Managerial Economics Business Strategy Chapter 5 The Production

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

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

Production Analysis • Production Function n n Q = F(K, L) 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, 3 e. ©The Mc. Graw-Hill Companies, Inc. , 1999

Total Product • Cobb-Douglas Production Function • Example: Q = F(K, L) = K. 5 L. 5 n n K is fixed at 16 units. 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, 3 e. ©The Mc. Graw-Hill Companies, Inc. , 1999

Marginal Product of Labor • MPL = DQ/DL • Measures the output produced by the last worker. • Slope of the production function Michael R. Baye, Managerial Economics and Business Strategy, 3 e. ©The Mc. Graw-Hill Companies, Inc. , 1999

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

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

Linear Isoquants • Capital and labor are perfect substitutes K Increasing Output Q 1 Q 2 Q 3 L Michael R. Baye, Managerial Economics and Business Strategy, 3 e. ©The Mc. Graw-Hill Companies, Inc. , 1999

Leontief Isoquants • Capital and labor are perfect complements • Capital and labor are used in fixedproportions Q K Q Q 1 3 2 Increasi ng Output Michael R. Baye, Managerial Economics and Business Strategy, 3 e. ©The Mc. Graw-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 K Q 3 Q Q 2 Increasing Output 1 L Michael R. Baye, Managerial Economics and Business Strategy, 3 e. ©The Mc. Graw-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 C 0 C 1 L K New Isocost Line for a decrease in the wage (price of labor). Michael R. Baye, Managerial Economics and Business Strategy, 3 e. ©The Mc. Graw-Hill Companies, Inc. , 1999 L

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

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

Cost Analysis • Types of Costs n n Fixed costs (FC) Variable costs (VC) Total costs (TC) Sunk costs Michael R. Baye, Managerial Economics and Business Strategy, 3 e. ©The Mc. Graw-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) VC(Q): Costs that vary with output FC: Costs that do not vary with output F C Q Michael R. Baye, Managerial Economics and Business Strategy, 3 e. ©The Mc. Graw-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 C(Q) = VC + FC VC( Q) F C Q Michael R. Baye, Managerial Economics and Business Strategy, 3 e. ©The Mc. Graw-Hill Companies, Inc. , 1999

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

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

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

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

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

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

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

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

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