Question

Suppose a consumer has the following utility function defined over the 2 goods X and Y: a. If this consumer originally consumed 10 units of X and 24 units of Y, and if the consumption of X were increased to 12 units, how much Y would be would the consumer be willing to give up and maintain the initial level of satisfaction

Answer 1

Y = 22 units (Approx)

Step-by-step explanation:

Note:

The utility function is not given, the utility function is as follows.

U(X ,Y) = 2X +
`16Y^(1/2)`

So,

U(X ,Y) = 2X +
`16Y^(1/2)`

When X = 10 and Y = 24 units

U(10 ,24) = 2(10) +
`16(24)^(1/2)`

U(10 ,24) = 98.4

U(10 ,24) = 99 Units (Approx)

So,

U(X ,Y) = 2X +
`16Y^(1/2)`

When X = 12 Find Y

99 units = 2(12) +
`16Y^(1/2)`

75 =
`16Y^(1/2)`

Y = 21.97

Y = 22 units (Approx)