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# Suppose the production function of a firm is: Q =100L^0.5K^0.5 The price per unit of capital (r) and labor (w) are $40 and$50, respectively. a) Determine the type of returns to scale. b) If the firm is contracted to produce 1118 units of output, determine the quantity of capital and labor that the firm should use to minimize the total costs. c) Using bordered Hessian, prove that the second-order conditions for minimum is satisfied. d) Prove that the combination of capital and labor inputs derived in (b) is the efficient combination of capital and labor [Hint: Efficient combination of K and L is achieved when MPL/MPK= w/r].

OCW Scholar - Principles of Microeconomics