Chapter 10R, Problem 2FRQ

a)

To determine

Marginal product of the third robot.

Explanation of Solution

Robots	Total output/product (pairs) or Total utility	Total cost	Marginal utility or marginal product(TUn-1-TUn)	Marginal cost(TCn-1-TCn)
0	0	40
1	2	90	2 (2-0 = 2)	50 (90-40 = 50)
2	5	140	3 (5-2 = 3)	50
3	10	190	5	50
4	15	240	5	50
5	19	290	4	50
6	22	340	3	50
7	24	390	2	50
8	25	440	1	50

The marginal product of the third robot is 5.

Economics Concept Introduction

Introduction: Marginal output refers to the extra or additional output which is incurred by using one additional unit of production.

b)

To determine

Robots that are needed to acquire before the beginning of diminishing marginal utility.

Explanation of Solution

Robots	Total output/product (pairs) or Total utility	Total cost	Marginal utility or marginal product(TUn-1-TUn)	Marginal cost(TCn-1-TCn)
0	0	40
1	2	90	2 (2-0 = 2)	50 (90-40 = 50)
2	5	140	3 (5-2 = 3)	50
3	10	190	5	50
4	15	240	5	50
5	19	290	4	50
6	22	340	3	50
7	24	390	2	50
8	25	440	1	50

Before the beginning of diminishing marginal utility, 4 robots are needed to acquire.

Economics Concept Introduction

Introduction: Marginal utility is the utility or satisfaction which is availed by using or consuming one additional unit.

c)

To determine

Marginal cost of the 15^th pair of shoes.

Explanation of Solution

Robots	Total output/product (pairs) or Total utility	Total cost	Marginal utility or marginal product(TUn-1-TUn)	Marginal cost(TCn-1-TCn)
0	0	40
1	2	90	2 (2-0 = 2)	50 (90-40 = 50)
2	5	140	3 (5-2 = 3)	50
3	10	190	5	50
4	15	240	5	50
5	19	290	4	50
6	22	340	3	50
7	24	390	2	50
8	25	440	1	50

Marginal cost of the 15^th pair of shoes is 50.

Economics Concept Introduction

Introduction: Marginal cost refers to the expense or cost that is incurred by using one additional

unit of production to get maximum output.

d)

To determine

Number of robots that firm should hire to maximize profit and profit at this level of output.

Explanation of Solution

Robots	Total output/product (pairs) or Total utility	Total cost	Marginal utility or marginal product(TUn-1-TUn)	Marginal cost(TCn-1-TCn)	Price (per pair)	Total Revenue (Price × Quantity)	Profit (Total revenue − Total cost)
0	0	40			$30		-40
1	2	90	2 (2-0 = 2)	50 (90-40 = 50)	30	$60	-30
2	5	140	3 (5-2 = 3)	50	30	150	10
3	10	190	5	50	30	300	110
4	15	240	5	50	30	450	210
5	19	290	4	50	30	570	280
6	22	340	3	50	30	660	320
7	24	390	2	50	30	720	330
8	25	440	1	50	30	750	310

The firm should hire 7 robots to maximize profit. Here, the profit would be $330.

Economics Concept Introduction

Introduction: Profit refers to the difference of total revenue and total cost.