Chapter 16 - International Trade - Problems 3, 4, 5, & 6

Chapter 16 –I recommend working through the problems and calculating the tables by hand and thinking about intuition behind the conclusions. It takes a bit of time to learn how to do this quickly. But once you get it, all you need to do is look at the comparative advantage table (like the table at 16.2) and you should have a pretty good idea of what’ll happen to these economies with free trade.

 Problems 3, 4, 5, & 6 


Solutions Outline

Given population, labor productivities (the table), and preferences and pricing units

Under Autarky:

  1. Find per capita consumption of each good for each country.
  2. Find prices of all products in all countries.
  3. Wages?

Comparative Advantage is when…?

Under Free Trade:

  1. Who has comparative advantage in each good?
  2. When countries specialize, what is the new production of each good in each country? (The pattern of production)
  3. What are the new prices of each good in each country?
  4. New wages for workers in each country?
  5. Find new per capital consumption

Finally, compare these results, production, prices and wages.  



Chapter 16 – Problem 3 – Comparative advantage and trade. 


Solution on page 434. The emphasis on of this question is on the patterns of trade given comparative advantage.



Chapter 16 – Problem 4 – Trade in the apple and computer economy: Consider the apple-computer trade example given in Section 16.5. Now suppose that because of a new technology, the North becomes more productive at producing computers: one unit of labor can now produce 20 computers instead of 16.


(a) Autarky: Redo Table 16.3 to reflect this change. Assume the other parameter values are unchanged. 


Setup of North-South Problem

North

South

Labor Force………………………………………

100

400

Number of apples one worker can produce….

160

100

Number of computers one worker can produce

20

2

Assume that folk spend half their income on apples and half on computers.



North & South Under Autarky

North

South

Wage, w (in apples)

Price of a computer, p

160 apples

8 apples 

100 apples

50 apples 

Consumption of apples (per person)

Consumption of computers (per person)

80 apples 

10 computers 

50 apples 

1 computer  

Fraction of labor working to produce apples

Fraction of labor working to produce computers

All these given

50%

50%

50%

50%

Total production in the apple sector

Total production in the computer sector

8000 apples 

1000 computers 

20000 

400 


If you were in the North (where computers cost only 8 apples) you’d want to buy computers there and sell them in the south (where computers give 50 apples).


You could have rewritten the table above to show that apples are comparatively less expensive in the south – you could take apples from the south and exchange them for relatively more computers in the north.


The North has a comparative advantage in computers and the South a CA in apples. We know this because the computers are cheaper in North and apples are cheaper in South.  




(b) Free trade: Do the same thing for Table 16.4.


North & South Under Free Trade

North

South

Fraction of labor working to produce apples

Fraction of labor working to produce computers

0

100%

100%

0

Total production in the apple sector

Total production in the computer sector

0 apples 

2000 computers 

40000 

0 comps

Wage, w (in apples)

Price of a computer, p

400 apples

 

20 apples 

100 apples 

20 apples 

Consumption of apples (per person)

Consumption of computers (per person)

200 apples 

10 computers 

50 apples 

2.5 computer  




(c) Discuss the differences. How do the gains from trade change? Who benefits from the improvement in technology in the North? 


North – consumption of apples has gone dramatically up. In the south, the consumption of computers has increased.


Also, compared to the free trade example in the book, (see Table 16.4), the better Computer production technology in the North leads to higher computer production compared to without the technology advance.




Chapter 16 – Problem 5 – An improvement in Southern apples: In the same apple-computer trade example given in Section 16.5, suppose that because of a technology transfer, the South becomes just as productive as the North at producing apples: one unit of Southern labor can now produce 160 apples instead of 100.


(a) Autarky: Redo Table 16.3 to reflect this change. Assume the other parameter values are unchanged. 


Setup of North-South Problem

North

South

Labor Force………………………………………

100

400

Number of apples one worker can produce….

160

160

Number of computers one worker can produce

16

2

Assume that folk spend half their income on apples and half on computers.



North & South Under Autarky

North

South

Wage, w (in apples)

Price of a computer, p

160 apples

10 apples 

160 apples

80 apples 

Consumption of apples (per person)

Consumption of computers (per person)

80 apples 

8 computers 

80 apples 

1 computer  

Fraction of labor working to produce apples

Fraction of labor working to produce computers

50%

50%

50%

50%

Total production in the apple sector

Total production in the computer sector

8000 apples 

800 computers 

32000 

400 


The wage in the South has increased from 100 to 160. The price of a computer in the South has increased from 50 to 80 apples. Consumption of apples in the South under Autarky has increased from 50 to 80. And total production of apples in the South has increased from 20000 to 32000 apples.




(b) Free trade: Do the same thing for Table 16.4. 

North & South Under Free Trade

North

South

Fraction of labor working to produce apples

Fraction of labor working to produce computers

0

100%

100%

0

Total production in the apple sector

Total production in the computer sector

0 apples 

1600 computers 

64000 

0 comps

Wage, w (in apples)

Price of a computer, p

640 apples 

 

40 apples 

160 apples 

40 apples 

Consumption of apples (per person)

Consumption of computers (per person)

320 apples 

8 computers 

80 apples 

2 computer  




(c) Discuss the differences. How do the gains from trade change? Who benefits from the improvement in technology in the South?


Under free trade and compared to before the technology transfer (that is, comparing to Table 16.4 in the book), total apple production in the South is increased 64,000. I emboldened all the changed numbers.

The wages has increased in both countries. North gets 120 more apples with 320 – and the same number of computers. South gets an extra 30 apples with 80 – and gets the same number of computers.


The price of a computer has increased in both countries too – since the only change is that South is a bit better at apple production, this implies that computers arerelatively more difficult to produce, and this is reflected in the slightly higher price for computers (the Baumol effect, wikipedia it).  

Economic-Intuition may be drawn from this regarding increases in service-sector prices – with manufacturing productivity increasing more and more with globalization (think: foreign manufacturing purchasing developed country technology), while the service sector innovates at a slower pace, this would imply that with free trade, that service sector prices should become relatively more expensive.




Chapter 16 – Problem 6 – An improvement in Southern computers. Now suppose that the technological innovation occurs in the computer sector in the South: one unit of Southern labor can now produce 10 computers instead of 2. (Other parameters again take their original values).


(a) Does the North still have a comparative advantage in producing computers? If we allow these two economies to trade, will there be any reason for them to trade? Explain. 


Note (in the table just below) that now, North can produce 160 apples or 16 computers with one unit of labor. The South can produce 100 apples and 10 computers with one unit of labor.

To discover if there are gains from trade to be made from comparative advantage, we want to know the relative price of computers   and . If you remember from the book’s example in Table 16.3,  with the lower price in North it meant North had a comparative advantage in the production of computers.


Thus no country has a comparative advantage over the other, and thus there are no gains from trade to be made. Even if both countries specialized in one good or the other, it wouldn’t result in a lower price or increased production. Another way to think about this is to think about arbitrage – if you were an international trader, where before you could buy a computer in North for 10 and resell it in South for 50, earning an easy profit – now computers costs 10 in both countries, you wouldn’t even recoup your transport costs.


Recreating the Tables:

Setup of North-South Problem

North

South

Labor Force………………………………………

100

400

Number of apples one worker can produce….

160

100

Number of computers one worker can produce

16

10

Assume that folk spend half their income on apples and half on computers.



North & South Under Autarky

North

South

Wage, w (in apples)

Price of a computer, p

160 apples

10 apples 

100 apples

10 apples 

Consumption of apples (per person)

Consumption of computers (per person)

80 apples 

8 computers 

50 apples 

5 computers  

Fraction of labor working to produce apples

Fraction of labor working to produce computers

50%

50%

50%

50%

Total production in the apple sector

Total production in the computer sector

8000 apples 

800 computers 

20000 

2000 


North and South Under Free Trade – there is no reason to recreate this table since there will be no free trade.




(b) How does the change affect the North? In particular, compare Northern economic performance before the Southern innovation with Northern economic performance after the innovation. 


To answer this question you want to compare the Table you created above to Table 16.4 on page 419.

If with old arrangement of technologies, the North exported computers to the South, consuming 200 apples and 8 computers. With the new arrangement of technologies we’re effectively returned to autarky, where North gets 80 apples and 8 computers. North is unequivocally worse-off with the South acquisition of better computer production technology. Fie!


The South unambiguously benefits from getting the better computer making technology.




(c) Discuss your findings. What do they mean for the case for free trade? (Be sure to note how the North would fare under autarky.) 


Firstly, regarding free-trade of goods, this doesn’t really make an argument against free-trade. Autarky vs Free Trade: the North is no worse off with free trade, the South is better off. If it happened to be the case that one country had a comparative advantage over the other it would be trivial to prove the advantages of trade.


This models does seem to make the case for preventing the export of technology. If South could somehow have been prevented from acquiring the improved computer production then North would be better off with free trade, however South would be made worse off. This seems to make the argument that countries benefit more from trade the more unlike they are.  


Also to note – the top trading partners of developed countries (US, Eurozone, Japan) tend to be other developed economies. Suggesting that there are large benefits from trade between similar countries that are simply not captured in this model of international trade (see Paul Krugman’s Nobel winning models).




Comments