, the two countries differ in:

A. tastes. D. relative availabilities of factors of production.

B. military capabilities. E. labor productivities.

C. size.

2. In the 2-factor, 2 good Heckscher-Ohlin model, a change from autarky (no trade) to trade will benefit the owners of:

A. capital.

B. the relatively abundant factor of production.

C. the relatively scarce factor of production.

D. the relatively inelastic factor of production

E. the factor of production with the largest elasticity of substitution.
3. One way in which the Heckscher-Ohlin model differs from the Ricardo model of comparative advantage is by assuming that __________ is (are) identical in all countries.

A. factor of production endowments D. technology

B. scale economies E. opportunity costs

C. factor of production intensities


4. According to the Hecksher-Ohlin model,

A. everyone automatically gains from trade

B. the scarce factor necessarily gains from trade

C. the gainers could compensate the losers and still retain gains.

D. a country gains if its exports have a high value added.

E. None of the above.


5. Starting from an autarky (no-trade) situation with Heckscher-Ohlin model, if Country H is relatively labor abundant, then once trade begins:

A. wages and rents should rise in H.

B. wages and rents should fall in H.

C. wages should rise and rents should fall in H.

D. wages should fall and rents should rise in H.

E. None of the above.


6. Suppose that there are two factors, capital and land, and that the United States is relatively land endowed while the European Union is relatively capital-endowed. According to the Heckscher-Ohlin model,

A. European landowners should support US-European free trade.

B. European capitalists should support US-European free trade.

C. all capitalists in both countries should support free trade.

D. all landowners should support free trade.

E. None of the above.


7. Assume that only two countries, A and B, exist.

Consider the following data: Countries



Factor Endowments A B

Labor Force 45 20

Capital Stock 15 10
If good S is capital intensive, then following the Heckscher-Ohlin Theory,

      1. country A will export good S.

      2. country B will export good S.

      3. both countries will export good S.

      4. trade will not occur between these two countries.

      5. Insufficient information is given.


MC Question: 1.D, 2.B, 3.D, 4.C, 5.C, 6.B, 7.B
False, True, Or Uncertain, Explain Why (Questions in Heckscher-Ohlin Theory)

Question 1

“Opening up free trade does hurt people in import-competing industries in the short run. But in the long run, when people and resources can move between industries, everybody ends up gaining from free trade.”



Question 2

“American workers gain from free trade with China because free trade lowers prices of clothing in the United States and American workers spent very large portion of their income on clothing”


True False questions

Question1

“Opening up free trade does hurt people in import-competing industries in the short run. But in the long run, when people and resources can move between industries, everybody ends up gaining from free trade.”



False – Opening up free trade is likely to hurt some people. Owner of specialized factors in import-competing industries and owners of factors used intensively in import-competing industries will lose from free trade both in the short and in the long run.

Question2

“American workers gain from free trade with China because free trade lowers prices of clothing in the United States and American workers spent very large portion of their income on clothing”



False – Free trade lowers clothing prices in the United States but it lowers real wage of American worker too. Since wage income is the main source of American workers we may conclude that their income goes down with opening up trade with China.


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