Question

soda                                  chips                                 pizza

27                                      18                                      40

21                                      15                                      35

12                                      12                                      25

1.As a cool co-worker you are invited to every party. You choose 5 items which works out to be __ soda __ chips and __ pizza before becoming full according to the marginal utility (MU) listed above.

a)You encounter the same at a concession stand where soda, chips and pizza are priced at $3, 1.50 and 5 respectively and choose 5 items which now is __ soda __ chips and __ pizza. How does the free selection differ from the paid? Why?

b)What is the difference in MU among the last items you selected for free?

2.What is the difference in MU/$ among the last items you paid for?

a)If four items were handed to you randomly, would you expect these differences to be bigger or smaller? Why?

b)You never paid for a 2nd soda or a 2nd pizza. If you chose a 2nd pizza slice and then were offered a 2nd soda in its place, you would demand _________ sodas in the place of a 2^nd slice.

3.Pizza price divided by soda price also equals _   

Answer 1

Solution:

1. When no price is to be paid, the items chosen will purely depend on the marginal utility derived from the items. The trick is to choose items in order of their marginal utilities. From the given table, it is easy to see that highest MU is obtained from 1st pizza slice. Next, 35 > 27 and 35 > 18, meaning second slice of pizza gives higher utility than either of other 2 items. So, 2 slices of pizza are chosen. In the table, next high MU is 27, so 1st bottle of soda is chosen as 3rd item. As 25 is next in MU order, 3rd slice of pizza will also be chosen. Finally 21 > 18, so 2nd second bottle of soda will be chosen over the 1st packet of chips, as the final item.

So, ultimately the 5 items chosen are: 2 soda, 0 chips and 3 pizzas.

a) Now, given the prices: price of soda, Ps = $3; price of chips, Pc = $1.5; and price of pizza, Pz = $5, we do not look purely at respective marginal utilities, but the ratio of marginal utility per unit price.

So with ratios as MUs/Ps, MUc/Pc and MUz/Pz, we have following new table:

MUs/Ps = MUs/3	MUc/Pc = MUc/1.5	MUz/Pz = MUz/5
27/3 = 9	18/1.5 = 12	40/5 = 8
21/3 = 7	15/1.5 = 10	35/5 = 7
12/3 = 4	12/1.5 = 8	25/5 = 5

Now, it is easy to see and compare the ratios. Clearly the ordering is high for first 2 chips packs, they will be chosen. Similarly, 3rd item will be 1st bottle of soda, 4th and 5th items will be 1st pizza slice, and 3rd chips pack (both deriving required ratio of 8). So, now the items we have are: 1 soda, 3 chips, and 1 pizza.

NOTE: the budget or income to be spent on items is not given here, otherwise the chosen items will depend on the amount of income to be spent as well.

b) Under free selection, the last 2 items chosen were 3rd pizza slice (giving MU of 25) and 2nd bottle of soda (giving MU of 21), hence, required difference = 25 - 21 = 4

2. Under paid selection, last two items are 1st pizza slice ( giving MU/$ = 8) and 3rd pack of chips ( giving MU/$ of 8), so required difference is 8 - 8 = 0

a) We try to maximize the utility, and that takes place as the MU/$ difference is as much lower as possible. Thus, we can say that if random handover would have taken place rather than the optimized one, surely the difference would be expected to be bigger.

b) MU/$ for 2nd slice of pizza = 7. MU/$ for second bottle of soda also equals 7. Had the second slice of pizza been demanded, but 2nd slice of soda offered, only 1 soda bottle would be demanded.

3. Again, as we said we wish for MU/$ difference to be as small as possible, meaning in case of pizza and soda, we require,

MUs/Ps = MUz/Pz

So, Pz/Ps = MUz/MUs

So, pizza price divided by soda price equals the ratio of marginal utility from pizza over marginal utility from soda. This ratio is also named as marginal rate of substitution of pizza for soda.