A firm’s production function is given by Q = K²L/K + 4L where K and L denote capital and labour, respectively.
(a) Show that this production function is homogeneous of degree 2.
(b) Calculate the marginal products, MP_K and MP_L and hence verify that Euler’s theorem holds for this function. The firm currently uses 40 units of capital and 15 units of labour.
(c) Calculate the marginal rate of technical substitution and give a brief interpretation of this number.
(d) The firm decides to reduce capital by 0.5 units. Use the small increments formula to estimate the increase in labour needed to increase the total output by 1 unit.