(a)  Find the short-run cost function, SRTC(q) and marginal cost function, MC(q), assuming that k = 27, and letting w and v denote the price of labor and capital. (b)  Find the long-run cost function and the long-run marginal cost function (L and k are both chosen optimally). (c)  Give a formal definition of increasing, decreasing, and constant returns to sale, and determine if the production function above exhibits increasing, decreasing or constant returns to scale. (d)  Derive the firm’s contingent labor demand function

An accountant for a car rental company was recently asked to report the firm's costs of producing various levels of output. The accountant knows that the most recent estimate available of the firm's cost function is   C(Q) = 100 + 10Q + Q^2, where costs are measured in thousands of dollars and output is measured in thousands of hours rented. a. What is the average fixed cost of producing 2 units of output? b. What is the average variable cost of producing 2 units of output? c. What is the average total cost of producing 2 units of output? d. What is the marginal cost of producing 2 units of output? e. What is the relation between the answers to (a), (b), and (c) above? Is this a general property of average cost curves?

c) If a business has a long-run cost (TC) function given by TC = aq° – bq² + cq where q = the rate of output, and a, b and c are all positive parameters, show that average cost is always positive if and only if b² 0.

Given Q=100K^0.5L^0.5 ,w= 30, r=40 i) Find the quantity of labour and capital that the firm should use in order to minimize the cost of producing 1444 units of output ii) What is this minimum cost?