Question

Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either call her on the land-line phone for five cents per minute or he can drive to see her, at a round-trip cost of $2 in gasoline money. He has a total of $10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilimometer that measures his total utility from personal visits and from phone minutes. Using the values in the table below, figure out the points on Jeremy’s consumption choice budget constraint (it may be helpful to do a sketch) and identify his utility-maximizing point. Explain how you determined his utility maximizing point (using one of the methods described in class and in the text.)

Your answer must use correct economic terminology and demonstrate understanding of the economic concept of utility maximization

Round Trips Total Utility Phone Minutes Total Utility

0 0 0 0

1 80 20 200

2 150 40 380

3 210 60 540

4 260 80 680

5 300 100 800

6 330 120 900

7 200 140 980

8 180 160 1040

9 160 180 1080

10 140 200 1100

Answer 1

The table would be as below. Note that the phone minute is sorted reversely.

RT	TU	MU	MU/P	PM	TU	MU	MU/P
0	0			200	1100	1	20
1	80	80	40	180	1080	2	40
2	150	70	35	160	1040	3	60
3	210	60	30	140	980	4	80
4	260	50	25	120	900	5	100
5	300	40	20	100	800	6	120
6	330	30	15	80	680	7	140
7	200	-130	-65	60	540	8	160
8	180	-20	-10	40	380	9	180
9	160	-20	-10	20	200	10	200
10	140	-20	-10	0	0

Jeremy's budget constraint would be as , and for the given values, we have . This is the required Jeremy's consumption choice budget constraint. The combinations for each RT is matched in the table above correspondingly, and the combination of RT and PM in the table would exhaust the income.

We have , ie the change in utility for a unit increase in quantity consumed. The utility would be maximum where for the combination be exhausting utility, and the marginal utility per price is given in the table above.

Hence, the utility would be maximum where RT=1 & PM=180, ie utility would be maximum for 1 roundtrip and 180 phone minutes, given the prices and income.