A firm faces a production function given by q = √kl where q is the output, k is the firm's amount of capital equipment and I is the amount of labour-time employed. (a) In the short run, the amount of capital equipment is fixed at k 100. The rental rate for k is v= $1, and the wage rate for l is w = $2. Calculate the firm's short-run average cost (SAC) and short-run marginal cost (SMC) functions. Graph the SAC and the SMC curves for the firm. (b) (c) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC curve at its lowest point. Calculate the long-run total cost of production. For w= $2, v = = $1, graph the long-run total cost curve. Show that this is an envelope for the short-run curves computed in part (a).

A firm operates in the short run with the production function Q = 10 K0.5 L 0.5, where Q is output, K is capital, and L is labor. The price of capital is $100 per unit, and the wage rate is $50 per unit of labor. How many units of capital and labor should the firm use to minimize its total cost while producing 400 units of output?

A firm’s short-run production function is in the form of                        q = aLK +(bL^2)K −(cL^3)K , wherea, b, c > 0 are parameters. K is a constant. (a) Derive the marginal product of labor.(b) Find the level of L, expressed in terms of the parameters, at which the law ofdiminishing marginal product kicks in.

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL= $1 and PK = $1.What is the smallest total cost necessary to produce Q = 100?

In the short run, a firm which has production function f(L, M) = 4L1/2M1/2 must use 4 machines. If the cost of labor is £4 per unit and the cost of machines is £4 per unit, what is the short-run total cost of producing 48 units of output? Use Lagrange

A firm has the following Cobb-Douglas production function:         q=(L^α)(K^1-α)0<α < 1 is a parameter. Suppose in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20.(a) Derive the marginal cost of the firm (expressed in terms of α and q).(b) Derive the average variable cost of the firm (expressed in terms of α and q).(c) Derive the cost function of the firm.

Please help solve for (b) what is long run cost in a?

A firm's production function is given by Q = 2K2 L/2 Unit capital and labor costs are $4 and $9, respectively. a) What is the cost function for the firm? b) If the firm is contracted to provide 144 units of output, what is the firm's constraint? Constraint: b) Find the values of K and L which minimize total input costs under the production constraint. K = units L= units