Question

It’s a warm day, and you’re thirsty. You’ve walked into a convenience store with your friends, and you’re considering whether to purchase water or a soda. Because you’ve taken ECO 210, you begin to put numbers to the amount of utility (satisfaction) you expect to get from each drink. Using the numbers provided, calculate the marginal utility from each additional bottle of soda or water you might buy.

Quantity	Total Utility Bottles of water	Marginal Utility Bottles of water	Total Utility Bottles of soda	Marginal Utility Bottles of soda
0	0		0
1	10		12
2	18		19
3	24		24
4	28		27

Prices matter, of course. When you check you learn that bottles of water in this store sell for $1 each, while bottles of soda sell for $2 each. So the question becomes, is a bottle of soda worth the extra money given the preferences identified above.

Copy the numbers from the “Marginal Utility” columns above, and then calculate marginal utility per dollar spent in the table below.

Quantity	Marginal Utility Bottles of water	Marginal Utility of water/$1	Marginal Utility Bottles of soda	Marginal Utility of soda/$2
0
1
2
3
4

Given the information provided above, what should you buy first—a bottle of water or a soda? Why?

If you were thirsty enough to drink two bottles of something (and you had enough money), what would be the second drink you would buy? Why?

Assuming you wanted to spend $5 on drinks, what would you buy? How many bottles of water? How many bottles of soda? Why?

To connect this a little more closely to demand curves, let’s assume the convenience store lowered the price of sodas to $1 a bottle (and left water at $1 a bottle). Complete the table below.

Quantity	Marginal Utility Bottles of water	Marginal Utility of water/$1	Marginal Utility Bottles of soda	Marginal Utility of soda/$1
0
1
2
3
4

With this new information, what should you buy first—a bottle of water or a soda? Why?

If you were thirsty enough to drink two bottles of something (and you had enough money), what would be the second drink you would buy? Why?

Assuming you wanted to spend $5 on drinks, what would you buy? How many bottles of water? How many bottles of soda? Why?

Answer 1

1.

quantity	TUwater	MUwater	TUsoda	MUsoda
0	0	0	0	0
1	10	10-0= 10	12	12-0 =12
2	18	18-10 = 8	19	19-12= 7
3	24	24- 18= 6	24	24- 19= 5
4	28	28- 24= 4	27	27 - 24 - 3

Marginal Utiltiy is the change in Total Utility when one more unit of a good is consumed. MU = TU_n- TU_n-1

2.

quantity	MUwater	MU$water	MUsoda	MU$soda
0	0	0	0	0
1	10	10/1 = 10	12	12/2= 6
2	8	8/1 = 8	7	7/2 = 3.5
3	6	6/1 = 6	5	5/2 = 2.5
4	4	4/1 = 4	3	3/2= 1.5

Marginal utility of dollar (MU$) = MU / price

Since the MU$ for the first rupee spent is highest for first bottle of water (10), the consumer will buy water first.

Since the MU$ for second water of bottle (8) > MU$ for first bottle of soda, the second drink bought would be water too.

If the consumer had $5, he would buy 3 bottles of water and 1 bottle of soda. This would exhaust his total income as $1 x 3 + $2 x 1 = $5 and satisfy the principle of equi marginal utility- that the marginal utility of dollar from consumption of last units of both goods should be equal. The MU$ from third bottle of water = MU$ from first bottle of soda = 6.

3.

quantity	MUwater	MU$water	MUsoda	MU$soda
0	0	0	0	0
1	10	10/1 = 10	12	12/1= 12
2	8	8/1 = 8	7	7/1 = 7
3	6	6/1 = 6	5	5/1 = 5
4	4	4/1 = 4	3	3/1= 3

Since the MU$ for the first rupee spent is highest for first bottle of soda now (12), the consumer will buy soda first.

The consumer would buy first bottle of soda and second drink would be first bottle of water as it has second highest MU$ (10).

If the consumer had $5, he would buy 3 bottles of water and 2 bottle of soda. This would exhaust his total income as $1 x 3 + $1 x 2 = $5. This would be because: soda first bottle (12) > water first bottle (10) > water second bottle (8) > soda second bottle (7) > water third bottle (6).