A second firm's production function is given by the equation
Q = 12L.5K.5.
Input prices are $36 per labor unit and $16 per capital unit, and P = $10.
a. In the short run, the firm has a fixed amount of capital, K = 9. Create a spreadsheet to model this production setting. Determine the firm's profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your spreadsheet's optimizer.
b. Once again, the firm seeks to produce the level of output found in part (a) by adjusting both labor and capital in the long run. Find the least-cost input proportions. Confirm that MPL ∕ PL = MPK ∕ PK.
c. Suppose the input price of labor falls to 18. Determine the new least-cost input amounts in the long run. Provide an intuitive explanation for the change in inputs caused by the lower labor price.