Marshallian Demand function

^· U(x,y) = x^0.6 y^0.4

^· M = p_x x + p_y y……………..(1) income function

^· L = x^0.6 y^0.4 + λ( M - p_x x - p_y y)

^· L = x^0.6 y^0.4 + λ M - λ p_x x - λ p_y y

^· DL/dx = 0.6 x ^-0.4 y^0.4 - λ p_x……….(2) differentiation WRT x

^· DL/dy = 0.4 x ^0.6 y ^-0.6- λ p_y……….(3) differentiation WRT y

By dividing equation 2 and 3, we get

· y = 2 p_x x/ 3 p_y ……….(4)

· x = 3 p_y y / 2 p_x,,……….(5)

By putting equation 4 and 5 in equation 1, to get Marshallian Demand function

· y^m = 2M / 5p_y

· x^m = 3M / 5 p_x

 

Hicksian Demand function

^· U(x,y) = x^0.6 y^0.4

^· M = p_x x + p_y y……………..(6) income function

^· L = p_x x + p_y y + λ (U - x^0.6 y^0.4 )

^· L = p_x x + p_y y + λ U - λ x^0.6 y^0.4 )

· DL/dx = p_x – λ 0.6 x ^-0.4 y^0.4……….(7) differentiation WRT x

· DL/dy = p_y - λ 0.4 x ^0.6 y ^-0.6……….(8) differentiation WRT y

By dividing equation 7 and 8, we get

· y = 2 p_x x/ 3 p_y ……….(9)

· x = 3 p_y y / 2 p_x,,……….(10)

By putting equation 9 and 10 in utility function to get Hicksian Demand function

· x^h = U [ 3 p_y/ 2 p_x] ^0.4

· y^h = U [ 2 p_x / 3 p_y] ^0.6

 

Solution 1 : - Marshallian Demand for x : - x^m = 3M / 5 p_x

Solution 2: - Marshallian Demand for y :- y^m = 2M / 5p_y

Solution 3: - Hicksian Demand for x : - x^h = U [ 3 p_y/ 2 p_x] ^0.4

Solution 4: - Hicksian Demand for y: - y^h = U [ 2 p_x / 3 p_y] ^0.6