If the production function is z = 3x2 – 4xy + 3y2 where x is the lab

1.	If the production function is z = 3x2 – 4xy + 3y2 where x is the labour and y is the capital, find the marginal productivities of x and y when x = 1, y = 2.
Answer» Marginal productivity of labour, \(\frac{∂z}{∂x}\) = 6x – 4y Marginal productivity of labour when x = 1, y = 2 is \((\frac{∂z}{∂x})_{(1,2)}\) = 6(1) – 4(1) = 6 – 4 = 2 Marginal productivity of capital, \(\frac{∂z}{∂y}\) = 0 – 4x(1) + 3(2y) = -4x + 6y Marginal productivity of capital when x = 1, y = 2 is \((\frac{∂z}{∂y})_{(1,2)}\) = -4(1) + 6(2) = -4 + 12 = 8

If the production function is z = 3x2 – 4xy + 3y2 where x is the labour and y is the capital, find the marginal productivities of x and y when x = 1, y = 2.

Answer»

Marginal productivity of labour, \(\frac{∂z}{∂x}\) = 6x – 4y

Marginal productivity of labour when x = 1, y = 2 is

\((\frac{∂z}{∂x})_{(1,2)}\) = 6(1) – 4(1)

= 6 – 4

= 2

Marginal productivity of capital, \(\frac{∂z}{∂y}\) = 0 – 4x(1) + 3(2y)

= -4x + 6y

Marginal productivity of capital when x = 1, y = 2 is

\((\frac{∂z}{∂y})_{(1,2)}\) = -4(1) + 6(2)

= -4 + 12

= 8