A firm’s production function is given by Q = AKL where A is a positive constant. Unit costs of capital and labour are $2 and $1, respectively. The firm spends a total of $1000 on these inputs.
(a) Write down the cost constraint.
(b) Write down expressions for the marginal products of capital and labour.
(c) Use the fact that at the maximum output, the ratio of the input prices is equal to the ratio of their marginal products to show that L = 2K.
(d) Use your answers to parts (a) and (c) to find the values of K and L which maximise output.