1. For each of the following cases determine the following: (a) the pretrade relative prices; (b) the direction of comparative advantage; and (c) the limits to the relative wage rate.

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 pretrade 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, W_{A}/(E
x W_{B})

Britain's comparative advantage in S implies that P_{SA} > E x P_{SB}

Perfect competition implies P_{SA} = W_{A} x hours_{SA},
P_{SB} = W_{B} x hours_{SB}

Thus, W_{A} x hours_{SA }> E x W_{B} x hours_{SB}

Therefore W_{A}/(E x W_{B}) > hours_{SB}/hours_{SA}

America's comparative advantage in T implies that P_{TA} < E x P_{TB}

Perfect competition implies P_{TA} = W_{A} x hours_{TA},
P_{TB} = W_{B} x hours_{TB}

Thus, W_{A} x hours_{TA }< E x W_{B} x hours_{TB}

Therefore W_{A}/(E x W_{B}) < hours_{TB}/hours_{TA}

Combining hours_{SB}/hours_{SA} < W_{A}/(E x W_{B})
< hours_{TB}/hours_{TA}

Substituting values 15/6 < W_{A}/(E x W_{B}) < 12/2

Dividing yields 2.5 < W_{A}/(E x W_{B}) < 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

A has an absolute and comparative advantage in T. B has an absolute and comparative advantage in S. The pretrade relative prices are shown in the table below:

CASE 2 | Country |
||

(a) Opportunity cost |
A | B | |

S | yd. T/bu. S | 10/4 = 2.5 | 5/5 = 1 |

T | bu. S/yd. T | 4/10 = 0.40 | 1 |

(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, W_{A}/(E
x W_{B})

Britain's comparative advantage in S implies that P_{SA} > E x P_{SB}

Perfect competition implies P_{SA} = W_{A} x hours_{SA},
P_{SB} = W_{B} x hours_{SB}

Thus, W_{A} x hours_{SA }> E x W_{B} x hours_{SB}

Therefore W_{A}/(E x W_{B}) > hours_{SB}/hours_{SA}

America's comparative advantage in T implies that P_{TA} < E x P_{TB}

Perfect competition implies P_{TA} = W_{A} x hours_{TA},
P_{TB} = W_{B} x hours_{TB}

Thus, W_{A} x hours_{TA }< E x W_{B} x hours_{TB}

Therefore W_{A}/(E x W_{B}) < hours_{TB}/hours_{TA}

Combining hours_{SB}/hours_{SA} < W_{A}/(E x W_{B})
< hours_{TB}/hours_{TA}

Substituting values 5/10 < W_{A}/(E x W_{B}) < 5/4

Dividing yields 0.5 < W_{A}/(E x W_{B}) < 1.25

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

B 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 pretrade relative prices are shown in the table below:

CASE 3 | Country |
||

(a) Opportunity cost |
A | B | |

S | yd. T/bu. S | 10/20 = 0.5 | 8/4 = 2 |

T | bu. S/yd. T | 2 | 0.5 |

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

(c) The limits to the relative wage rate, W_{A}/(E
x W_{B})

America's comparative advantage in S implies that P_{SA} < E x P_{SB}

Perfect competition implies P_{SA} = W_{A} x hours_{SA},
P_{SB} = W_{B} x hours_{SB}

Thus, W_{A} x hours_{SA }< E x W_{B} x hours_{SB}

Therefore W_{A}/(E x W_{B}) < hours_{SB}/hours_{SA}

Britain's comparative advantage in T implies that P_{TA} > E x P_{TB}

Perfect competition implies P_{TA} = W_{A} x hours_{TA},
P_{TB} = W_{B} x hours_{TB}

Thus, W_{A} x hours_{TA }> E x W_{B} x hours_{TB}

Therefore W_{A}/(E x W_{B}) > hours_{TB}/hours_{TA}

Combining hours_{TB}/hours_{TA} < W_{A}/(E
x W_{B}) < hours_{SB}/hours_{SA}

Substituting values 4/20 < W_{A}/(E x W_{B}) < 8/10

Dividing yields 0.20 < W_{A}/(E x W_{B}) < 0.80

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

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

CASE 4 | Country |
||

(a) Opportunity cost |
A | B | |

S | yd. T/bu. S | 4/2 = 2 | 9/3 = 3 |

T | bu. S/yd. T | 0.5 | 1/3 = 0.33 |

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

(c) The limits to the relative wage rate, W_{A}/(E
x W_{B})

America's comparative advantage in S implies that P_{SA} < E x P_{SB}

Perfect competition implies P_{SA} = W_{A} x hours_{SA},
P_{SB} = W_{B} x hours_{SB}

Thus, W_{A} x hours_{SA }< E x W_{B} x hours_{SB}

Therefore W_{A}/(E x W_{B}) < hours_{SB}/hours_{SA}

Britain's comparative advantage in T implies that P_{TA} > E x P_{TB}

Perfect competition implies P_{TA} = W_{A} x hours_{TA},
P_{TB} = W_{B} x hours_{TB}

Thus, W_{A} x hours_{TA }> E x W_{B} x hours_{TB}

Therefore W_{A}/(E x W_{B}) > hours_{TB}/hours_{TA}

Combining hours_{TB}/hours_{TA} < W_{A}/(E
x W_{B}) < hours_{SB}/hours_{SA}

Substituting values 3/2 < W_{A}/(E x W_{B}) < 9/4

Dividing yields 1.5 < W_{A}/(E x W_{B}) < 2.25

2. 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. 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 |
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 | ||

S | -1 | 2/3 | -1/3 |

T | 1/2 | -1 | -1/2 |

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 unit of S, while 4 hours are required to produce 1 unit 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) = 4000 (bu/yr)

The intercept on the T axis will be

20000 (hours/year)/4 (hours/yd) = 5000 (yd/yr)

The autarky price (Ps/Pt) = 5/4 = 1.25 (yd/bu).

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

Note that the world relative price is (Ps/Pt) = 2 (yd/bu), the relative price of S. Since A's autarky price is less (1.25 yd/bu), A will export S and import T. It follows that A's imports = 2,000 yd. T. To pay for this, A must export 1,000 bu. S

{ [2000 (yd/yr)] divided by [2 (yd/bu) ]equals 1000 (bu/yr)}

The graph for questions 5 & 6 was drawn on the board in class.

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.

**Suggested answers:**

a. "Developed countries have nothing to gain by trading with developing countries." This statement is generally untrue. When relative prices differ between countries, either developed or developing, a country can be better off by increasing production of its comparative advantage goods and trading for comparative disadvantage goods in its desired consumption bundle. However, when the developing country is very small, free trade will cause its terms of trade to conform to the autarky relative price found in the large developed country. In this case, the developing country gets all the gains from trade.

b. "Developed countries get all the gains from trade when they trade with developing countries because they can dictate their prices to these countries." This is also generally untrue. Gains from trade come about from the exposure to prices that are different from autarky prices. This means that the slope of the ToT differs from that of the PPF. As noted above, in the extreme big country/small country case, the big country's terms of trade do not change and it gets none of the gains from trade. In this case, the developing country receives ALL of the gains from trade. This surprising result is known as "the importance of being unimportant."

c. "The United States can no longer compete in world markets because American wages are too high." This statement is only true in those sectors of the economy where wage gains have exceeded productivity gains. Indeed, the wages in sectors such as aircraft and computers are some of the highest in the USA, and yet these industries are major exporters.

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

Note 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 |
A | B | |

S | hours/bu. S | 4 | 8 |

T | hours/yd. T | 2 | 4 |

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

There is no incentive for trade. America and Britain face the same opportunity costs: in autarky, the relative price of S (Ps/Pt) equals 2 (yd./bu. ).

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.

Country A imports Soybeans and would prefer a lower relative price of S. Country B exports Soybeans and would prefer a higher relative price of S.

11. 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.

P_{SA}= W_{A} (hours_{SA})
= $10(4) = $40

P_{SB}= W_{B} (hours_{SB}) = $5(9) = $45

P_{TA}= W_{A} (hours_{TA})
= $10(2) = $20

P_{TB}= W_{B} (hours_{TB})
= $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?

P_{SA}= W_{A} (hours_{SA})
= $12(4) = $48

P_{SB}= W_{B} (hours_{SB})
= $5(9) = $45

P_{TA}= W_{A} (hours_{TA})
= $12(2) = $24

P_{TB}= W_{B} (hours_{TB})
= $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.

In case 3 we found the limits on the relative wage to be as shown below.

0.20 < W_{A}/(E x W_{B}) < 0.80

If we substitute $10 for W_{A} and solve for (E x W_{B}),
we find

10/0.8 < (E x W_{B}) < 10/0.2

12.50 < (E x W_{B}) <
50

The British wage must lie between $12.50 and $50 per hour for trade to occur along the lines of comparative advantage.

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.

Complete specialization results from the assumption of constant opportunity costs. Once trade opens, a country finds that it can sell its comparative advantage good for more than the cost of production. Further, the cost of producing one more unit never changes until the country reaches complete specialization. Thus it is profitable for the comparative advantage industry to expand until it has absorbed all of the country's resources.

These resources are released from the comparative disadvantage industry. The world price of this good is less than the autarky price. Under perfect competition in autarky, this industry would have earned a zero economic profit. With trade, its profits are negative. Given constant opportunity costs, its marginal cost remains constant even as the industry contracts. Eventually, the industry disappears.

14. 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

Given 10,000 worker-hours, A could produce up to 1,000 bu. S per year, using all of its labor in S. Using all of its labor in T, A could produce up to 500 yd. T per year. Its PPF is linear between these two points.

Now, the scientists in A have doubled labor productivity in producing
__both goods__. This cuts the hours_{XA}
in half. A's PPF shifts out (doubles). A could produce up to 2,000 bu. S per year or
1,000 yd. T per year.

Cut hours_{XA}
in half |
Country |
||

Labor hours per unit of good,
hours |
A | B | |

S | hours/bu. S | 10/2=5 | 8 |

T | hours/yd. T | 20/2=10 | 4 |

What would happen to the pattern of comparative advantage? Derive and explain.

Before the technological gain, B had an absolute advantage in both S and T, but their comparative advantage (greatest absolute advantage) was in T. With the technological progress A will now have an absolute advantage in S. However, the pattern of comparative advantage does not change, because the opportunity costs have not changed. A still has a comparative advantage in S, B still has a comparative advantage in T.

The pretrade relative prices are shown in the table below:

CASE 3 -- Before | Country |
||

(a) Opportunity cost |
A | B | |

S | yd. T/bu. S | 10/20 = 0.5 | 8/4 = 2 |

T | bu. S/yd. T | 2 | 0.5 |

CASE 3 -- After | Country |
||

(a) Opportunity cost |
A | B | |

S | yd. T/bu. S | 5/10 = 0.5 | 8/4 = 2 |

T | bu. S/yd. T | 2 | 0.5 |

15. 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

Given 40,000 worker-hours, A could produce up to 10,000 bu. S per year, using all of its labor in S. Using all of its labor in T, A could produce up to 20,000 yd. T per year. Its PPF is linear between these two points.

Now, the scientists in A have doubled labor productivity in producing
__ good S__. This cuts the hours_{SA} in
half. A's PPF rotates out along the S axis. A could produce up
to 20,000 bu. S per year.

Cut hours_{SA} in half |
Country |
||

Labor hours per unit of good,
hours |
A | B | |

S | hours/bu. S | 4/2=2 | 9 |

T | hours/yd. T | 2 | 3 |

What would happen to the pattern of comparative advantage? Derive and explain.

Before the technological gain, A had an absolute advantage in both S and T, but their comparative advantage (greatest absolute advantage) was in A. The technological progress in their comparative advantage good only strengthens their advantage. The pattern of comparative advantage does not change. A has a comparative advantage in S, B has a comparative advantage in T.

The pretrade relative prices are shown in the table below:

CASE 4-- Before | Country |
||

(a) Opportunity cost |
A | B | |

S | yd. T/bu. S | 4/2 = 2 | 9/3 = 3 |

T | bu. S/yd. T | 0.5 | 1/3 = 0.33 |

CASE 4-- After | Country |
||

(a) Opportunity cost |
A | B | |

S | yd. T/bu. S | 2/2 = 1 | 9/3 = 3 |

T | bu. S/yd. T | 0.5 | 1/3 = 0.33 |