1. A firm's production technology is Y = A * K^0.25 * L^0.75, where the technology level A=8. For such a production function the marginal product of capital is MPK = 0.25 * 8 * K^-0.75 * L^0.75 The firm is stuck with K=81 but is flexible on workers. If the price of the firm's output is P=20 and the cost of a unit of capital is R=8.33, how many workers should the firm have? Round your answer to the whole worker.   The answer is 10. I just need to know how to solve it

5. Selpats produces pens with the production function f(k, l) = 200vkl. The price of capital is wk = 40 and the price of labor is wL = 10. (i) Determine the optimal input bundle for producing y pens in the long run and find the long-run cost function. (ii) Determine the optimal input bundle for producing y = 10,000 pens in the long run. (iii) Now suppose that capital is fixed at k = 25 in the short run. Find the short-run total cost function and the short-run marginal cost function. Explain the relationship between the short-run and long-run marginal costs when y = 10,000. (iv) Suppose that the price of output is p. Which value of y maximizes short-run profit? р.

A firm has two opportunities for a new plant location, one is in China and the other is inMexico. The firm's production function is given by q = L 0.5 K 0.5 , In China, the cost of laboris w=$15 and the cost of capital is r=$5. In Mexico, w=$10 and r=$10. The firm wants toproduce 100 units of output. Which location should the firm choose for their new plant?Explain why.Note: Please round the optimal amounts of capital and labor at each location to the nearest whole number when making your calculations.Hint: cost-minimization rule.

Let us consider the cost implications of the short-run production schedule from assignment number 7, where capital was fixed at 2 units of capital. Labor:  0 1 2 3 4 5 6 7 8 9 Output:  0 6 24 60 120 170 210 240 260 270 In this scenario, since we only have two inputs (Capital and Labor), and since the amount of capital is fixed, the cost of total cost capital would also be Total Fixed Cost (TFC) and since labor is variable, the total cost of labor would be Total Variable Cost (TVC). In that context, assume that the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is also $30 per unit of labor per period. (a) Use this information set up a diagram (using excel) that shows total cost (TC) and total variable cost (TVC) of the firm per period in the short run with the level of output on the horizontal axi