Question

Quantity of Pita Wraps	Marginal Utility	Quantity of Bubble Tea	Marginal Utility
1	60	1	40
2	42	2	30
3	30	3	21
4	12	4	15
5	0	5	6
6	-6	6	3
7	-10	7	0

Keegan has $30 to spend on Pita Wraps and Bubble Tea. The price of a Pita Wrap is $6 and the price of a glass of Bubble Tea is $3. Table 10-1 shows his total utility from different quantities of the two items.  


Refer to Table 10-1. What is Keegan's optimal consumption bundle?

Answer 1

At the optimal consumption bundle marginal utility per dollar is equal for each good.

Qw	MUw	MUw/Pw= MUw/$6	Qt	MUt	MUt/Pt= MUt/$3
1	60	10	1	40	13.33
2	42	7	2	30	10
3	30	5	3	21	7
4	12	2	4	15	5
5	0	0	5	6	2
6	-6	-1	6	3	1
7	-10	-1.67	7	0	0

MU per dollar is equal for both the goods at various quantities . But we can see that Keegan's income is $30. So, we have to see that bundle at which she exhaust all of her money income.

When she consumes 3 units of Pita wraps and 4 units of Bubble tea . Her marginal utility per dollar for both goods is equal to 5. And we can also see that this bundle also satisfies the budget constraint because Pw W + Pt T = M

(6)(3) + (3)(4)= 18+12 = $30 , i.e satisfies the budget constraint.

Hence, Keegan's optimal consumption bundle is (3 Pita wraps ,4 Bubble tea).