Suppose that an indifference curve for two goods, X and Y, has the equation . If 30 units of X are purchased, how many units of Y must be purchased to remain on this indifference curve?
A) units of Y.
B) 57,600 units of Y.
C) 64 units of Y.
D) 87 units of Y.
E) 101 units of Y.

Question

Suppose that an indifference curve for two goods, X and Y, has the equation  . If 30 units of X are purchased, how many units of Y must be purchased to remain on this indifference curve? ​
A) units of Y. 
B) 57,600 units of Y. 
C) 64 units of Y. 
D) 87 units of Y. 
E) 101 units of Y.

Quizplus · Accepted Answer

To remain on the same indifference curve, the consumer must be equally satisfied with the combination of X and Y. This means that the combination of (30 units of X, Y) must provide the same level of utility as the combination of (X*, 64 units of Y), where X* is an unknown quantity of X.

To find X*, we need to solve the equation of the indifference curve for X:

X = 2Y^2

Substitute 30 for X and solve for Y:

30 = 2Y^2

Y^2 = 30/2 = 15

Y = sqrt(15) = 3.87 (approximately)

Therefore, to remain on the same indifference curve, the consumer must purchase 64 units of Y (approximately), given that they are already purchasing 30 units of X. The answer is C) 64 units of Y.

Suppose That an Indifference Curve for Two Goods, X and Y