Question

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Refer to the table above. Assume that the price of good X is $2 per unit, the price of good Y is $5 per unit, and that the consumer spends a total of $44 on both goods.  What combination of X and Y will the consumer purchase in order to maximize utility?

	A.	We don’t have enough information of determine his consumption bundle.
	B.	He will spend more on X than on Y because X is less expensive than Y.
	C.	He will purchase 4 units of Y and 4 units of X.
	D.	He will purchase 2 units of Y and 2 units of X.
	E.	He will purchase 6 units of Y and 7 units of X.

Answer 1

Option (E).

Utility is maximized when (MUX/PX) = (MUY/PY), where

MU = Change in Total utility (TU) / Change in Quantity (Q)

Budget constraint: 44 = 2X + 5Y

QX	TUX	MUX	MUX/PX	QY	TUY	MUY	MUY/PY
1	24			1	85
2	42	18	9	2	130	45	9
3	56	14	7	3	160	30	6
4	66	10	5	4	185	25	5
5	74	8	4	5	200	15	3
6	80	6	3	6	210	10	2
7	84	4	2	7	215	5	1

Therefore, (MUX/PX) = (MUY/PY) is satisfied for following bundles:

(1) (MUX/PX) = (MUY/PY) = 9 when X = 2, Y = 2 and Total cost ($) = 2 x 2 + 5 x 2 = 4 + 10 = 14 < Budget

(2) (MUX/PX) = (MUY/PY) = 5 when X = 4, Y = 4 and Total cost ($) = 2 x 4 + 5 x 4 = 8 + 20 = 28 < Budget

(3) (MUX/PX) = (MUY/PY) = 3 when X = 6, Y = 5 and Total cost ($) = 2 x 6 + 5 x 5 = 12 + 25 = 37 < Budget

(4) (MUX/PX) = (MUY/PY) = 2 when X = 7, Y = 6 and Total cost ($) = 2 x 7 + 5 x 6 = 14 + 30 = 44 = Budget