- The utility function of an individual takes the form (...

- The utility function of an individual takes the form ( U(x, y)=(x+2)^{2}(y+3)^{3} ) and the current consumption bundle is ( (x, y)=(2,1) ). a) Calculate the current utility level. b) Calculate the marginal utilities for each commodity when the consumption bundle is ( (x, y)=(2,1) ) c) Calculate the percentage change in ( x ) by using differentials if he/she wants to increase his/her utility level by ( 10 % ) (hold ( y ) as constant).

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Transcript

0:00 Hi there.

00:01 So for this problem, we are given the following function that depends on x and y.

00:07 So this is the utility function that is x plus 2 and that to the square times y plus 3 and that to the 3.

00:17 And the current consumption bundle is xy that equals to 2 1.

00:25 Okay.

00:27 So for part a of this problem, we are asked about to calculate the current utility level.

00:34 So then what we need to do is to substitute the values that we are given here.

00:43 So that will be then the value of x, that is 2 in this case, 2 plus 2, that to the square plus 1 plus 3, and that to the 3.

00:52 Simplifying this, this will give us the value of 1 ,024.

00:57 So that will be the solution for part a of this problem.

01:01 Now for part b, we are asked calculate the marginal utilities for hide it.

01:16 Okay, so for part b, the marginal utility of ads, mu ads, will be the partial derivative of you with respect to ads, which equals to two times adds plus two, that times y plus three to the three.

01:37 Now we just evaluate this at the value that we are given.

01:41 So that will be two times two plus two.

01:45 Then this one plus three and that to the three.

01:48 This will give us a value of 512.

01:53 Okay...

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