Chapter 3, Problem 2PA

Subpart (a):

To determine

Calculate the member of required labor.

Explanation of Solution

Number of workers required to produce one unit of goods can be calculated using the following formula.

$\text{Required labor}=\frac{1}{\text{Total production per person}}$ (1)

Substitute the respective values in Equation (1) to calculate the required number of person to produce one unit of car in U.S.

$\begin{array}{c}\text{Required labor}=\frac{1}{\text{4}}\\ =0.25\end{array}$

Required labor to produce one unit of car in U.S. is 0.25.

Table 1 illustrates the workers required to produce a car and a ton of grain in the U.S. and the Japan that obtained by using Equation (1).

Table 1

	Workers required to produce
	One Car	One Ton of Grain
U.S.	0.25 workers	0.10 workers
Japan	0.25 workers	0.20 workers

Economics Concept Introduction

Concept introduction:

Production Possibility Frontier (PPF): PPF refers to the maximum possible combinations of output of goods or services that an economy can attain by efficiently utilizing and employing full resources.

Subpart (b):

To determine

Draw the production possibility frontier.

Explanation of Solution

Figure 1 shows the productive capacity of two countries.

In Figure 1, the horizontal axis measures the quantity of grains produced by both the countries and the vertical axis measures the quantity of cars produced. If either economy, that is, the U.S. or Japan devotes all of its 100 million workers in producing cars each economy can produce 400 million cars in a year $(=4\times 100\text{)}$, and it is the vertical intercept of the production possibilities frontier for both Japan and the U.S. If the U.S. or the Japan devotes all of its 100 million workers in production of grains, then the U.S. can produce 1,000 million tons of grains $(=100\times 10)$ in a year; whereas Japan can produce only 500 million tons of grains per year $(=5\times 100)$, which are the horizontal intercepts of the PPF for the U.S. and Japan, respectively. Since the opportunity costs remain constant throughout, the production possibilities frontiers are in a straight line.

Economics Concept Introduction

Concept introduction:

Production Possibility Frontier (PPF): PPF refers to the maximum possible combinations of output of goods or services that an economy can attain by efficiently utilizing and employing full resources.

Subpart (c):

To determine

Calculate the opportunity cost.

Explanation of Solution

Opportunity cost of a car for the U.S. is calculated as follows.

$\begin{array}{c}{\text{Opportunity cost of a car}}_{\text{US}}\text{ =}\frac{{\text{Cost of producing grain}}_{\text{U}\text{.S}\text{.}}}{{\text{Cost of producing car}}_{\text{U}\text{.S}\text{.}}}\\ =\frac{10}{4}\\ =2.5\text{ tons of grains}\end{array}$

Thus, the opportunity cost of a car for the U.S. is 2.5 tons of grains.

Opportunity cost of a car for Japan is calculated as follows.

$\begin{array}{c}{\text{Opportunity cost of a car}}_{\text{Japan}}\text{ =}\frac{{\text{Cost of producing grain}}_{\text{Japan}}}{{\text{Cost of producing car}}_{\text{Japan}}}\\ =\frac{5}{4}\\ =1.25\text{ tons of grains}\end{array}$

Thus, the opportunity cost of a car for Japan is 1.25 tons of grains.

Opportunity cost of producing a ton of grains in the U.S. is calculated as follows

$\begin{array}{c}{\text{Opportunity cost of a ton of grains}}_{\text{US}}\text{ =}\frac{{\text{Cost of producing car}}_{\text{U}\text{.S}\text{.}}}{{\text{Cost of producing grain}}_{\text{U}\text{.S}\text{.}}}\\ =\frac{4}{10}\\ =0.4\text{ cars}\end{array}$

Thus, the opportunity cost of producing a ton of grains in the U.S. is 0.4 units of cars.

Opportunity cost of producing a ton of grains in Japan is calculated as follows.

$\begin{array}{c}{\text{Opportunity cost of a ton of grains}}_{\text{Japan}}\text{ =}\frac{{\text{Cost of producing car}}_{\text{Japan}}}{{\text{Cost of producing grain}}_{\text{Japan}}}\\ =\frac{4}{5}\\ =0.8\text{ cars}\end{array}$

Thus, the opportunity cost of producing a ton of grains in Japan is 0.8 units of cars.

The results can be tabulated in Table 2 below.

Table 2

	Opportunity Cost
	One Car	One Ton of Grain
U.S.	2.5 tons of grains	0.4 units of car
Japan	1.25 tons of grains	0.8 units of car

Economics Concept Introduction

Concept introduction:

Opportunity cost: Opportunity cost is the cost of a foregone alternative, that is, the loss of other alternative when one alternative is chosen.

Subpart (d):

To determine

Find the country that has absolute advantage in the production of goods.

Explanation of Solution

Neither of these countries has an absolute advantage in producing cars. This is because they are equally productive in the production of a car (4 cars per worker per year). However, in the production of grains, the United States has an absolute advantage because it is more productive than Japan. The U.S. can produce 10 tons of grains per worker per year; whereas Japan can produce only 5 tons of grains per worker per year.

Economics Concept Introduction

Concept introduction:

Absolute advantage: It is the ability to produce a good using fewer inputs than another producer.

Subpart (e):

To determine

Find the country that has absolute advantage in the production of goods.

Explanation of Solution

Japan has a comparative advantage in producing cars because it has a lower opportunity cost in terms of given up grains(1.25 tons of grains for one car) compared to the U.S. (2.5 tons of grains for one car). Similarly, the United States has a comparative advantage in producing grain, because it has a lower opportunity cost in terms of given up cars (0.4 units of cars for a ton of grains).

Economics Concept Introduction

Concept introduction:

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

Subpart (f):

To determine

Calculate the total production before the trade.

Explanation of Solution

Without trade and with half the workers in each country producing each of the goods, the United States would produce 200 million cars $(50\times 4)$ and 500 million tons of grain $(50\times 10)$. Japan would produce 200 million cars $(50\times 4)$ and 250 million tons of grain $(50\times 5)$.

Economics Concept Introduction

Concept introduction:

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

Subpart (g):

To determine

Gains from trade for the U.S. and Japan.

Explanation of Solution

Firstly, consider the situation without trade in which each country is producing some cars and some grains. Suppose the United States shifts its one worker from producing cars to producing grain, then that worker would produce 4 cars and 10 additional tons of grain. Now suppose, with trade, the United States offers to trade 7 tons of grain to Japan for 4 cars. The United States would encourage this because the cost of producing 4 cars in the United States is 10 tons of grain. So by trading, the United States can gain 4 cars for a cost of only 7 tons of grain. Hence, it is better off by 3 tons of grain.

The same is applicable for Japan, if Japan changes one worker from producing grain to producing cars. That worker would produce 4 more cars and 5 fewer tons of grain. Japan will take the trade because Japan will be better off by 2 tons of grain.

So with the trade and the change of one worker in both the United States and Japan, each country gets the same amount of cars as before but gets additional tons of grain (3 tons of grains for the United States and 2 tons of grains for Japan) making both countries better off.

Economics Concept Introduction

Concept introduction:

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