In: Economics
Juliette and Andrew regularly go to the movies, where they like to consume popcorn and slushies. At the movies, Juliette’s utility function is given by UJ=√P×S, where P is the number of cups of popcorn, and S is the number of slushies she consumes. Andrew’s utility function is given by UA=P+S.
a. Compute the utility Juliette and Andrew receive from the following combinations of popcorn and slushies:
Units of Popcorn | Units of Slushies | Juliette's Utility | Andrew's Utility |
---|---|---|---|
1 | 1 |
1 |
2 |
2 | 2 |
2 |
4 |
3 | 3 |
3 |
6 |
b. Suppose that Juliette and Andrew are each consuming 2 popcorns and 2 slushies. Who gets the most happiness from her or his movie snacks?
Juliette
It's not possible to say.
Both get equal happiness.
Andrew
c. Suppose that Juliette has consumed 2 popcorns and 3 slushies. What is the approximate marginal utility Juliette will receive if she eats another cup of popcorn?
0.49
0.45
0.61
0.55
What is the approximate marginal utility she will receive if, instead, she drinks another slushie?
0.45
0.38
0.61
0.55
d. When Andrew is consuming 1 popcorn and 1 slushie, another popcorn will increase his utility by 1 unit. When Andrew is consuming 8 popcorns and 1 slushie, another popcorn will again increase his utility by 1 unit.
Which assumption of consumer preferences might Andrew’s particular utility function violate?
Transitivity
For most goods, more is better than less
Completeness and rankability
The more a consumer has of a good, the less one is willing to give up of something else to get more of it
Juliette’s utility function appears to violate the same assumption.
False
True
a) The values in the table for utilities given in the table are correct.
b) Andrew gets more happiness as his utility from consuming 2 slushies and 2 popcorns is 4 which is more than Juliette which is 2. Utility is a measure of satisfaction the consumer gets from consuming the goods.
c)
Thus the answers for the first part of c) is 0.55 and second part is 0.38.
d) Andrew's utility function violates the assumption that
The more a consumer has of a good, the less one is willing to give up of something else to get more of it.
In Andrew's case the utility he gets from consuming another one of popcorn or slushie is 1 irrespective of his current utility level (i.e his marginal utility is 1) which is contrary to the assumption of diminishing marginal utility for a consumer.
In the case of Juliette it is FALSE as her utility from
consuming another unit of either a popcorn or slushie reduces as
her utility level increases. She has diminishing marginal utility.
Her marginal utility for popcorn is
which is a function which decreases as the value of P (quantity of
popcorn) increases. Her marginal utility for slushie
is
which is a function which decreases as the value of S (quantity of
slushie) increases.