Question

Consider the following Cobb-Douglas production function: y(K,L) = 2K^(0.4)*L^(0.6), where K denotes the amount of capital and L denotes the amount of labour employed in the production process.

a) Compute the marginal productivity of capital, the marginal productivity of labour, and the MRTS (marginal rate of technical substitution) between capital and labour. Let input prices be r for capital and w for labour. A representative firm seeks to minimize its cost of producing 100 units of output.

b) By applying the Lagrangian method, derive the optimal demands for capital and labour.

c) What is the impact of an increase in w on the optimal demand for labour?

d) If w = r = 1, what is the cost of producing 100 units of output?

Answer 1