Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Managerial Economics & Business Strategy Chapter 5 The Production Process and Costs

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Overview I. Production Analysis n Total Product, Marginal Product, Average Product n Isoquants n Isocosts n Cost Minimization II. Cost Analysis n Total Cost, Variable Cost, Fixed Costs n Cubic Cost Function n Cost Relations III. Multi-Product Cost Functions

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Production Analysis Production Function n Q = F(K,L) n The maximum amount of output that can be produced with K units of capital and L units of labor. Short-Run vs. Long-Run Decisions Fixed vs. Variable Inputs

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Total Product Cobb-Douglas Production Function Example: Q = F(K,L) = K.5 L.5 n K is fixed at 16 units. n Short run production function: Q = (16).5 L.5 = 4 L.5 n Production when 100 units of labor are used? Q = 4 (100).5 = 4(10) = 40 units

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Marginal Product of Labor MP L = Q/ L Measures the output produced by the last worker. Slope of the production function

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Average Product of Labor AP L = Q/L This is the accounting measure of productivity.

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Q L Q=F(K,L) Increasi ng Margina l Returns Diminishing Marginal Returns Negative Marginal Returns MP AP Stages of Production

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Isoquant The combinations of inputs (K, L) that yield the producer the same level of output. The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output. L

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Linear Isoquants Capital and labor are perfect substitutes Q3Q3 Q2Q2 Q1Q1 Increasing Output L K

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Leontief Isoquants Capital and labor are perfect complements Capital and labor are used in fixed- proportions Q3Q3 Q2Q2 Q1Q1 K Increasi ng Output

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Cobb-Douglas Isoquants Inputs are not perfectly substitutable Diminishing marginal rate of technical substitution Most production processes have isoquants of this shape Q1Q1 Q2Q2 Q3Q3 K L Increasing Output

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Isocost The combinations of inputs that cost the producer the same amount of money For given input prices, isocosts farther from the origin are associated with higher costs. Changes in input prices change the slope of the isocost line K L C1C1 C0C0 L K New Isocost Line for a decrease in the wage (price of labor).

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Cost Minimization Marginal product per dollar spent should be equal for all inputs: Expressed differently

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Cost Minimization Q L K Point of Cost Minimizati on Slope of Isocost = Slope of Isoquant

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Cost Analysis Types of Costs n Fixed costs (FC) n Variable costs (VC) n Total costs (TC) n Sunk costs

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Total and Variable Costs C(Q): Minimum total cost of producing alternative levels of output: C(Q) = VC + FC VC(Q): Costs that vary with output FC: Costs that do not vary with output $ Q C(Q) = VC + FC VC( Q) FCFC

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Fixed and Sunk Costs FC: Costs that do not change as output changes Sunk Cost: A cost that is forever lost after it has been paid $ Q FCFC C(Q) = VC + FC VC( Q)

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Some Definitions Average Total Cost ATC = AVC + AFC ATC = C(Q)/Q Average Variable Cost AVC = VC(Q)/Q Average Fixed Cost AFC = FC/Q Marginal Cost MC = C/ Q $ Q ATC AVC AF C MC

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Fixed Cost $ Q ATC AVC MC ATC AVC Q0Q0 AFC Fixed Cost Q 0 (ATC-AVC) = Q 0 AFC = Q 0 (FC/ Q 0 ) = FC

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Variable Cost $ Q ATC AVC MC AVC Variable Cost Q0Q0 Q 0 AVC = Q 0 [VC(Q 0 )/ Q 0 ] = VC(Q 0 )

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 $ Q ATC AVC MC ATC Total Cost Q0Q0 Q 0 ATC = Q 0 [C(Q 0 )/ Q 0 ] = C(Q 0 ) Total Cost

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Economies of Scale LRAC $ Output Economies of Scale Diseconomies of Scale

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 An Example n Total Cost: C(Q) = 10 + Q + Q 2 n Variable cost function: VC(Q) = Q + Q 2 n Variable cost of producing 2 units: VC(2) = 2 + (2) 2 = 6 n Fixed costs: FC = 10 n Marginal cost function: MC(Q) = 1 + 2Q n Marginal cost of producing 2 units: MC(2) = 1 + 2(2) = 5

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Multi-Product Cost Function C(Q 1, Q 2 ): Cost of producing two outputs jointly

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Economies of Scope C(Q 1, Q 2 ) < C(Q 1, 0) + C(0, Q 2 ) It is cheaper to produce the two outputs jointly instead of separately. Examples?

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Cost Complementarity The marginal cost of producing good 1 declines as more of good two is produced: MC 1 / Q 2 < 0. Examples?

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Quadratic Multi-Product Cost Function C(Q 1, Q 2 ) = f + aQ 1 Q 2 + (Q 1 ) 2 + (Q 2 ) 2 MC 1 (Q 1, Q 2 ) = aQ 2 + 2Q 1 MC 2 (Q 1, Q 2 ) = aQ 1 + 2Q 2 Cost complementarity: a < 0 Economies of scope: f > aQ 1 Q 2 C(Q 1,0) + C(0, Q 2 ) = f + (Q 1 ) 2 + f + (Q 2 ) 2 C(Q 1, Q 2 ) = f + aQ 1 Q 2 + (Q 1 ) 2 + (Q 2 ) 2 f > aQ 1 Q 2 : Joint production is cheaper

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 A Numerical Example: C(Q 1, Q 2 ) = Q 1 Q 2 + (Q 1 ) 2 + (Q 2 ) 2 Cost Complementarity? Yes, since a = -2 < 0 MC 1 (Q 1, Q 2 ) = -2Q 2 + 2Q 1 Economies of Scope? Yes, since 90 > -2Q 1 Q 2 Implications for Merger?