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

Answer:

Y = 22 units (Approx)

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)