Question

4. Problems and Applications Q4 An economy consists of three workers: Charles, Gilberto, and Lorenzo. Each works 10 hours a day and can produce two services: mowing lawns and washing cars. In an hour, Charles can either mow 1 lawn or wash 1 car; Gilberto can either mow 1 lawn or wash 2 cars; and Lorenzo can either mow 2 lawns or wash 1 car. For each of the scenarios listed in the following table, determine how many lawns will be mowed and how many cars will be washed per day and enter these values into the corresponding row. Scenario Lawns Mowed Cars Washed All three spend all their time mowing lawns. (A) All three spend all their time washing cars. (B) All three spend half their time on each activity. (C) Charles spends half his time on each activity, while Gilberto only washes cars and Lorenzo only mows lawns. (D) In the table below, identify the opportunity cost of washing cars for each worker. Worker Opportunity Cost of Washing Cars Charles Gilberto Lorenzo Assume that the resources best suited to producing a particular service are preferentially used in the production of that service and that as the economy moves down along the production possibilities frontier, one worker at a time is transferred from mowing lawns to washing cars. Using the blue points (circle symbol), graph the production possibilities frontier (PPF) for this economy on the following graph. Then use the black point (plus symbol) to identify point A, the green point (triangle symbol) to identify point B, the orange point (square symbol) to identify point C, and the purple point (diamond symbol) to identify point D on the graph. PPFABCD0510152025303540455050454035302520151050Quantity of Lawns MowedQuantity of Cars Washed True or False: The production possibilities frontier has a kinked shape because each worker faces a constant trade-off between mowing lawns and washing cars. True False Indicate whether each of the following allocations is efficient or inefficient. Allocation Efficient Inefficient A B C D

Answer 1

Scenario	Lawns Mowed	Cars Washed
All three spend all their time mowing lawns. (A)	40
All three spend all their time washing cars. (B)		40
All three spend half their time on each activity. (C)	20	20
Charles spends half his time on each activity, while Gilberto only washes cars and Lorenzo only mows lawns. (D)	25	25

All three spend all their time mowing lawns. (A):- 1*10 + 1*10 + 2*10 =40

All three spend all their time washing cars. (B):- 1*10 + 2*10 + 1*10 =40

All three spend half their time on each activity. (C):-

For mowing:- 1*5 + 1*5 + 2*5=20

For Cars:- 1*5 + 2*5 + 1*5 =20

Charles spends half his time on each activity, while Gilberto only washes cars and Lorenzo only mows lawns. (D):-

For Mowing:- 1*5 +2*10 =25

For Cars:- 1*5 +2*10=25

In the table below, identify the opportunity cost of washing cars for each worker.

Worker	Opportunity Cost of Washing Cars
Charles	1 washing car = 1 mowing
Gilberto	1 washing car =1/2 mowing
Lorenzo	1 washing car =2 mowing

Question:- True or False: The production possibilities frontier has a kinked shape because each worker faces a constant trade-off between mowing lawns and washing cars.

Correct Answer:- True

Reason:- The production possibilities frontier has a kinked shape because each worker faces a constant trade-off between mowing lawns and washing cars. Charles, is equally productive in both tasks. Gilberto is twice productive in washing cars than mowing while Lorenzo has greater productivity in the mowing of lawns.