Chapter 15, Problem 1SQP

(a):

To determine

Opportunity cost of producing diamonds.

Explanation of Solution

The opportunity cost of producing a commodity can be calculated by dividing the total quantity of Pearls lost with the Diamonds gained for the country. Country A produces either 150 tons of Diamonds or 75 ton of Pearls. Thus, the opportunity cost can be calculated as follows:

$\begin{array}{c}\text{Opportunity cost}=\frac{\text{Quantity of Pearls lost}}{\text{Quantity of Diamonds gained}}\\ =\frac{75}{150}\\ =\frac{1}{2}\end{array}$

Therefore, the opportunity cost of producing a ton of Diamond is $\frac{1}{2}$ tons of Pearls in Country A. Similarly, Country B can produce either 90 tons of Diamonds or 180 tons of Pearls. Thus, the opportunity cost of producing Diamonds for Country B can be calculated as follows:

$\begin{array}{c}{\text{Opportunity cost}}_{\text{B}}=\frac{\text{Quantity of Pearls lost}}{\text{Quantity of Diamonds gained}}\\ =\frac{180}{90}\\ =2\end{array}$

Thus, the opportunity cost of producing a ton of Diamond for Country B is equal to 2 tons of Pearls.

Economics Concept Introduction

Opportunity cost: Opportunity cost is the cost of the next best alternatives that is foregone while making the choices. When the resources are used for the production of Commodity A, Commodity B that could be made with that same quantity of resource will be the opportunity cost.

(b):

To determine

Opportunity cost of producing Pearls.

Explanation of Solution

The opportunity cost of producing Pearl can be calculated by dividing the total quantity of Diamonds lost with the Pearls gained for the country. Country A produces either 150 tons of Diamonds or 75 ton of Pearl. Thus, the opportunity cost can be calculated as follows:

$\begin{array}{c}\text{Opportunity cost}=\frac{\text{Quantity of Diamonds lost}}{\text{Quantity of Pearls gained}}\\ =\frac{150}{75}\\ =2\end{array}$

Therefore, the opportunity cost of producing a ton of Pearl is 2 tons of Pearls in Country A. Similarly, Country B can produce either 90 tons of Diamonds or 180 tons of Pearls. Thus, the opportunity cost of producing Pearl for B can be calculated as follows:

$\begin{array}{c}{\text{Opportunity cost}}_{\text{B}}=\frac{\text{Quantity of Diamonds lost}}{\text{Quantity of Pearls gained}}\\ =\frac{90}{180}\\ =\frac{1}{2}\end{array}$

Thus, the opportunity cost of producing a ton of Pearl for Country B is equal to $\frac{1}{2}$ tons of Diamonds.

(c):

To determine

Commodity in which A has a comparative advantage.

Explanation of Solution

The absolute advantage is the ability of the country to produce the commodity or service by a country using the same or fewer resources than the other countries. The comparative advantage is the advantage to produce a commodity at a lower opportunity cost than the other countries.

In the case of Country A, the opportunity cost of producing a ton of Diamond is $\frac{1}{2}$ tons of Pearls whereas the opportunity cost of producing a ton of Pearl is 2 tons of Diamonds. Country B can produce a ton of Diamonds with an opportunity cost of 2 tons of Pearl and Pearl at an opportunity cost of $\frac{1}{2}$ tons of Diamonds. Thus, Country A could produce Diamonds at a lower opportunity cost than Country B. Hence, Country A has comparative advantage in the production of Diamonds.

(d):

To determine

Commodity in which Country B has a comparative advantage.

Explanation of Solution

In the case of Country A, the opportunity cost of producing a ton of Diamond is $\frac{1}{2}$ tons of Pearls whereas the opportunity cost of producing a ton of Pearl is 2 tons of Diamonds. Country B can produce a ton of Diamonds with an opportunity cost of 2 tons of Pearl and Pearl at an opportunity cost of $\frac{1}{2}$ tons of Diamonds.

From this, it can be identified that Country B could produce Pearls at a lower opportunity cost than Country A. This indicates that Country B has comparative advantage in the production of Pearls.

(e):

To determine

Benefit of specialization.

Explanation of Solution

Country A is in its PPC Curve B where it produces 100 tons of Diamonds and 25 tons of Pearls. Country B is on its PPC curve C where it produces 30 tons of Diamonds and 120 tons of Pearls. Thus, the total output is 130 tons of Diamonds and 145 tons of Pearls. When the country specializes, Country A produces only Diamonds, which is 150 tons and B produces only Pearls, which is 180 tons. Thus, the total output increases due to specialization by 20 tons of Diamonds and 35 tons of Pearls. This can be illustrated in a table as follows:

	Diamonds (in tons per year)	Pearls (In tons per year)
Before Specialization
A (PPC point at B)	100	25
B (PP C point at C)	30	120
Total Output	130	145
After Specialization
A (PPC point at A)	150	0
B (PP C point at D)	0	180
Total Output	150	180

Thus, the total output of Diamonds and Pearls increases as the economy specializes in the production of commodities in which they have comparative advantages.

(f):

To determine

Graphical representation of specialization and trade benefit for the countries.

Explanation of Solution

When there is no specialization and trade between A and B, Country A operates at PPC point B where it produces and consumes 100 tons of Diamonds and 25 tons of Pearls. The case with Country B is different and it operates at Point C of the PPC where it produces and consumes 30 tons of Diamonds and 120 tons of Pearls. When the country specializes, Country A produces 150 tons of Diamonds and Country B produces 180 tons of pearls.

When the trade takes place, Country A trades 50 tons of Diamonds in exchange for 50 tons of Pearls with Country B. This means that Country A is able to consume 100 tons of Diamonds and 50 tons of Pearl whereas Country B is able to consume 50 tons of Diamonds and 130 tons of Pearls. Thus, both countries are able to achieve a consumption point beyond their PPC which can be illustrated as follows: