Suppose that the ¯rm's production technology is F(K;L) where K is the level of capital and L is the level of labour. Suppose the cost of capital is r, and the cost of labour is w.

(a) Describe the slope of the isocost and isoquant curves, and hence derive a relationship between the productivity of capital and the productivity of labour.

(b) Would the relationship that you derived in (a) still hold if (i) F(K;L) = K + L or (ii) F(K;L) = min(K;L). Explain your answer.