3. Columns 1 through 3 in the table below show the marginal utility which a part

Question

3.      Columns 1 through 3 in the table below show the marginal utility which a particular consumer would get by purchasing various quantities of products A, B, and C.

Unit of product

(1)

Marginal utility, A

(2)

Marginal utility, B

(3)

Marginal utility, C

First

18

39

12

Second

16

36

10

Third

14

33

9

Fourth

12

30

8

Fifth

10

27

7

Sixth

8

24

5

Seventh

6

21

3

      If the prices of A, B, and C are $2, $3, and $1, respectively, and the consumer has $26 to spend on these three products, what combination of the three products should be purchased in order to maximize utility?

Unit of product

(1)

Marginal utility, A

(2)

Marginal utility, B

(3)

Marginal utility, C

First

18

39

12

Second

16

36

10

Third

14

33

9

Fourth

12

30

8

Fifth

10

27

7

Sixth

8

24

5

Seventh

6

21

3

Explanation / Answer

To calculate this we first need to find the per rupee utility of each product at each level and on doing so we will see that the per rupee utility of product B is highest for all seven units of product being:

1st unit's utility 13

2nd unit's utility 12

3rd unit's utility 11

4th unit's utility 10

5th unit's utility 9

6th unit's utility 8

7th unit's utility 7 (Formula = utility/per unit cost)

So seven units of the product B must be purchased.

Remaining amount of rupees = $(26 - 7*3) = $5

Now we see the marginal utility per rupee is maximum for product C.

So 5 units of product C must be purchased.

Thus in order to maximise the utility 7 units of product B and 5 units of product C must be purchased.

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