To determine the slopes of the production possibilities frontiers (PPFs) for England and Spain, we need to calculate how many units of bread can be sacrificed to produce one additional unit of cheese. This will give us the opportunity cost of producing cheese in terms of bread for each country.
England:
- Labor Hours for Cheese: 2 hours
- Labor Hours for Bread: 3 hours
- Units Produced in 24 Hours:
- Cheese: 12 units
- Bread: 8 units
Opportunity Cost of Producing Cheese (England):
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For every cheese (which takes 2 hours) produced, England would sacrifice spending those 2 hours producing bread.
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In 2 hours, England can produce: \[ \text{Bread produced in 2 hours} = \frac{2 \text{ hours}}{3 \text{ hours/unit}} = \frac{2}{3} \text{ units of bread} \] Thus, the opportunity cost of 1 cheese is \(\frac{2}{3}\) units of bread.
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Therefore, the slope of England’s PPF (rise/run) is: \[ \text{Slope (England)} = -\frac{2/3}{1} = -\frac{2}{3} \]
Spain:
- Labor Hours for Cheese: 3 hours
- Labor Hours for Bread: 6 hours
- Units Produced in 24 Hours:
- Cheese: 8 units
- Bread: 4 units
Opportunity Cost of Producing Cheese (Spain):
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For every cheese (which takes 3 hours), Spain would sacrifice spending those 3 hours producing bread.
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In 3 hours, Spain can produce: \[ \text{Bread produced in 3 hours} = \frac{3 \text{ hours}}{6 \text{ hours/unit}} = \frac{1}{2} \text{ units of bread} \] Thus, the opportunity cost of 1 cheese is \(\frac{1}{2}\) units of bread.
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Therefore, the slope of Spain’s PPF is: \[ \text{Slope (Spain)} = -\frac{1/2}{1} = -\frac{1}{2} \]
Final Slopes
- Slope of England's PPF: \(-\frac{2}{3}\)
- Slope of Spain's PPF: \(-\frac{1}{2}\)
Conclusion:
The correct answer is: d. the slope of England’s production possibilities frontier would be -0.67 and the slope of Spain’s production possibilities frontier would be -0.5.
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