Question

Suppose that as a consumer you have $34 per month to spend on munchies—either pizzas, which cost $6 each, or Twinkies, which cost $4 each. Suppose further that your preferences are given by the following total utility table. Copy the tables below to submit and solve for the missing marginal utility information in each. Remember that they must show diminishing marginal utility as more of each product is consumed. Graph the budget constraint with Pizzas on the horizontal axis and Twinkies on the vertical axis. What are the intercepts? Can you express the budget constraint as an algebraic equation for a line? # of Pizzas 1 2 3 4 5 6 7 Marginal Utility Total Utility 60 108 138 156 162 166 166 # of Twinkies 1 2 3 4 5 6 7 Marginal Utility Total Utility 44 76 100 120 136 148 152 Should you purchase a Twinkie first or a Pizza first to get the “biggest bang for the buck”? How can you tell? What should you purchase second, third, etc. until you exhaust your budget? Make sure that your answer satisfies the utility maximizing rule and mathematical proof. Confirm that the combination of Twinkies and Pizzas you end up with will maximize your total utility by computing the total utility from other points on the budget line and comparing them to what you chose.

Answer 1

1) Budget constraint line:

34 = 6p + 4t where p = number of pizzas and t is number of twinkies

2) Graph.

p is on x acis; t is on y axis

Intercepts :

x intercept : When t = 0 ; p = 5.66

y intercept : When p = 0 ; t = 8.5

3)

Pizzas	Marginal Utility	Marginal Utility
1	60	60
2	48	108
3	30	138
4	18	156
5	6	162
6	4	166
7	0	166

Twinkies	Marginal Utilty	Marginal Utility
1	44	44
2	34	76
3	24	100
4	20	120
5	16	136
6	12	148
7	4	152

4)

Just on the basis of MU, We wouold have bought a Pizza first because its MU is greater than that of Twinkies. But, since we also need to keep in mind the budget constraint, it is better if we compare on the basis of MU per dollar rather than just MU.

Pizzas	Marginal Utility	Total Utility	MU per dollar
1	60	60	10
2	48	108	8
3	30	138	5
4	18	156	3
5	6	162	1
6	4	166	0.666666667
7	0	166	0
Twinkies	Marginal Utility	Total Utility	MU per dollar
1	44	44	11
2	34	76	8.5
3	24	100	6
4	20	120	5
5	16	136	4
6	12	148	3
7	4	152	1

Now based on per dollar MU , we choose next item on the basis of comparing MU per dollar.

Buying sequence	Item	Total Cost
1st	Twinky	4
2nd	Pizza	10
3rd	Tinky	14
4th	Pizza	20
5th	Twinky	24
6th	Pizza	30
7th	Twinky	34

Thus max utility when : 4 twinkies and 3 pizzas

Max utility = 120 + 138

= 258

Utility for other combinations on or below budget constraint

Pizza	Twinky	Total Utility
1	7	212
2	5	244
3	4	258
4	2	232
5	1	206
0	8	152