question_answer

Let production function of firm Z be\[Q=6{{L}^{1/3}}{{K}^{2/3}}\].Find out maximum possible output that the firm can produce with 1,000 units of labour and 729 units of K.

Answer:

Given, \[Q=6{{L}^{1/3}}{{K}^{2/3}}\Rightarrow 6{{(1,000)}^{1/3}}{{(729)}^{2/3}}\Rightarrow 6\times {{(10)}^{1}}\times {{(9)}^{2}}\Rightarrow 6\times 10\times 81\Rightarrow Q=4,860\] So, the maximum output that firm 'Z' can produce with 1,000 units of L and 729 units of K is 4,860.     (1)