Here's the link to the Solutions

1.    For each of the following cases determine the following: (a) the pre-trade relative prices; (b) the direction of comparative advantage; and (c) the limits to the relative wage rate. I've done Case I for you as an example.

CASE 1

Country

Labor hours per unit of good, hours XC

A B
S hours/bu. S 6 15
T hours/yd. T 2 12

A has an absolute advantage in both S and T, but their comparative advantage (greatest absolute advantage) is in T. B has a comparative advantage (least absolute disadvantage) in S. The pre-trade relative prices are shown in the table below:

CASE 1

Country

(a) Opportunity cost

A B
S yd. T/bu. S 6/2 = 3 15/12 = 5/4 = 1.25
T bu. S/yd. T 1/3 = 0.33 4/5 = 0.80

(b)    Britain has a lower opportunity cost (relative price) of S, and therefore a comparative advantage in this good. America has a comparative advantage in T.

(c)    The limits to the relative wage rate, WA/(E x WB)

Britain's comparative advantage in S implies that PSA > E x PSB
Perfect competition implies PSA = WA x hoursSA, PSB = WB x hoursSB
Thus,  WA x hoursSA > E x WB x hoursSB
Therefore WA/(E x WB) > hoursSB/hoursSA

America's comparative advantage in T implies that PTA < E x PTB
Perfect competition implies PTA = WA x hoursTA, PTB = WB x hoursTB
Thus,  WA x hoursTA < E x WB x hoursTB
Therefore WA/(E x WB) < hoursTB/hoursTA

Combining  hoursSB/hoursSA < WA/(E x WB) < hoursTB/hoursTA
Substituting values  15/6 < WA/(E x WB) < 12/2
Dividing yields  2.5 < WA/(E x WB) < 6

 

CASE 2

Country

Labor hours per unit of good, hours XC

A B
S hours/bu. S 10 5
T hours/yd. T 4 5

 

CASE 3

Country

Labor hours per unit of good, hours XC

A B
S hours/bu. S 10 8
T hours/yd. T 20 4

 

CASE 4

Country

Labor hours per unit of good, hours XC

A B
S hours/bu. S 4 9
T hours/yd. T 2 3

2.   (not assigned) Show that if country A has absolute advantage in S while country B has absolute advantage in T, A has comparative advantage in S, and B has comparative advantage in T.

Proof given in lecture.

3.   (not assigned) Show that if a country has comparative advantage in S it has comparative disadvantage in T.

Proof given in lecture.

4.    Using the data from Table 3.3, show the effect on world output if each country moved toward specialization in the production of its comparative disadvantage good.

TABLE 3.3, page 66

Country

Labor hours per unit of good, hours XC

A B
S hours/bu. S 3 12
T hours/yd. T 6 8

In this example, the comparative advantage goods are: 

A's = S, B's = T

Let A produce one less S;
let B produce one less T.

Gain (loss) Country World
A B Net gain (loss)
S      
T      

As countries increase the output of their comparative disadvantage goods, world output goes down. 

5.    Suppose there are 20,000 hours of labor available in country A. Five hours of labor are required to produce 1 bushel of S, while 4 hours are required to produce 1 yard of T. Find the shape and dimensions of A's PPF.

The intercept on the S axis will be

20000 (hours/year)/5 (hours/bu) = ______ (bu/yr)

The intercept on the T axis will be

 

The autarky price (Ps/Pt) = ________ (yd/bu).

6.    Use the information in Exercise 5 plus the following additional data to graph A's trade triangle: world relative price = 2 (yd/bu); A's imports = 2,000; A's exports = ?

7.    Evaluate the following statements:

    a.    Developed countries have nothing to gain by trading with developing countries.

    b.    Developed countries get all the gains from trade when they trade with developing countries because they can dictate their prices to these countries.

    c.    The United States can no longer compete in world markets because American wages are too high.

8.    Show that less-than-complete specialization in production leads to a lower level of welfare than complete specialization.

Hint: Your graph should show that complete specialization in production allows for greater GDP and a higher CIC than could be attained with partial specialization for a given terms of trade. 

9.    Suppose that the technologies available to A and B are given by the following table:

EXERCISE 9

Country

Labor hours per unit of good, hours XC

A B
S hours/bu. S 4 8
T hours/yd. T 2 4

Are there any incentives for trade in the example? Explain.

10.    For case 2 in question 1, which country would prefer a terms of trade of 1.1 (yd.T/bu.S) rather than an international price of 2? Explain.

11.    (USE THIS ANSWER AS AN EXAMPLE TO HELP WITH QUESTION 12.) Consider two countries, A and B, with the technologies given by case 4 in question 1. Suppose that the wage rate in A, Wa, equals $10 per hour and the wage rate in B, when measured in dollars, E x Wb, equals $5 per hour. Calculate the pretrade price of S and T in both A and B. 

PSA= WA (hoursSA) = $10(4) = $40

PSB= WB (hoursSB) = $5(9) = $45

PTA= WA (hoursTA) = $10(2) = $20

PTB= WB (hoursTB) = $5(3) = $15

Is there a basis for mutually beneficial trade? Why or why not?

Yes, there is a clear basis for mutually beneficial trade. Soybeans are cheaper in America, A; Textiles are cheaper in Britain, B.

Suppose that Wa rises to $12 per hour. Everything else held constant, what would happen to trade patterns? Why?

PSA= WA (hoursSA) = $12(4) = $48

PSB= WB (hoursSB) = $5(9) = $45

PTA= WA (hoursTA) = $12(2) = $24

PTB= WB (hoursTB) = $5(3) = $15

Now there is no basis for trade. A's wages are too high relative to its productivity.

What options would be available to A to resolve this situation?

The most obvious answer would be to cut wages, but this proposal is likely to encounter resistance. A change in the exchange rate would be more palatable. A weaker dollar would raise the dollar value of British wages. For example, if E rose from $2 to $2.40 per pound, the original relative wage would be restored.

12.    Consider two countries, A and B, with the technologies given by case 3 in question 1. Suppose that the wage rate in A, Wa, equals $10 per hour; then, for mutually beneficial trade to occur, the wage rate in B, when measured in dollars, E x Wb, must lie in a range from $X to $Y. Calculate X and Y and explain your answer.

13.    The classical model predicts that countries will completely specialize in the production of their comparative advantage good. Explain why the opportunity to engage in international trade would lead to this result.

14.    (not assigned) Suppose that country A has 10,000 worker-hours available for production and that it initially has the technology given by case 3 of question 1. Derive its PPF and determine its exact dimensions. Now, suppose that scientists in A develop a technology that doubles labor productivity in both industries. What would happen to A's PPF? Derive and explain. What would happen to the pattern of comparative advantage? Derive and explain.

CASE 3

Country

Labor hours per unit of good, hours XC

A B
S hours/bu. S 10 8
T hours/yd. T 20 4

15.   (not assigned) Suppose that country A has 40,000 worker-hours available for production and that it initially has the technology given by case 4 of question 1. Derive its PPF and determine its exact dimensions. Now, suppose that scientists in A develop a technology that doubles labor productivity in producing good S. What would happen to A's PPF? Derive and explain. What would happen to the pattern of comparative advantage? Derive and explain.

CASE 4

Country

Labor hours per unit of good, hours XC

A B
S hours/bu. S 4 9
T hours/yd. T 2 3

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