Chapter 3, Problem 8PA

Subpart (a):

To determine

The production possibility frontier.

Explanation of Solution

Figure -1 illustrates production possibility frontier.

Figure 1 shows the production possibilities frontiers for the two countries; U.S. and China. In Figure 1, the horizontal axis measures the quantity of shirts produced by both the countries and the vertical axis measures the quantity of computers produced. If either worker of the two countries, that is an American or a Chinese worker devotes all his labor hours in producing shirts, each worker can produce 100 shirts in a year. Then, it is the vertical intercept of the PPF for both the American and the Chinese worker. If they devote all of their time to the production of computers, then the U.S. worker can produce 20 computers in a year, while the Chinese worker can produce only 10 computers per year. These are the horizontal intercepts of the PPF for the U.S. and the Chinese worker, respectively. Since the opportunity costs remain constant throughout, the production possibilities frontiers are a straight line. Without trade, the workers in each country spend half their time producing each good, then the United States will have 50 shirts and 10 computers and China will have 50 shirts and 5 computers.

Economics Concept Introduction

Concept introduction:

Production possibility frontier (PPF): PPF is a curve depicting all maximum output possibilities for two goods, given a set of inputs consisting of resources and other factors.

Subpart (b):

To determine

Opportunity cost and price of the good.

Explanation of Solution

To determine the export pattern of shirts, the comparative advantage is to be known (which is based on opportunity cost).

Opportunity cost of shirts in the U.S. is calculated as,

$\begin{array}{c}{\text{Opportunity cost shirt}}_{\text{U}\text{.S}\text{.}}=\frac{\text{Cost of computers produced per hour}}{\text{Cost of shirts produced per hour}}\\ =\frac{20}{100}\\ =0.2\text{ computers}\end{array}$

Thus, the price of 1 shirt in the U.S. is 0.2 computers.

Opportunity cost of shirts in China is calculated as,

$\begin{array}{c}{\text{Opportunity cost shirt}}_{\text{China}}=\frac{\text{Cost of computers produced per hour}}{\text{Cost of shirts produced per hour}}\\ =\frac{10}{100}\\ =0.1\text{ computers}\end{array}$

Thus, the price of 1 shirt in China is 0.1 computers.

Since China has a lower opportunity cost of shirts, China has a comparative advantage in its production. So, China will produce and export shirts to the U.S. in exchange for computers from the U.S. since the latter has a comparative advantage in the production of computers (5 shirts $(100/20)$).

The range of prices of shirts at which trade can occur is between 0.1 and 0.2 computers, per computer.

An example would be a price of 0.15 computers. Suppose China produced only shirts (100 shirts) and exported 50 shirts in exchange for 7.5 $(50\times 0.15)$ computers. This would make China better off than before trade, as China could only produce 50 shirts and 5 computers without trade.

The United States is also benefited from this trade. Suppose American workers produced only computers (20 computers) and traded 7.5 of computers to China for 50 shirts. The U.S. would have 12.5 (20-7.5) computers and 50 shirts. Thus, the U.S. would be better off than before trade (10 computers and 50 shirts).

Economics Concept Introduction

Concept introduction:

Production possibility frontier (PPF): PPF is a curve depicting all maximum output possibilities for two goods, given a set of inputs consisting of resources and other factors.

Opportunity cost: Opportunity cost is the cost of foregone alternative, that is, loss of an alternative when another alternative is chosen.

Comparative advantage: It refers to the ability to produce a good at a lower opportunity   cost than another producer.

Subpart (c):

To determine

Opportunity cost and price of the good.

Explanation of Solution

For the calculation of price, the calculation of opportunity cost is required.

Opportunity cost of a computer in the U.S. is calculated as,

$\begin{array}{c}{\text{Opportunity cost computer}}_{\text{U}\text{.S}\text{.}}=\frac{\text{Cost of shirts produced per hour}}{\text{Cost of computer produced per hour}}\\ =\frac{100}{20}\\ =5\text{ shirts}\end{array}$

Thus, the price of 1 computer in the U.S. is 5 shirts.

Opportunity cost of a computer in China is calculated as,

$\begin{array}{c}{\text{Opportunity cost computer}}_{\text{China}}=\frac{\text{Cost of shirts produced per hour}}{\text{Cost of computer produced per hour}}\\ =\frac{100}{10}\\ =10\text{ shirts}\end{array}$

Thus, the price of 1 computer in China is 10 shirts.

The range of prices of computers at which trade can occur is between 5 and 10 shirts per computer. This is because, at a price lower than 5 shirts, the U.S. will choose to produce its own shirts and will be unwilling to export computers, as the opportunity cost of a shirt for the U.S. is 0.2 $(1/5)$ computers. Likewise, at a price higher than 10 shirts per computer, China will choose to produce its own computers and will be unwilling to import computers, as the opportunity cost of a computer is 10 shirts for China.

Economics Concept Introduction

Concept introduction:

Production possibility frontier (PPF): PPF is a curve depicting all maximum output possibilities for two goods, given a set of inputs consisting of resources and other factors.

Opportunity cost: Opportunity cost is the cost of foregone alternative, that is, loss of an alternative when another alternative is chosen.

Comparative advantage: It refers to the ability to produce a good at a lower opportunity   cost than another producer.

Subpart (d):

To determine

Gains from the trade.

Explanation of Solution

Gains from trade are based on comparative advantage, which is based on opportunity cost. To gain from trade, one of the producers must have comparative advantage in the production of a good. When China produces the same amount of goods as the U.S., the productivity of both the countries remains the same. Hence, the opportunity cost remains the same. In such an instance, neither country would have comparative advantage in the production of both computers and shirts. This implies that there will be no gain from trade available for both the countries.

Economics Concept Introduction

Concept introduction:

Specialization: Specialization refers to allocate the work according to their efficiency. If an individual, company or country has produced a good at lower opportunity cost, then that particular individual, company or country should produce those goods.

Trade: The trade refers to the exchange of capital, goods, and services across different countries.