Chapter 9R, Problem 2FRQ

a)

To determine

The quantity after which M will begin to experience diminishing marginal utility.

Explanation of Solution

Cheese			Crackers
Quantity (pounds)	Total Utility	Marginal Utility (TUn-TUo)	Quantity(boxes)	Total Utility	Marginal Utility
1	200		1	100
2	360	160	2	200	100
3	440	80	3	250	50
4	480	40	4	270	20
5	500	20	5	280	10

  $\begin{array}{l}\text{Marginal Utility }\left(\text{MU}\right)\text{ for cheese }\\ \text{ = TUn}-\text{TUo}\\ \text{second unit:}\\ \text{ = (360}-\text{200)}\\ \text{ = 160}\end{array}$

  $\begin{array}{l}\hfill \\ \begin{array}{l}\text{third unit:}\\ \text{ = 440}-\text{360}\end{array}\hfill \\ \text{ = 80}\hfill \end{array}$

  $\begin{array}{l}\\ \text{fourth unit:}\\ \text{= }\begin{array}{l}\left(\text{480}-\text{440}\right)\hfill \end{array}\\ \text{= 40}\end{array}$

  $\begin{array}{l}\\ \text{fifth unit:}\\ \text{= }\left(\text{500}-\text{480}\right)\\ \text{= 20}\end{array}$

  $\begin{array}{l}\text{Marginal Utility }\left(\text{MU}\right)\text{ for crackers = TUn}-\text{TUo}\\ \text{second unit:}\\ \text{= (200}-\text{100)}\\ \text{= 100}\end{array}$$$

  $\begin{array}{l}\hfill \\ \begin{array}{l}\text{third unit:}\\ \text{= 250}-\text{200}\end{array}\hfill \\ \text{= 50}\hfill \end{array}$

  $\begin{array}{l}\\ \text{fourth unit:}\\ \text{= }\begin{array}{l}\left(\text{270}-\text{250}\right)\hfill \end{array}\\ \text{= 20}\end{array}$

  $\begin{array}{l}\\ \text{fifth unit:}\\ \text{= }\left(\text{280}-\text{270}\right)\\ \text{= 10}\end{array}$

Therefore, the quantity where M will start experiencing diminishing marginal utility is 3.

Economics Concept Introduction

Introduction: Marginal utility is the benefit that a person consumes or enjoys while using an additional unit of a good.

b)

To determine

Marginal utility of the third pound of cheese.

Explanation of Solution

Cheese			Crackers
Quantity (pounds)	Total Utility	Marginal Utility (TUn-TUo)	Quantity(boxes)	Total Utility	Marginal Utility
1	200		1	100
2	360	160	2	200	100
3	440	80	3	250	50
4	480	40	4	270	20
5	500	20	5	280	10

The old total utility of the third unit of cheese is 360 and the new is 440, then

  $\begin{array}{l}\begin{array}{l}\text{Marginal Utility }\left(\text{MU}\right)\\ \text{= TUn}-\text{TUo}\end{array}\hfill \\ \text{= 440}-\text{360}\hfill \\ \text{= 80}\hfill \end{array}$

The marginal utility of the third pound of cheese is 80.

Economics Concept Introduction

Introduction: Marginal utility is the benefit that a person consumes or enjoys while using an additional unit of a good.

c)

To determine

Marginal utility per dollar of the fourth pound of cheese.

Explanation of Solution

Cheese			Crackers
Quantity (pounds)	Total Utility	Marginal Utility (TUn-TUo)	Quantity(boxes)	Total Utility	Marginal Utility
1	200		1	100
2	360	160	2	200	100
3	440	80	3	250	50
4	480	40	4	270	20
5	500	20	5	280	10

The marginal utility of the fourth pound of cheese is 40 which is calculated by subtracting the previous total utility from the new total utility.

Economics Concept Introduction

Introduction: Marginal utility is the benefit that a person consumes or enjoys while using an additional unit of a good.

d)

To determine

The adjustment of consumption of cheese and crackers by using the concept of marginal analysis to maximize the total utility if M has a budget of $20, spending 3 pounds of cheese and 4 boxes of crackers.

Explanation of Solution

At 3 pounds of cheese and 4 boxes of crackers, M is experiencing the highest total utility because the price of cheese per pound is $4 and the price of crackers per box is $2 and by consuming 3 pounds of cheese and 4 boxes of crackers M will get the total utility of 1820 which is not possible otherwise. As if M will consume 4 pounds of cheese and 2 boxes of crackers then the utility will decrease.

Economics Concept Introduction

Introduction: Marginal analysis refers to the examination of additional benefits and additional costs by using one additional unit of a good.