Question

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 1

Marginal productivity of labour, `(delz)/(delx)` = 6x – 4y

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

`((delz)/(delx))_{(1,2)}` = 6(1) – 4(1)

= 6 – 4

= 2

Marginal productivity of capital, `(delz)/(dely)` = 0 – 4x(1) + 3(2y)

= -4x + 6y

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

`((delz)/(dely))_{(1,2)}` = -4(1) + 6(2)

= -4 + 12

= 8