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Math  /  Data & Statistics

QuestionToble 3-11 Assume that Jamaica and Norway can switch between producing coolers and producing radios at a constant rate. Output Produced in One Day \begin{tabular}{|l|c|c|} \hline & Coolers & Radios \\ \hline Jamaica & 12 & 6 \\ \hline Norway & 24 & 3 \\ \hline \end{tabular}
Refer to Table 3-11. Assume that Jamaica and Norway each has 4 days available for production. Originally, each country divided its time equally between the production of coolers and radios. Now, each country spends all its time producing the good in which it has a comparative advantage. As a result, the total output of radios increased by a. 12 . b. 9 . c. 6. d. 3 .

Studdy Solution

STEP 1

1. Jamaica and Norway can switch between producing coolers and radios at a constant rate.
2. Each country has 4 days available for production.
3. Initially, each country divides its time equally between the production of coolers and radios.
4. Comparative advantage will determine which good each country will specialize in.
5. Jamaica produces 12 coolers or 6 radios per day.
6. Norway produces 24 coolers or 3 radios per day.
7. We need to determine the increase in the total output of radios when each country specializes according to their comparative advantage.

STEP 2

1. Calculate initial production when each country splits their time equally.
2. Determine which good each country has a comparative advantage in.
3. Calculate production when each country specializes in the good in which they have a comparative advantage.
4. Compare the total output of radios before and after specialization and determine the increase.

STEP 3

Calculate the initial production for Jamaica when it splits its 4 days equally between coolers and radios.
Days spent on each good=42=2 days\text{Days spent on each good} = \frac{4}{2} = 2 \text{ days}
Coolers produced by Jamaica=2 days×12 coolers/day=24 coolers\text{Coolers produced by Jamaica} = 2 \text{ days} \times 12 \text{ coolers/day} = 24 \text{ coolers}
Radios produced by Jamaica=2 days×6 radios/day=12 radios\text{Radios produced by Jamaica} = 2 \text{ days} \times 6 \text{ radios/day} = 12 \text{ radios}

STEP 4

Calculate the initial production for Norway when it splits its 4 days equally between coolers and radios.
Days spent on each good=42=2 days\text{Days spent on each good} = \frac{4}{2} = 2 \text{ days}
Coolers produced by Norway=2 days×24 coolers/day=48 coolers\text{Coolers produced by Norway} = 2 \text{ days} \times 24 \text{ coolers/day} = 48 \text{ coolers}
Radios produced by Norway=2 days×3 radios/day=6 radios\text{Radios produced by Norway} = 2 \text{ days} \times 3 \text{ radios/day} = 6 \text{ radios}

STEP 5

Determine the opportunity cost of producing coolers and radios for each country to find the comparative advantage.
Opportunity cost of 1 cooler in Jamaica=6 radios12 coolers=0.5 radios\text{Opportunity cost of 1 cooler in Jamaica} = \frac{6 \text{ radios}}{12 \text{ coolers}} = 0.5 \text{ radios}
Opportunity cost of 1 radio in Jamaica=12 coolers6 radios=2 coolers\text{Opportunity cost of 1 radio in Jamaica} = \frac{12 \text{ coolers}}{6 \text{ radios}} = 2 \text{ coolers}
Opportunity cost of 1 cooler in Norway=3 radios24 coolers=0.125 radios\text{Opportunity cost of 1 cooler in Norway} = \frac{3 \text{ radios}}{24 \text{ coolers}} = 0.125 \text{ radios}
Opportunity cost of 1 radio in Norway=24 coolers3 radios=8 coolers\text{Opportunity cost of 1 radio in Norway} = \frac{24 \text{ coolers}}{3 \text{ radios}} = 8 \text{ coolers}

STEP 6

Determine which good each country has a comparative advantage in.
Jamaica’s opportunity cost of 1 radio(=2 coolers)<Norway’s opportunity cost of 1 radio(=8 coolers)\text{Jamaica's opportunity cost of 1 radio} ( = 2 \text{ coolers}) < \text{Norway's opportunity cost of 1 radio} ( = 8 \text{ coolers})
Jamaica has a comparative advantage in producing radios.\text{Jamaica has a comparative advantage in producing radios.}
Norway’s opportunity cost of 1 cooler(=0.125 radios)<Jamaica’s opportunity cost of 1 cooler(=0.5 radios)\text{Norway's opportunity cost of 1 cooler} ( = 0.125 \text{ radios}) < \text{Jamaica's opportunity cost of 1 cooler} ( = 0.5 \text{ radios})
Norway has a comparative advantage in producing coolers.\text{Norway has a comparative advantage in producing coolers.}

STEP 7

Calculate the production when Jamaica specializes in radios (4 days) and Norway specializes in coolers (4 days).
Radios produced by Jamaica=4 days×6 radios/day=24 radios\text{Radios produced by Jamaica} = 4 \text{ days} \times 6 \text{ radios/day} = 24 \text{ radios}
Coolers produced by Norway=4 days×24 coolers/day=96 coolers\text{Coolers produced by Norway} = 4 \text{ days} \times 24 \text{ coolers/day} = 96 \text{ coolers}

STEP 8

Calculate the total output of radios before and after specialization and determine the increase.
Initial total output of radios=12 radios (Jamaica)+6 radios (Norway)=18 radios\text{Initial total output of radios} = 12 \text{ radios (Jamaica)} + 6 \text{ radios (Norway)} = 18 \text{ radios}
Total output of radios after specialization=24 radios (Jamaica)+0 radios (Norway)=24 radios\text{Total output of radios after specialization} = 24 \text{ radios (Jamaica)} + 0 \text{ radios (Norway)} = 24 \text{ radios}
Increase in total output of radios=24 radios−18 radios=6 radios\text{Increase in total output of radios} = 24 \text{ radios} - 18 \text{ radios} = 6 \text{ radios}
The total output of radios increased by 6\boxed{6}.

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