Suppose that the utility function for two goods X and Y is given by , and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility?

Question

Suppose that the utility function for two goods X and Y is given by  , and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility? ​

Quizplus · Accepted Answer

To maintain the same level of utility, we need to equate the initial utility function with the new one when the consumer buys 2 units of Y and some X. 
11ea984b_aff8_5d09_9029_8714db686f03_TB4005_11 = 11ea984b_aff8_ab2c_9029_4b999f658cf6_TB4005_11
2X + 6Y = 2Y + 4X
2X = 4Y
X = 2Y/4
X = Y/2
So, the consumer must buy 1 unit of X if they buy 2 units of Y to maintain the same level of utility. Thus, the answer is option C.

Suppose That the Utility Function for Two Goods X and Y