Question

Suppose that as a consumer you have $34 per month to spend for munchies, either on pizzas which cost $6 each or on twinkies which cost $4 each. Suppose further that your preferences are given by the following total utility table.

	Count
	1	2	3	4	5	6	7
TU for Pizza	60	108	138	156	162	166	166
TU for Twinkies	44	76	100	120	136	148	152

1. Use the utility maximizing rule to identify the consumer equilibrium, that is, what combination of twinkies and pizzas will maximize your total utility. (Hint: What should you purchase second, third, etc. until you exhaust your budget?)

2. Confirm that the consumer equilibrium generates the highest combined total utility of any affordable combination of goods.

Answer 1

MU = change in TU

MU/P = Marginal utility/price of the good

Q	TU(PIZZA)	MU(PIZZA)	MU/P	TU(TWINKIES)	MU(TWINKIES)	MU/P
1	60	60	10	44	44	11
2	108	48	8	76	32	8
3	138	30	5	100	24	6
4	156	18	3	120	20	5
5	162	6	1	136	16	4
6	166	4	0.67	148	12	3
7	166	0	0	152	4	1

The consumer will maximize his utility where the MU/P for Pizza = MU/P for Twinkies

Budget = 34

so, the consumer will first buy 1st unit of twinkies as MU/P is highest then 1st unit of Pizza as MU/P is 2nd highest and then 2nd unit of both pizza and twinkies and goes on consuming the unit in the same manner until he exhausts his budget.

so, he will buy 3 units of Pizza and 4 units of Twinkies as it will also exhaust his budget

Total utility = 138+120 = 258

Suppose he buys 2 units of P and 5 units of T, then TU = 108+136 = 244

OR 4 units of P and 2 units of T, then TU = 156+76 =232

OR, 3 units of both, then TU = 138+100 = 238

So, TU is maximum at any affordable combinations as per the utility-maximizing rule