Question

B. Chuck has been hired by the Academic Department of a Community College to t-u-t-o-r students who are struggling in the Math classes. Chuck does not have Internet service at home, so he can either go to a local store that provides Internet for ten cents per minute and Skype students or he can drive to Campus to meet them. The Community College is located 20 miles from Chuck’s home and the round-trip costs of $5 in gasoline money. In both cases, he can only t-u-t-o-r one student. He has a total of $20 per week to spend on t-u-t-o-r-ing. To make his preferred choice, Chuck uses a handy utilimometer that measures his total utility from Skype call and from Campus visits. Using the values given in the following table, figure out the points on Chuck’s consumption choice budget constraint (it may be helpful to do a sketch) and identify his utility-maximizing point. Also, take Chuck’s total utility information, and use the marginal utility approach to confirm the choice of Internet minutes and campus visits that maximize Chuck’s utility

Campus visits	Total Utility	Internet 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

Cost of campus visit=Pc=$5

Cost of 20 minutes internet time=Pm=20*0.1=$2

Campus Visits, C	Total Utility form campus visits, TUc	Marginal Utility MUc	MUc/Pc=Muc/5	Internet minutes, M	Total Utility form internet minutes, TUm	Marginal Utility MUm	MUm/Pm=MUm/2
0	0			0	0
1	80	80	16	20	200	200	100
2	150	70	14	40	380	180	90
3	210	60	12	60	540	160	80
4	260	50	10	80	680	140	70
5	300	40	8	100	800	120	60
6	330	30	6	120	900	100	50
7	200	-130	-26	140	980	80	40
8	180	-20	-4	160	1040	60	30
9	160	-20	-4	180	1080	40	20
10	140	-20	-4	200	1100	20	10

Budget amount=B=$20

Maximum possible number of campus visits=B/Pc=20/5=4

Maximum number of internet minutes=B/Pm=20/0.1=200

Budget constraint can be shown by following diagram

Chuck will maximize utility by choosing the campus visits and internet minutes combination such that

MUm/Pm>MUc/Pc or MUm/Pm=MUc/Pc

We can see that MUm/Pm is higher than MUc/Pm till M=180

First we select this level.

Amount spent=180*0.1=$18

Balance left=20-18=$2

This is less than the price of single campus visit. So, Campus visit is not feasible at this budget.

He would spend the remaining amount in internet minutes only.

So,

Utility maximizing campus visits=0

Utility maximizing internet minutes =200

Maximum Utility=1100