Question

You just won a $100 shopping spree at a store that sells only dvds and cds. you are trying to determine what combination of these two goods would maximize your utility. the price of cds is $10 and dvds are $20. below is the total utility you receive from consuming these goods. cds total utility dvds total utility 1 60 1 160 2 110 2 300 3 150 3 420 4 180 4 520 5 200 5 600 6 210 6 660

Answer 1

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 $\frac{Marginal Utility (MU}{Price (P)}$ 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

$Marginal Utility (MU) = Total utility (TU) of current unit - Total utility (TU) of previous unit$

For Instance,

$MU_{CD2} = TU_{CD2} - TU_{CD1}$

$MU_{CD2} = 110 - 60$

$MU_{CD2} = 50$

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

$MU/P_{CD1} = \frac{60}{10} = 6$ and

$MU/P_{DVD1} = \frac{160}{20} = 8$  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

4             DVD         20     80

Total        5 DVD       100    600

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

1                 CD            10        10

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.