Question

Find the marginal productivities of capital (K) and labour (L) if P = 8L – 2K + 3K² – 2L² + 7KL when K = 3 and L = 1.

Answer 1

P = 8L – 2K + 3K² – 2L² + 7KL

Marginal productivity of labour, `(del"P")/(del"L")` = 8 – 0 + 0 – 2(2L) + 7K(1)

= 8 – 4L + 7K

Marginal productivity of labour when K = 3 and L = 1 is

`((del"P")/(del"L"))_((3;1))` = 8 – 4 + 21

= 29 – 4

= 25

Marginal productivity of capital, `(del"P")/(del"K")` = 0 – 2(1) + 3(2K) – 0 + 7L(1)

= -2 + 6K + 7L

Marginal productivity of capital when K = 3 and L = 1 is

`((del"P")/(del"K"))_((3;1))`

= -2 + 18 + 7

= -2 + 25

= 23