Managerial Economics Business Strategy Chapter 5 The Production
Managerial Economics & Business Strategy Chapter 5 The Production Process and Costs
Guiding the Production Process • Two Roles of the Manager • Produce as much as possible n How do you induce maximum worker effort from you employees? • Allow to earn tips • Profit sharing • Employ the right level of inputs n n How many workers/inputs do you hire? Hire labor until the value of marginal product of labor equals the wage • VMPL = w, where VMPL = P x MPL. n Hire capital until the value of marginal product of capital equals the rental rate • VMPK = r, where VMPK = P x MPK.
Can we do it? ? (number 11) • You are a manager for Herman Miller – a major manufacturer of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is Q=2(K 1/2)(L 1/2) where K represents capital equipment and L is labor. Your company has already spent a total of $10, 000 on the 4 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. If workers at the firm are paid a competitive wage of $100 and chairs can be sold for $200 each, what is your profit-maximizing level of output and labor usage? What is your maximum profit?
Typical Production Functions • Linear n n Q = F(K, L) = a. K + b. L Inputs are perfect substitutes • Leontief n n n Q = F(K, L) = min{b. K, c. L} Also called fixed proportions production function Need one left and one right shoe • Cobb-Douglas n n Q=F(K, L) = K 1/2 L 1/2 Shows that goods are substitutes, but not perfect substitutes
Leontief? ? ? • Q = F(K, L) = min{6 K, 5 L} • How much output is produced when 4 units of labor and 8 units of capital are employed? • Q = F(8, 4) = min{6*8, 5*4} = min{48, 20} • Q = 20 units of output
How do you find the MPL and MPK of the production function?
Can we do it? • How many units of labor should we employ if the wage rate is $2. 00, the price of the output is $10. 00, capital is fixed at 1, and the production function is given by Q = f(K, L) = K 0. 5 L 0. 5 • MPL = 0. 5 K 0. 5 L-0. 5 • VMPL = 10(0. 5(1)L-0. 5) = 5 L-0. 5 • Hire until VMP = w n n 5(1/L 0. 5) = 2 5/2 = L 0. 5 25/4 = L 6. 25 units of labor should be hired
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