Question

5. Complete the following table (next page) reflecting the total utility from either of two types of activities (per week): 1) “in-home” entertainment (friends visiting, etc.); and “on the town” entertainment (movies, restaurant meals, and the like). The price of in-home entertainment is $60. The price of a night on the town is $150.

In-Home Event				On-the-Town Event
# times/week	Total Utility	Marginal Utility	MU/P	# times/week	Total Utility	Marginal Utility	MU/P
0	0			0	0
1	400			1	800
2	780			2	1500
3	1100			3	1900
4	1380			4	2200
5	1500			5	2400
6	1600			6	2500
7	1650			7	2550

Now, imagine a “poor” graduate student with a weekly income of $330. What is her optimal allocation of spending between these two activities? What is her total utility with this allocation? What would be the graduate student’s allocation if the price of an “On-the-town” event fell to $60? What would be her total utility now? (Work with whole number quantities).

Answer 1

In-Home Event				On-the-Town Event
#	Total Utility	Marginal Utility	MU/P (P=60)	#	Total Utility	Marginal Utility	MU/P (P=150)	MU//P (P=60)
times/week				times/week
0	0			0	0
1	400	400	6.66666667	1	800	800	5.33333333	13.33333
2	780	380	6.33333333	2	1500	700	4.66666667	11.66667
3	1100	320	5.33333333	3	1900	400	2.66666667	6.666667
4	1380	280	4.66666667	4	2200	300	2	5
5	1500	120	2	5	2400	200	1.33333333	3.333333
6	1600	100	1.66666667	6	2500	100	0.66666667	1.666667
7	1650	50	0.83333333	7	2550	50	0.33333333	0.833333

With the given income of $330,the student will purchase until her MU/P for In home = MU/P of on the town events

So,the student will purchase 3 units of In home Event and 1 unit of On the Town Event

Total utility = 1100+800 = 1900

When the price of On the town event falls to $60,then, the student will purchase

3 units of On the Town event and 2 units of In home Event

Total Utility = 780+1900 = 2680