ECONOMICS W/CONNECT+20  >C<
ECONOMICS W/CONNECT+20 >C<
20th Edition
ISBN: 9781259714993
Author: McConnell
Publisher: MCG CUSTOM
Question
Book Icon
Chapter 7, Problem 4P

Subpart (a):

To determine

Utility maximizing output.

Subpart (a):

Expert Solution
Check Mark

Explanation of Solution

According to the maximization of the utility method, the marginal utility received from the last dollar spent on each commodity should be equal. Thus, it compares the utility of the dollar. The utility per dollar spent can be calculated by dividing the marginal utility of the unit by its price.

The utility maximizing combination of goods can be calculated at the point where the last dollar spent on each commodity yields the same level of utility. Thus, the marginal utility per dollar spent on each commodity can be calculated using the following formula as follows:

Marginal utility per dollar spent=Marginal utility from unitPrice of unit (1)

To calculate the marginal utility (MU) per dollar for the first unit of good A, substitute the respective values in equation (1).

Table -1 shows the value of marginal utility per dollar for the different goods and their prices that are obtained by using equation (1).

Table -1

MU per dollar unit 1 MU per dollar unit 2 MU per dollar unit 3 MU per dollar unit 4 MU per dollar unit 5 MU per dollar unit 6 MU per dollar unit 7 MU per dollar unit 8
Good A 4.00 3.00 2.50 2.00 1.50 1.00 0.83 0.67
Good B 4.00 2.50 2.00 1.50 1.17 0.83 0.33 0.17
Good C 3.75 3.00 2.00 1.75 1.25 1.00 0.88 0.75
Good D 1.5. 1.25 1.00 0.75 0.54 0.29 0.17 0.08
savings 5.00 4.00 3.00 2.00 1.00 0.50 0.25 0.13

Since, the marginal utility of a dollar is 5 for 1 unit of saving, he will go for it. Then, he will go for the consumption of Good A, B and another unit of savings which gives 4 utils of marginal utility per dollar. Then, the consumption of the first unit of good C will take place which gives 3.75 utils of marginal utility per dollar. Then, he will go for the 2nd unit of Good A and C along with the third unit of saving which provides 3 utils of marginal utility per dollar. Then, he will consume the 3rd unit of Good A and 2nd unit of Good B for marginal utility per dollar worth 2.50 utils. Finally, the 4th unit of Good A and savings along with 3rd unit of Good B and C which gives 2 utils of marginal utility per dollar is consumed. As a result, his total budget would exhaust and cease his consumption, where his utility would be at the maximum.

The utility maximizing output combination is the combination where the marginal utility per dollar spent on each commodity is equal. Analyzing the table, we can see that 4 units of good A and D, 3 units of Good B and C and 4 units of savings will provide an individual with the marginal utility per dollar worth 2 utils. Since, no unit of good D provides marginal utility per dollar worth 2 utils, no unit of good D will be consumed.

Economics Concept Introduction

Concept introduction:

Utility: It can be explained as the benefit or the satisfaction which is derived from the consumption of a good or service by the consumer.

Marginal utility: It is the extra satisfaction that a consumer derives from the consumption of an additional unit of the specific good or service.

Utility maximizing combination: The utility maximizing combination is such that the last rupee spent on each commodity should yield the same level of an additional utility or the marginal utility spent on each commodity should be equal.

Utility per dollar spent: It is the utility of one dollar spent on the unit. It can be calculated by dividing the marginal utility with the initial price.

Subpart (b):

To determine

Utility maximizing output.

Subpart (b):

Expert Solution
Check Mark

Explanation of Solution

According to the marginal utility per dollar, the consumer consumes the goods and services until when it gives the equal marginal utility per dollar which are worth 2 utils. It is at 4 units of savings, the marginal utility per dollar equals to 2 units and thus, the consumer will choose to save $4.

Economics Concept Introduction

Concept introduction:

Utility: It can be explained as the benefit or the satisfaction which is derived from the consumption of a good or service by the consumer.

Marginal utility: It is the extra satisfaction that a consumer derives from the consumption of an additional unit of the specific good or service.

Utility maximizing combination: The utility maximizing combination is such that the last rupee spent on each commodity should yield the same level of an additional utility or the marginal utility spent on each commodity should be equal.

Utility per dollar spent: It is the utility of one dollar spent on the unit. It can be calculated by dividing the marginal utility with the initial price.

Subpart (c):

To determine

Utility maximizing output.

Subpart (c):

Expert Solution
Check Mark

Explanation of Solution

The utility maximizing combination is 4Units of Good A, 3 units of Good B, 3 units of Good C, 0 unit of Good D and 4 Unit of savings. With this combination, the total budget of the consumer gets exhausted. This can be verified by substituting the values as follows:

Total budget=(UnitsGood A+UnitsGood B+UnitsGood C+UnitsGood D+UnitsSavings)=(4×18)+(3×6)+(3×4)+(0×24)+(4×1)=72+18+12+0+4=106

Since the total budget is $106 which is equal to the cost of the utility maximizing combination, the total budget gets exhausted with this combination of goods and savings.

Economics Concept Introduction

Concept introduction:

Utility: It can be explained as the benefit or the satisfaction which is derived from the consumption of a good or service by the consumer.

Marginal utility: It is the extra satisfaction that a consumer derives from the consumption of an additional unit of the specific good or service.

Utility maximizing combination: The utility maximizing combination is such that the last rupee spent on each commodity should yield the same level of an additional utility or the marginal utility spent on each commodity should be equal.

Utility per dollar spent: It is the utility of one dollar spent on the unit. It can be calculated by dividing the marginal utility with the initial price.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105. Column 1 Column 2 Column 3 Column 4 Units Units Units Units of A MU of B MU of C MU of D MU 1 72 1 24 1 15 1 36 54 15 12 2 30 3 45 3 12 3 8. 3 24 4 36 4 7 4 18 27 7 5 5 13 6 18 6 5 6 4 6 7 7 15 7 2 7 3.5 7 8 12 8 1 8 3 8 2 а. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule. In other words, show it works when using this rule.
Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D.  Column 5 shows the marginal utility Ricardo gets from saving.  Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105.   What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility?           How many dollars will Ricardo choose to save?           Check your answers by substituting them into the algebraic statement of the utility‑maximizing rule. In other words, show it works when using this rule.
Columns 1 through 4 in the following table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respectively, $18, $6, $4, and $24 and that Ricardo has an income of $106. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:9780190931919
Author:NEWNAN
Publisher:Oxford University Press
Text book image
Principles of Economics (12th Edition)
Economics
ISBN:9780134078779
Author:Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:PEARSON
Text book image
Engineering Economy (17th Edition)
Economics
ISBN:9780134870069
Author:William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:PEARSON
Text book image
Principles of Economics (MindTap Course List)
Economics
ISBN:9781305585126
Author:N. Gregory Mankiw
Publisher:Cengage Learning
Text book image
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Text book image
Managerial Economics & Business Strategy (Mcgraw-...
Economics
ISBN:9781259290619
Author:Michael Baye, Jeff Prince
Publisher:McGraw-Hill Education