Question

Consider the fixed proportions case where U(x,y) = min[xy] In the fixed proportions case, the demand function for x is x _____and the demand function for y is y____

Plugging these demand functions back into the utility function yields the indirect utility function which equals V= _____
Starting with the indirect utility function, then solving for 1 and letting E =_____

Answer 1

In the fixed proportions case: x = y, y = x,
`\(V = \min(x,y) = x = y\), and \(E = xP_x + yP_y\)`.

In the perfect substitutes case: x = 0 when
`\(P_y > P_x\), y = 0 when \(P_x > P_y\), V = E, and E = I`.

In the fixed proportions case where
`\(U(x,y) = \min(x,y)\)`:

- The demand function for x is x = y.

- The demand function for y is y = x.

- Plugging these demand functions back into the utility function yields the indirect utility function which equals V = min(x,y) = x = y.

- Starting with the indirect utility function, then solving for I and letting E = I yields the expenditure function which takes the form of
`\(E = xP_x + yP_y\)`.

In the case of perfect substitutes where U(x,y) = x + y:

- When
`\(P_y > P_x\)`, the demand function for x is x = 0 and the demand function for y is
`\(y = E/P_y\)`.

- When
`\(P_x > P_y\)`, the demand function for y is y = 0 and the demand function for x is
`\(x = E/P_x\)`.

- Plugging these demand functions back into the utility function yields the indirect utility function which can be written in general terms as V = E.

- Starting with the indirect utility function, then solving for E and letting E = I yields the expenditure function which takes the form of E = I.

Question:

Consider the fixed proportions case where U(x,y) = min[x,y]

In the fixed proportions case, the demand function for x is x = ___ and the demand function for y is y = ____.

Plugging these demand functions back into the utility function yields the indirect utility function which equals V = _____

Starting with the indirect utility function, then solving for 1 and letting E = I yields the expenditure function which takes the form of E = ___

Consider the case of perfect substitutes where U(x,y)-x+y

In this perfect substitutes case, when
`P_y > P_x` the demand function for x is x = ___ and the demand function for y is y = __.

When
`p_x > P_y` the demand function for y is y = ___ and the demand function for y is x = __ when and the demand function for y is x = __.

Plugging these demand functions back into the utility function yields the indirect utility function which can be written in general terms as V = __.

Starting with the indirect utility function, then solving for l and letting E = I yields the expenditure function which takes the form of E = __.