Question

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

Answer 1

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.