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 How do you induce maximum worker effort from you employees? Allow to earn tips Profit sharing Employ the right level of inputs 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. 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(K1/2)(L1/2) 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 Q = F(K,L) = aK + bL Inputs are perfect substitutes Leontief Q = F(K,L) = min{bK,cL} Also called fixed proportions production function Need one left and one right shoe Cobb-Douglas Q=F(K,L) = K1/2L1/2 Shows that goods are substitutes, but not perfect substitutes

Leontief??? Q = F(K,L) = min{6K, 5L} 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) = K0.5L0.5 MPL = 0.5K0.5L-0.5 VMPL = 10(0.5(1)L-0.5) = 5L-0.5 Hire until VMP = w 5(1/L0.5) = 2 5/2 = L0.5 25/4 = L 6.25 units of labor should be hired