The production function for a firm which use capital and labor as input is1 f(k, l) = 2k 1 3 l 1 3 . The price for its output is p = 12, and the...

The production function for a firm which use capital and labor as input is1 f(k, l) = 2k 1 3 l 1 3 . The price for its output is p = 12, and the price for capital and labor input are v = 2 and w = 4. (a) Write down firm's profit maximization problem in terms of input choices k and l. (b) Solve this profit maximization to derive firm's optimal input demands k ∗ and l ∗ . (c) When the firm uses optimal input level k ∗ and l ∗ , what are the firm's output quantity and corresponding profit?