Answer: I will derive maximum satisfaction by choosing 5 DVDs, since my total marginal utility is the highest then.
We follow these steps in order to arrive at the answer:
We first calculate the Marginal Utilities (MU) and for CDs and DVDs.
Price of CD = $10
Price of DVD = $20
We calculate the Marginal Utility per unit first.
The marginal utilities of the first units of Cd and DVD are equal to the total utility of CD and DVD.
We use the following formula to find the MU of each additional unit thereafter
For Instance,
We calculate the MU for DVDs also similarly.
Then we divide the MU by the per unit price of the product so that we can rank the products in order of preference for both CDs and DVDs.
For instance MU/P for the first CD and DVD are
and
and so on.
The table with the calculations are as follows:
CDs Total Utility MU MU/P DVDs Total utility MU MU/P
1 60 60 6 1 160 160 8
2 110 50 5 2 300 140 7
3 150 40 4 3 420 120 6
4 180 30 3 4 520 100 5
5 200 20 2 5 600 80 4
6 210 10 1 6 660 60 3
We then select the products based on the highest ranks in the MU/P columns. The options that have the highest ranks are highlighted in bold font in the table above.
We observe that MU/P are the highest for the first 2 th DVDs, but after that the ranks of 6,5,4 and 3 are there for both CDs and DVDs.
In this case, we list out both the courses of actions available and write down their individual MUs until the total price reaches the budget of $100. Then we find the total of the MUs of each option.
Option 1
Rank CD or DVD Price MU
8 DVD 20 160
7 DVD 20 140
6 DVD 20 120
5 DVD 20 100
<u>4 DVD 20 80</u>
<u>Total 5 DVD 100 600</u>
Option 2
Rank CD or DVD Price MU
8 DVD 20 160
7 DVD 20 140
6 DVD 20 120
5 DVD 20 100
4 CD 10 40
3 CD 10 30
2 CD 10 20
<u>1 CD 10 10</u>
Total 2DVDs, 6CDs $100 510
As a consumer, I can choose either of the options listed above, or any other combination. However, these two options above show the maximum and minimum utilities of a combination of the two products with a budget of $100.
Any other combination will result in the total of the Marginal utilities column being between 600 and 510.
In economics, we say that the consumer is satisfied if he maximizes his utility. Hence we will choose that option which has the maximum utility i.e. option A.