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Sem 5 Prep
← Intl TradeThe law of comparative advantage

Formulas for this chapter

Opportunity cost from a productivity table

OC of one unit of X = (output of Y per hour) / (output of X per hour)

Whenever a table gives output per labour hour for two goods. The nation with the lower opportunity cost of a good has the comparative advantage in it.

Output of X per hour
The good whose opportunity cost you want
Output of Y per hour
The good given up, in the same country

Opportunity cost as a relative price

P(X) / P(Y) = opportunity cost of X in terms of Y

Under constant costs, and given that prices equal costs and the nation produces both goods. It is also the absolute slope of the production possibility frontier, the marginal rate of transformation.

P(X) / P(Y)
Relative commodity price of X
Slope
Absolute slope of the transformation curve, constant under constant costs

Range of mutually beneficial trade

exporter's domestic ratio < traded block < importer's domestic ratio (class example: 4C < 6W < 12C)

Whenever a question asks for the limits of trade, or whether a stated exchange is acceptable to both nations. Compute each bound from that nation's own productivities.

Lower bound
What the exporting nation could get for the block at home
Upper bound
What the block would cost the importing nation at home

Total gain and its split

Total gain = upper bound - lower bound Exporter's gain = terms - lower bound Importer's gain = upper bound - terms

Once the range is known. The two gains always add to the total, which is the check. The midpoint of the range splits the gain equally.

Terms
The agreed exchange, in units of the good given for the traded block
Total gain
The width of the range, in units of the second good

Labour-time saving, restated in goods

Gain in goods = hours saved x own output per hour of the good you measure in

When the class asks for the gain in cloth rather than in hours. The United Kingdom saves 3 hours at 2 yards per hour, which is 6 yards.

Hours saved
Home cost of the import minus the cost of the export, in hours
Own output per hour
Productivity in whichever good the answer is to be stated in
Step 4 of 28
The real wordsTheory

Finding the smaller absolute disadvantage

Compare the United Kingdom with the United States good by good.

  • Wheat: 1 against 6. The United Kingdom is six times less productive, a ratio of 1:6
  • Cloth: 2 against 4. The United Kingdom is only half as productive, a ratio of 2:4

2:4 is a smaller disadvantage than 1:6, so the United Kingdom's comparative advantage is cloth.

Mirror image for the United States: it is 6:1 better at wheat and only 4:2 better at cloth, so its comparative advantage is wheat.

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