Question

Help this is too hard

Answer 1

The utility function
`\(U(x, y) = x^(1/3) + y^(1/3)\)` indicates net substitutes
`(\((\partial U)/(\partial x) > 0\)` and
`\((\partial U)/(\partial y) > 0\))` and gross substitutes
`(\((\partial^2 U)/(\partial x \partial y) < 0\))`, making the correct choice (c) Net substitutes and gross substitutes.

In this utility function
`\(U(x, y) = x^(1/3) + y^(1/3)\)`, the partial derivatives provide insights into the relationship between goods x and y.

Calculate the partial derivatives with respect to x and y:

`\[ (\partial U)/(\partial x) = (1)/(3)x^(-2/3) \]\[ (\partial U)/(\partial y) = (1)/(3)y^(-2/3) \]`

Now, examine the signs:

1.
`\((\partial U)/(\partial x) > 0\) and \((\partial U)/(\partial y) > 0\)`: Net substitutes

2.
`\((\partial^2 U)/(\partial x \partial y) = (\partial^2 U)/(\partial y \partial x) < 0\)`: Gross complements

So, the correct answer is:

(c) Net substitutes and gross substitutes