a) The Open Chemical Ltd obtained the following estimate of the firm’s Production (Leontief production function): Q = F(K, L) = min {10.4K, 11L} How much output is produced when 22 units of labour and 19 units of capital are employed?
b) Prove the following (K = capital and L = labour):
(i) K/L = MPL/MPK;
(ii) The sum of the exponents of labour and capital in a Cobb–Douglas production function
measures the returns to scale; and
(iii) The exponents a and b of a production function Q = ALaKb are estimates of the output elasticities of labour and capital respectively
b) Prove the following (K = capital and L = labour):
(i) K/L = MPL/MPK;
(ii) The sum of the exponents of labour and capital in a Cobb–Douglas production function
measures the returns to scale; and
(iii) The exponents a and b of a production function Q = ALaKb are estimates of the output elasticities of labour and capital respectively