Answer to Question #232716 in Microeconomics for Awliyo

Question

1. A consumer consuming two commodities A and B, has a total income of 16birr with price A and B were 1birr and 4birr respectively

Given the following table
Q 1 2 3 4 5 6 7 8
TUA 30 55 75 90 100 100 90 75
TUB 100 180 240 280 300 300 280 260
a. Calculate marginal utility for good A and B
b. Draw the marginal and total utility for commodity A and show the relationship between them.
c. How many units of A and B should be consumed to maximize utility
d. Calculate the total utility at optimal choice

Answer 1

Total Utility refers to the total satisfaction derived from the consumption of a particular quantity of a good or service. Marginal Utility is the additional utility derived from consumption of an addition unit of good or service.

Marginal Utility = Change in Total Utility / Change in Quantity

The utility of the consumer is maximized when he spends his limited money income in such a way that the last dollar spent on each good or service will result in same amount of additional utility ie marginal utility.

MU of Good A / Price of Good A = MU of Good B / Price of Good B

(PART-A)

For Example, in Case of Good A,

MU at 2 units = (55 - 30) / (2 - 1) = 25 / 1 = 25

In Case of Good B,

MU at 2 units = (180 - 100) / (2 - 1) = 80 / 1 = 80

Similarly other calculations are being made.

(PART-B)

Relation between Total Utility and Marginal Utility in case of Good A

Total Utility refers to the total satisfaction that a consumer derives from the consumption of a specific quantity of a good or service. Marginal Utility refers the additional utility that a consumer gets from the consumption of an additional unit of a good or service.

Total Utility will increase till marginal utility is positive. Till 5 units total utility is increasing and marginal utility is also positive. At 6th unit, total utility becomes constant and marginal utility is zero. From 7th unit and onwards, marginal utility becomes negative and total utility also starts decreasing. 

(PART-C)

As per rule, the consumer enjoys maximum utility, when:

MU of Good A / Price of Good A = MU of Good B / Price of Good B

At 4 units of Good A,

MU of Good A / Price of Good A = 15 / 1 = 15

At 3 units of Good B

MU of Good B / Price of Good B = 60 / 4 = 15

Thus, utility maximization principle is satisfied.

Money spent on consuming 4 units of Good A = Price * Quantity = 1 * 4 = 4 birr

Money spent on consuming 3 units of Good B = 4 * 3 = 12 birr

Total money spent on both goods = 4 + 12 = 16 birr

Also, the total income of consumer = 16 birr.

So, 4 units of Good A and 3 units of Good B should be consumed, in order to maximize utility.

(PART-D)

In case of two goods, the consumer attains maximum utility when the condition given below is satisfied:

MU_A/P_A=MU_B/P_B

Subject to budget constraint.

Here, MU_A is marginal utility attained from good A.

MU_B is marginal utility attained from good B.

P_A is price of good A

P_B is price of good B.

The table given below shows the calculations

The combination of 4 units of good A and 3 units of good B satisfies the equilibrium condition as well as budget constraint shows below:

Income=P_AQ_A+P_BQ_B

=1(4)+4(3)

=16

Thus, 4 units of good A and 3 units of good B satisfies above condition.

The total utility attained is:

TU=TU_A+TU_B 

=90+240

=230

So,

(Total utility at optimal choice is 330 utils.)