Production

The production functions in Table 2.4 "Production of Cheese" and Table

2.5 "Production of Wine"represent industry production, not firm

production. The industry consists of many small firms in light of the

assumption of perfect competition.

Table 2.4 Production of Cheese

United States France

QC=LCaLC[hrs][hrslb] Q∗C=L∗Ca∗LCwhere

QC = quantity of cheese produced in the United States

LC = amount of labor applied to cheese production in the United States

aLC = unit labor requirement in cheese production in the United States (hours of labor

necessary to produce one unit of cheese)

∗All starred variables are defined in the same way but refer to the process in France.

Table 2.5 Production of Wine

United States France

QW=LWaLW[hrs][hrsgal] Q∗W=L∗Wa∗LWwhere

QW = quantity of wine produced in the United States

LW = amount of labor applied to wine production in the United States

aLW = unit labor requirement in wine production in the United States (hours of labor

necessary to produce one unit of wine)

United States France

∗All starred variables are defined in the same way but refer to the process in France.

The unit labor requirements define the technology of production in two

countries. Differences in these labor costs across countries represent

differences in technology.

Resource Constraint

The resource constraint in this model is also a labor constraint since

labor is the only factor of production (see Table 2.6 "Labor Constraints").

Table 2.6 Labor Constraints

United States France

LC + LW = L LC∗ + LW∗ = L∗where

L = the labor endowment in the United States (the total number of hours the workforce

is willing to provide)

When the resource constraint holds with equality, it implies that the

resource is fully employed. A more general specification of the model

would require only that the sum of labor applied in both industries be

less than or equal to the labor endowment. However, the assumptions of

the model will guarantee that production uses all available resources,

and so we can use the less general specification with the equal sign.

Questions on Comparative Advantage

The following questions were modelled on those in John Taylor, Principles of Microeconomics , chapter 18. Numbers have often been modified.

1. Labor productivity coefficients for the US and Mexico are given in the following table:

Country Corn Melons Labor Endowment

United States 5 2 1000

Mexico 1 1 1000

Note that this means that in the US,

Qx = 5 Lx

with Good X being corn, and

Qy = 2 Ly

with good Y being melons.

Questions:

a. Who has the absolute advantage in corn? in melons?b. Who has a comparative advantage in corn? in melons? Explain any

differences from your previous answer.c. What are the limits on relative price after trade opens between the two

countries?d. Suppose after trade the actual relative price is 2 melons for 3 bushel of

corn. Draw Production Possibility Frontiers and Trading Possibility Frontiers for the two countries.

Answer to question 1.

Answer to Comparative Advantage Question 1

a. Absolute advantage goes to the more productive country. The US therefore has an absolute advantage in both corn and melons.

b. Comparative advantage goes to the low opportunity cost producer. The opportunity cost of corn in the US is 2/5 melon. To produce a bushel of corn, we require 1/5 of a unit of labor, and 1/5 of a unit of labor could have produced 2/5 melon. You should be able to show that the opportunity cost of a melon in the US is 5/2 bushel of corn.

In Mexico, the opportunity cost of corn is 1 melon -- and the opportunity cost of a melon is 1 bushel of corn. One worker could have produced either good.

The US is therefore the low opportunity cost producer of corn (2/5 < 1) and Mexico the low opportunity cost producer of melons (1 < 5/2)

c. Price ratios after trade must lie between the Mexican and US pre-trade price ratios or relative prices. In Mexico before trade, 1 worker could produce either 1 bushel of corn or one melon; the Mexican price ratio would therefore be Px/Py = 1.

In the US, the activity requirement for corn was 1/5; the price of corn would therefore have been (at a minimum) (1/5) w. The activity requirement for melons is 1/2, so the US price of melons would have been (1/2) w (at a minimum). The US price ratio is therefore

Px/Py = (1/5) / (1/2) = 2/5.

Prices reflect opportunity costs in both the US and Mexico. The price ratio after trade must therefore lie between 2/5 and 1.

We assume a price ratio of 2/3, which does lie between 2/5 and 1. To draw the PPF, we must calculate the maximum possible production of corn and melons in the US and in Mexico.

Maximum outputsCountry Corn Melons

United States 5000 2000Mexico 1000 1000

After trade, the United States will specialize in corn and Mexico in melons. At the assumed relative price of 2/3, each US bushel of corn buys 2/3 of a melon. The whole 5000 bushels of US corn would therefore buy 10,000/3 = 3,333.33 melons -- beyond American production possibilities of 2000 melons.

Note: you might be worried that this is beyond Mexican production possibilities, too. If the US actually tried to buy more melons than Mexico produced, the price of Mexican melons would rise. The difficulty here comes

because we are simply assuming an international price for melons which might not be sustainable in the market. But before we can deal with the difficulty, we will have to turn to the study of how markets operate.

Each Mexican melon would buy 3/2 of a bushel of corn. The whole 1000 Mexican melons would therefore buy 1,500 bushels of corn -- beyond Mexican production possibilities.

Remember that Mexico was at an absolute disadvantage in the production of both goods. Nevertheless, her Trading Possibility Frontier does indicate that Mexico has more choices after trade than before trade.

2. Labor productivity coefficients for the US and Brazil are given by the following table:

Country Wheat Clothing Labor Endowment

United States 2 8 100

Brazil 1 2 120

Questions:

a. Who has the absolute advantage in which good?b. What is the opportunity cost of wheat in the US? in Brazil?c. What is the opportunity cost of clothing in the US? in Brazil?d. Who has the comparative advantage in which good?e. What are the limits of the post-trade relative price of wheat?f. Suppose the actual post-trade relative price of wheat to clothing is 3. Draw

the pre- and post-trade PPF and TPF. Who gains from trade?

Answer   to question 2.

Comparative Advantage Qu. 2 - Answer

a. The United States has the absolute advantage in both goods. One US worker produces 2 bushels of wheat, compared to the Brazilian worker's one; one US worker produces 8 units of clothing compared to the Brazilian worker's two.

b. The opportunity cost of a bushel of wheat in the US is 4 units of clothing; the opportunity cost of a bushel of wheat in Brazil is only 2 units of clothing. Brazil is

therefore the low opportunity cost producer of wheat, and after trade would be expected to specialize in wheat.

c. The opportunity cost of a unit of clothing in the US is 1/4 bushel of wheat; in Brazil it is 1/2 bushel. The US is the low opportunity cost producer of clothing.

d. Comparative advantage goes to the low opportunity cost producer. Brazil has the comparative advantage in wheat and the US in clothing.

e. Autarky price ratios will reflect opportunity costs and therefore Px/Py will be 4 in the US and 2 in Brazil before trade. After trade, the world relative prices will settle somewhere between 2 and 4.

f. To construct PPFs, we must find the maximum possible outputs. They are given by the following table:

Maximum output of

Country Wheat Clothing

United States 200 800

Brazil 120 240

After trade, with a price of wheat relative to clothing of 3, the US will specialize in clothing and its 1600 units of clothing will purchase 1600/3 units of wheat or 533.33 units of wheat -- more than it could have produced itself before trade.

Brazil will specialize in wheat, and its 120 units of wheat will purchase up to 360 units of clothing -- more than the 240 it could have produced itself before trade.