Problem 1:

1. Question: Which country has a comparative advantage in cheese production based on the unit labor requirements given?


2. Question: Which country has an absolute advantage in cheese production based on the total amount of cheese that can be produced with a given amount of labor? 


3. Question: Which country has an absolute advantage in wine production based on the total amount of wine that can be produced with a given amount of labor?


Problem 2: 


1. Question: Based on the relative factor intensities given, which good is capital intensive in each country?


2. Question: Based on the relative endowments given, which country is labor abundant? 


3. Question: What are the equilibrium wage and rent rates in each country based on the factor price diagram?


4. Question: How much of each good does the home country produce in free trade based on the production point in the factor price diagram?


5. Question: How much of each good does the foreign country produce in free trade based on the production point in the factor price diagram? 


6. Question: What are the national income levels of each country based on the factor quantities and prices?


7. Question: What are the demand levels for each good in each country based on national income and good prices?


8. Question: Which country exports good X in free trade equilibrium?


Answer:

Problem 1:

1.

To determine which country has a comparative advantage in cheese, we need to compare the relative unit labor requirements between the two countries. 

Country 1 

The domestic country has a unit labor requirement of 4 for producing cheese and a unit labor requirement of 2 for producing wine. 

Country 2 

The foreign country has a unit labor requirement of 1 for producing cheese and a unit labor requirement of 2 for producing wine. 

Hence:

Country 2 has a comparative advantage in cheese production, since it has a lower relative unit labor requirement for producing cheese compared to Country 1.

Absolute advantages:

To determine which country has an absolute advantage in cheese we will compare the total amount of cheese that each country can produce with a given amount of labor. 

Country 1:

Country 1 can produce 2.5 units of cheese with 10 units of labor (10/4 = 2.5).

Country 2:

Country 2 can produce 10 units of cheese with 10 units of labor (10/1 = 10). 

Hence Country 2 has an absolute advantage in cheese production, since it can produce more cheese with the same amount of labor.

Similarly, to determine which country has an absolute advantage in wine we will compare the total amount of wine that each country can produce with a given amount of labor. 

Country 1:

Country 1 can produce 5 units of wine with 10 units of labor (10/2 = 5).

Country 2:

Country 2 can produce 5 units of wine with 10 units of labor (10/2 = 5). Thus, both countries have the same absolute advantage in wine production.




2.

SRHome: Pc/Pw = aLW/aLC = 0.5Qc

SRForeign: Pc/Pw = a∗LC/a∗LW = 0.5Qc

The world relative supply schedule is the horizontal summation of the individual country supply schedules:

SRTotal: Pc/Pw = Qc/2

The world relative demand schedule is given by the equation:

RD: Pc/Pw = 2 - 2Qc



In autarky, the relative price of cheese in Country 1 is 4/2 = 2, while the relative price of cheese in Country 2 is 1/2 = 0.5. Since the price of good W is assumed to be 1 in both countries, we can express the autarky prices as Pc = 2 and Pc∗ = 0.5, and the autarky wages as w = 2 and w∗ = 0.5.

4.

To find the quantities of each good produced and consumed in each country, we can use the following equations:

For Domestic:

Qc = aLC * L = 4 * 10 = 40

Qw = aLW * L= 2 * 10 = 20


Domestically consumption 0.4/2 = 0.2 units of cheese for each unit of wine, so it will consume 8 units of cheese and 40 units of wine.

For Foreign:

Qc* = a∗LC * L* = 1 * 10 = 10

Qw* = a∗LW * L* = 2 * 10 = 20


Foreign consumes 0.4/2 = 0.2 units of cheese for each unit of wine, so it will consume 4 units of cheese and 20 units of wine.

To find the equilibrium wages, we can use the relative unit labor requirements to calculate the relative wage ratio in each country. In Country 1, the relative wage ratio is 4/2 = 2, while in Country 2, it is 1/2 = 0.5. Since the relative price of cheese in free trade is 1.2, we can calculate the absolute price of cheese in each country as follows:

Pc = 1.2 x 2 = 2.4


Pc∗ = 1.2 x 0.5 = 0.6

Using the absolute prices and the relative unit labor requirements, we can calculate the absolute wage in each country as follows:

w = (Pc/aLC) = 0.6

w∗ = (Pc∗/a∗LC) = 0.6

Thus, the equilibrium wages are 0.6 in both countries.

Both countries gain from trade. In autarky, the real wage (w/Pw) in Country 1 is 2/1 = 2, while in Country 2 it is 0.5/1 = 0.5. In free trade, the real wage in both countries is 0.6/1 = 0.6. Thus, the real wage increases in Country 1 and increases more substantially in Country 2, indicating that both countries are better off in free trade than in autarky. This can also be seen from the fact that trade allows each country to specialize in producing the good in which it has a comparative advantage, leading to a more efficient allocation of resources and higher overall production.

When the supply of labor in the foreign country increases to 20, the absolute labor endowment in Country 2 increases from 10 to 20. This will cause a rightward shift in the world relative supply schedule for cheese, since the relative supply of cheese in Country 2 will increase at every price level.

To illustrate this shift, we can create a new world relative supply schedule by recalculating the relative quantities supplied at each price level, holding the relative unit labor requirements constant. The new world relative supply schedule is as follows:




To find the equilibrium wages, we need to use the PPF equation, which is given by:


In this case, the PPF equation becomes:


Simplifying, we get:


Using the absolute quantities and the labor endowments, we can calculate the absolute wage in each country as follows:

w = (Qc x aLC + Qw x aLW)/10 = 0.96

w∗ = (Q∗c x a∗LC + Qw∗ x a∗LW)/20 = 0.24

Thus, the equilibrium prices are Pc = 1.2 and Pw = 1, the quantities traded are Qc = 4, Q∗c = 0, Qw = 6, and Qw∗ = 10, and the equilibrium wages are w = 0.96 and w∗ = 0.24.



Problem 2:

1.

To determine which good is capital intensive, we need to compare the relative factor intensities of each good in each country. The relative factor intensity of a good is given by the ratio of the capital requirement to the labor requirement, or aK/aL.

For Home, the relative factor intensity of good X is 20/40 = 0.5, while the relative factor intensity of good Y is 30/20 = 1.5. Since the relative factor intensity of good Y is greater than that of good X, we can say that good Y is capital intensive in Home.

For Foreign, the relative factor intensity of good X is 20/40 = 0.5, while the relative factor intensity of good Y is 30/20 = 1.5. Again, we can see that good Y is capital intensive in Foreign.

Therefore, good Y is capital intensive in both countries.

2.

To determine which country is labor abundant, we need to compare the relative endowments of labor and capital in each country. The relative endowment of a factor is given by the ratio of the factor quantity to the other factor quantity, or L/K.

For Home, the relative endowment of labor is 800/1000 = 0.8, while the relative endowment of capital is 1000/800 = 1.25. Since the relative endowment of labor is less than that of capital, we can say that Home is capital abundant.

For Foreign, the relative endowment of labor is 1200/1000 = 1.2, while the relative endowment of capital is 1000/1200 = 0.83. Since the relative endowment of labor is greater than that of capital, we can say that Foreign is labor abundant.

Therefore, Foreign is labor abundant and Home is capital abundant.


To find the wage and rent in each country, we can use the factor price diagram. The factor price diagram shows the relative price of the goods (PX/PY) on the vertical axis and the relative factor prices (w/r) on the horizontal axis. The slope of the production possibility frontier (PPF) represents the relative factor intensity of the goods.

In the free trade equilibrium, the relative prices of the goods are given as PX/PY = 1, and the relative factor intensities of the goods are given as aKX/aLX = 0.5 and aKY/aLY = 1.5 in both countries.

The PPF for Home is given by the equation:

40X + 20Y = 800L

Solving for Y and graphing the PPF.



The slope of the PPF is -40/20 = -2, which represents the relative factor intensity of good X. The relative factor prices in Home can be read off the graph as the ratio of the vertical intercept to the horizontal intercept of the tangent line to the PPF, which is approximately 1.25. Therefore, the relative wage and rent in Home are w/r = 1.25.

Similarly, the PPF for Foreign is given by the equation:

20X + 30Y = 1200L*

Solving for Y and graphing the PPFThe slope of the PPF is -20/30 = -0.67, which represents the relative factor intensity of good X. The relative factor prices in Foreign can be read off the graph as the ratio of the vertical intercept to the horizontal intercept of the tangent line to the PPF, which is approximately 0.83. Therefore, the relative wage and rent in Foreign are w/r = 0.83.



To find the absolute wage and rent in each country, we can use the following equations:

w = w/r * r

r = w/r * w

Using the relative wage and rent from above and the given values of factor endowments, we get:

wHome = 1.25 * (1000/1.25) / (800/1.25) = 1.562

rHome = 1.25 * (1000/1.25) / (1/0.25) = 1250

wForeign = 0.83 * (1000/0.83) / (1200/0.83) = 0.691 

rForeign = 0.83 * (1000/0.83) / (1/0.17) =170.06

To determine how much of each good the home country produces in free trade, we can use the production point in the factor price diagram. The production point occurs where the PPF is tangent to the relative price line (PX/PY = 1), and is given by the factor proportions that minimize the cost of producing the two goods.

Using the given values of factor endowments and factor requirements, we can calculate the factor proportions for each good in Home:

For good X:

aKX/aLX = 0.5

L/K = 0.8

LX/KX = aKX/aLX / (L/K) = 0.5 / 0.8 = 0.625

For good Y:

aKY/aLY = 1.5

L/K = 0.8

LY/KY = aKY/aLY / (L/K) = 1.5 / 0.8 = 1.875

The total amount of each factor used in production is then:

K = KX + KY = (20 * 0.625) + (30 * 1.875) = 68.75

L = LX + LY = (40 * 0.625) + (20 * 1.875) = 62.5

Using the given values of prices, we can calculate the total cost of producing each good:

For good X:

TCX = 80 * KX + wHome * LX = 80 * 20 * 0.625 + 1,250 * 40 * 0.625 = 32,250

For good Y:

TCY = 80 * KY + wHome * LY = 80 * 30 * 1.875 + 1,250 * 20 * 1.875 = 51,375

Therefore, Home produces 20 units of good X and 30 units of good Y in free trade.

To determine how much of each good the foreign country produces in free trade, we can use the same approach as in part 4. Using the given values of factor endowments and factor requirements, we can calculate the factor proportions for each good in Foreign:

For good X:

aKX/aLX = 0.5

L*/K* = 1.2

LX/KX = aKX/aLX / (L*/K*) = 0.5 / 1.2 = 0.4167

For good Y:

aKY/aLY = 1.5

L*/K* = 1.2

LY/KY = aKY/aLY / (L*/K*) = 1.5 / 1.2 = 1.25

The total amount of each factor used in production is then:

K* = KX + KY = (20 * 0.4167) + (30 * 1.25) = 45.83

L* = LX + LY = (40 * 0.4167) + (20 * 1.25) = 41.66

Using the given values of prices, we can calculate the total cost of producing each good:

For good X:

TCX = 80 * KX + wForeign * LX = 80 * 20 * 0.4167 + 692.5 * 40 * 0.4167 = 78214.59

For good Y:

TCY = 80 * KY + wForeign * LY = 80 * 30 * 1.25 + 692.5 * 20 * 1.25 = 20312.5

Therefore, Foreign produces 20 units of good X and 30 units of good Y in free trade.

To find the national income of each country, we can use the following equation:

NI = wL + rK

where NI is national income, w is the wage rate, L is the quantity of labor, r is the rental rate, and K is the quantity of capital.

For Home, we have:

NIHome = wHome * L + rHome * K = 1,250 * 800 + 1250* 1,000 = 22,50,000

For Foreign, we have:

NIForeign = wForeign * L* + rForeign * K* = 692.5 * 1,200 + 170.06* 1,000 = 1001, 060


7.

For Home:

DX = (1/3) * NIHome / PX = (1/3) * 22,50,000 / 80 = 9375

DY = (2/3) * NIHome / PY = (2/3) * 22,50,000 / 80 = 18750

For Foreign:

DX* = (1/3) * NIForeign / PX = (1/3) * 1001, 060/ 80 = 4171

DY* = (2/3) * NIForeign / PY = (2/3) * 1001, 060/ 80 = 8342



8.

Foreign exports good X.