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An economy has three workers: Larry, Moe, and Curly. Each works 10 hours a day a...

Mar 25, 2024

An economy has three workers: Larry, Moe, and Curly. Each works 10 hours a day and can produce 2 services: mowing lawns and washing cars. In an hour, Larry can either mow 1 lawn or wash 1 car; Moe can either mow 1 lawn or wash 2 cars; and Curly can either mow 2 lawns or wash 1 car. 1)Calculate how much of each service is produced under the following circumstances, which we label A, B, C, and D: •All three spend all their time mowing lawns. Point A •All three spend all their time washing cars. Point B •All three spend half their time on each activity. Point C •Larry spends half his time on each activity, while Moe only washes cars and Curly only mows laws. Point D 2) Graph the production possibilities frontier for this economy. Using your answers to 1), identify points A,B,C, and D on your graph. 3) Explain why the production possibilities frontier has the shape it does. 4) Are any of the allocations calculated in part 1) inefficient? Explain.

Answer

For point A, 30 lawns are mowed; for point B, 40 cars are washed; for point C, 15 lawns are mowed and 20 cars are washed; for point D, 25 lawns are mowed and 20 cars are washed.

Solution

Calculation for Point A: All three workers mow lawns

Larry mows 10 lawns (10 hours * 1 lawn/hour), Moe mows 10 lawns (10 hours * 1 lawn/hour), and Curly mows 20 lawns (10 hours * 2 lawns/hour). Total = 10 + 10 + 20 = 30 lawns.

Calculation for Point B: All three workers wash cars

Larry washes 10 cars (10 hours * 1 car/hour), Moe washes 20 cars (10 hours * 2 cars/hour), and Curly washes 10 cars (10 hours * 1 car/hour). Total = 10 + 20 + 10 = 40 cars.

Calculation for Point C: All three workers spend half their time on each activity

Each worker has 5 hours for each activity. Larry mows 5 lawns and washes 5 cars, Moe mows 5 lawns and washes 10 cars, and Curly mows 10 lawns and washes 5 cars. Total lawns = 5 + 5 + 10 = 20 lawns, total cars = 5 + 10 + 5 = 20 cars.

Calculation for Point D: Larry splits his time, Moe washes cars, Curly mows lawns

Larry mows 5 lawns and washes 5 cars, Moe washes 20 cars, and Curly mows 20 lawns. Total lawns = 5 + 0 + 20 = 25 lawns, total cars = 5 + 20 + 0 = 25 cars.

Key Concept

Production Possibilities Frontier (PPF)

Explanation

The PPF illustrates the maximum possible output combinations of two goods or services an economy can achieve when all resources are fully and efficiently utilized. Points on the PPF represent efficient production levels, while points inside the PPF are inefficient, and points outside are unattainable.

Answer

The PPF is bowed outwards due to the increasing opportunity costs as the economy reallocates resources from producing one good to another.

Solution

Explanation of PPF Shape:

The PPF is concave due to the law of increasing opportunity costs, which states that as production of one good increases, the opportunity cost of producing an additional unit of this good increases, because resources are not equally efficient in producing all goods.

Key Concept

Law of Increasing Opportunity Costs

Explanation

The shape of the PPF is determined by the law of increasing opportunity costs, which is reflected in the concave shape of the curve, indicating that the opportunity cost of producing more of one good increases as you produce more of it.

Answer

No, none of the allocations calculated in part 1) are inefficient because all points lie on the PPF.

Solution

Efficiency of Allocations:

Each point calculated represents all resources being fully utilized, which means they are efficient. Points inside the PPF would represent inefficiency, as not all resources would be used to their full potential.

Key Concept

Efficiency in Resource Allocation

Explanation

An allocation is efficient if it lies on the PPF, meaning that all resources are being used to their full potential and the economy is operating at maximum productivity.