Question

Jane has a budget of $15 to spend at the local scientific store. Her two favorite items are beakers (Product X) which cost $3 and petri dishes (Product Y) which cost $2. In the schedule below you can see the marginal utility for each of her favorite items. Which combination would maximize Jane’s utility?

Product X	Product Y
Quantity	MUx	Quantity	MUy
1	32	1	24
2	28	2	20
3	24	3	16
4	5	4	12
5	16	5	8

4 Beakers and 1 petri dishes

5 Beakers and 0 petri dishes

Answer 1

Product X (Price = 3)			Product Y (Price = 2)
Quantity	MUx	MUx/Px	Quantity	MUy	Muy/Py
1	32	10.6667	1	24	12
2	28	9.33333	2	20	10
3	24	8	3	16	8
4	5	1.66667	4	12	6
5	16	5.33333	5	8	4

Price of beakers (Product X) = $3

Price of petri dishes (Product Y) = $2

From the given data, calculate the marginal utility of money expenditure

MU of money expenditure = MU/Price

The utility maximizing condition is MUx/Px = MUy/Py

The expenditure should be equal to the budget or income.

In the question the budget is given $15

From the table it can be seen that only in one combination of both X and Y the marginal utility of money expenditure of both the goods is same.

At 3 units of Product X and at 3 units of Product Y, the marginal utility of money expenditure is same (MUx/Px = MUy/Py)

In this combination, the expenditure will be

3 of X = 3*$3 = $9

3 of Y = 3*$2 = $6

Total Expenditure will be $15 ($9 + $6).

The combination would maximize Jane’s utility will be 3 Beakers and 3 petri dishes.