Question

please help. show the exact points for the graph.

4. Problems and Applications Q4 An economy consists of three workers: Van, Carlos, and Felix. Each works 10 hours a day and can produce two services: mowing lawns and washing cars. In an hour, Van can either mow 1 own or wash 1 car; Carlos can either mow 1 lawn or wash 2 cars, and Felix can either mow 2 lawns or wash 1 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 (3) All three spend half their time on each activity. (C) Van spends hall his time on each activity, while Carlos only washes cars and Felix only mows lowns. (D) In the following table, identify the opportunity cost of washing cars for each worker. Worker Opportunity cost of Washing Cars Van Carlos Felix

Answer 1

Scenario Lawn Mowed Cars Washed All three spend all their time mowing lawn (A) All three spend all their time washing cars (B) All three spend half of their time on each activity (C) Van spends half his time on each activity, while Carlos only washes cars and Felix only mows lawns (D) 40 40 20 20 25 25

Workers Opportunity Cost of Washing Cars 1/1=1 lawn per car 1/2 lawn per car 2/1 = 2 lawns per car Van Carlos Felix

40 Carlos Van AD(a525) C20,20) 20 Felix Felix 10 cardles Van 20 30 40 Quantity of carcs washeod Quantity of lans mawed

Let us see how to draw this production possibility frontier. If all spends time only on mowing lawns, they can mow 40 lawns. Let us start from this point (40) on the Y-axis, which represents quantity of lawns mowed. Opportunity cost of washing a car is lowest for Carlos (0.5) compared to others. Hence, he will start from point A and he can move up to 20 cars towards X-axis by giving up 10 lawns. Hence, he can reach till point (20,30). The next person whose opportunity cost of washing cars is low is Van (1) compared to Felix (2). Hence, Van would start from (20,30) and can give up 10 lawns and maximum wash 10 cars and hence he can move up to (30,20). Finally, Felix would start from (30,20) and can give up 20 lawns for 10 cars and hence can move till (40,0).

Now, as shown in the diagram, point A (0,40) and B (40,0) lies on the frontier and point C (20,20) and D (25,25) lie below the frontier.

True or False: The production possibilities frontier consists of straight-line segments, rather than being smoothly bowed outward throughout, because each worker faces a constant trade-off between mowing lawns and washing cars. O True O False

This statement is true. As shown in the diagram, it consists of 3 line segments, from top to bottom, the segment represents production possibilities of Carlos, Van and Felix respectively.

Indicate whether each of the following allocations is efficient or inefficient. Allocation Efficient Inefficient

Points (scenarios) A and B are efficient as they lie on the frontier, where as points (scenarios) C and D are inefficient as they lie inside (below) the frontier. All points on the frontier are efficient, all points below frontier are inefficient and all points above frontier are infeasible.