Assume a firm has the following short-run production function: ) they would employ? ), what is the lowest level of labor ( q(L) = L + 2L² 3 Given the production function above, answer the following two questions: A) If this firm is going to maximize profits in the short-run by producing a strictly positive level of output ( Minimum level of labor = ) a wage of $10 ( ), what must be the price ( 9>0 Price = L B) Now suppose the firm must pay each unit a labor ( dollars L - w = 10 3 ). If this firm is maximizing their profits in the short-run by hiring 4 units of labor ( L = 4 L Р ) that they can charge for each unit of output they produce?

Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…

Consider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for production. The price of product is $p. The production function is Q (K; L) = 4L^1/4 K^1/4 . Assume that the hourly wage of workers is fixed at $w and the price per machine is $r Write out the optimal inputs quantities, L and K, as a function of parameters, p, w, and r

A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.