UTILITY MAXIMIZATION MODEL

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The theory of consumer behavior uses the law of diminishing marginal utility to explain how consumers allocate their incomes. The utility maximization model is built based on the following assumptions:

1. Consumers are assumed to be rational, trying to get the most value for their money.

2. Consumers’ incomes are limited because their individual resources are limited. They face a budget constraint.

3. Consumers have clear preferences for various goods and services, thus they know their MU for each successive units of the product.

4. Every item has a price tag. Consumers must choose among alternative goods with their limited money incomes.

The Utility Maximization rule states: consumers decide to allocate their money incomes so that the last dollar spent on each product purchased yields the same amount of extra marginal utility.

The algebraic statement is that consumers will allocate income in such a way that:

MU of product A / price of A = MU of product B / Price of B = MU of product C / price of C = etc.

It is marginal utility per dollar spent that is equalized. As long as one good provides more utility per dollar than another, the consumer will buy more of that good; as more of that product is bought, its MU diminishes until the amount of MU per dollar just equals that of the other products.

In the following example, it illustrated the consumption possibilities of this consumer under various income levels at fixed prices of Good X and Y.

GOOD X (PRICE=$1)

GOOD Y (PRICE = $2)

QUANTITY

MU

MU/P

TL UTILITY

QUANTITY

MU

MU/P

TL UTILITY

1

8

8

8

1

10

5

10

2

7

7

15

2

8

4

18

3

6

6

21

3

6

3

24

4

5

5

26

4

4

2

28

5

4

4

30

5

3

1.5

31

6

3

3

33

6

2

1

33

7

2

2

35

7

1

0.5

34

BY FOLLOWING UTILITY MAXIMIZATION RULE:

MUx / Px = MUy / Py

   

X

Y

    Mu/P

A

4

1

          5

B

5

2

          4

C

6

3

          3

D

7

4

          2

INCOME:

     

UTILITY SUM

   

A: X=4, Y=1, $1x4+$2x1 = $6

26+10=36

B: X=5, Y=2, $1x5+$2x2 = $9

30+18=48

C: X=6, Y=3, $1x6+$2x3 = $12

33+24=57

D: X=7, Y=4, $1x7+$2x4 = $15

35+28=63

 

As the income increases, total utility increases also. Therefore, higher income groups in our society usually enjoys more products and have higher total utility levels.

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