With reference to learning objectives and textbook Managerial Economics and Organizational Architecture by Brickley, Smith, and Zimmerman, 6th edition, A Production Grid and Isoquants, Short-Run Production Possibilities, Short-Run Costs, Short Run-Profit Maximization by a Perfectly Competitive.

Consider a firm that is perfectly competitive in its input and output markets. This firm produces a single homogeneous product using two inputs: labor (L) and capital (K). Both inputs (K and L) are flexible in the long run, but capital (K) is fixed in the short run. We denote the marginal productivity of labor as MPL and the marginal productivity of capital as MPK. For this firm, the marginal productivities of both capital and labor decline with the amount used of that input. At the same time, the marginal productivity of each input is positively related to the amount used by the other input. More formally: MPL/L<0, MPK/K<0, MPL/K>0, and MPK/L>0.

At present, the price of the firm's output is $3 per unit, the firm's wage rate (w) is $20 per hour and the Marginal Product of Labor (MPL) is 5 units per hour. As for Capital, the user cost of capital (r) is $ 2000 per month and the Marginal Product of Capital (MPK) is 1000 units per month.

Based on the available information, carefully explain what adjustments in the use of inputs, if any, you believe the firm would need to make to maximize profits or minimize losses both in the short run and in the long run. As part of the answer carefully explain the reasoning, while also outlining any caveats we may have on additional information needed. Specifically, explain what additional information we would need in order to decide whether profit maximization calls for an increase or decrease in the levels of production in the long run.

Please provide references as well.