Question

Consider the fixed proportions case where U(x,y) = min[xv/ 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 = 1 yields the expenditure function which takes the form of Consider the case of perfect substitutes where U(x,y)-x+y In this perfect substitutes case, when Py Px the demand function for x is x- When px>Py the demand function for y is y ▼ and the demand function for y is y- 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 = 1 yields the expenditure function which takes the form of

Answer 1

U(x, y) = min(x, y) P_x x + P_y y = I equation (1) x = y equation (2) P_x x + P_y x = I x = I/P_x + P_y y = I/P_x + P_y utility u = min (I/P_x + P_y, I/P_x + P_y) V = I/P_x + P_y u(x, y) = x + y If P_y > P_x implies only x will consume rightarrow x is cheaply P_x x + P_y y = I implies x = I/P_x y = 0 If P_x > P_y implies only y will consume rightarrow y is cheaply P_x x + P_y y = I, y = I/P_y x = 0 V(x, y) = I/P_x equation (A) If P_x < P_y V(x, y) = I/P_y equation (B) If P_y < P_x (A) implies E = I = V^bar P_x, P_x < P_y (B) implies E = I = V^bar P_y, P_y < P_x