MANAGERIAL ECONOMICS A Mathematical Approach M. J. ALHABEEB L. JOE MOFFITT Isenberg School of Management University of Massachusetts Amherst, MA, USA WILEY A JOHN WILEY & SONS, INC., PUBLICATION
PREFACE xix UNIT I METHODOLOGICAL PRELIMINARIES 1 Qualitative Fundamentals 3 1.1 Economic Theory and Managerial Economics 3 1.2 Some Methodological Fallacies 5 1.3 Paradigms, Models, and the Scientific Method 6 1.4 The Descriptive and Prescriptive Treatments 8 1.5 The Profit Function: Accounting versus Economics 8 1.6 Entrepreneurship, Management, and Leadership 9 Summary 11 Key Terms 12 Exercises 12 2 Quantitative Fundamentals 13 2.1 Introduction 13 2.2 Functions - 14 2.3 Exponents 16 2.4 Logarithms and the Number e 18 2.5 Differential Calculus 19 2.6 Multivariate and Equality Constrained Optimization 22 2.7 Inequality Constrained Optimization: Linear Programming 30 2.8 Selected Statistical Concepts 30 2.9 Maximum Likelihood Estimation 36 2.10 Ordinary and Nonlinear Least Squares Estimation 37
Summary 38 Key Terms 40 List of Formulas 40 Exercises 42 UNIT II DECISIONS AT THE CONSUMER LEVEL 3 Theory of Consumer Choice 47 3.1 Consumer Preferences 3.1.1 Indifference Curve 3.1.2 Marginal Rate of Substitution (MRS) 3.1.3 Nontypical Indifference Curves 3.2 Consumer's Affordability 3.2.1 Budget Line 3.2.2 Slope of the Budget Line 3.2.3 Shift, Swing, and Kink of the Budget Line The Shift The Swing The Kink 3.2.4 Three-Dimensional Budget 3.3 The Optimal Choice 3.3.1 Interior and Corner Solutions 3.3.2 Utility and Its Measurability 3.3.3 Utility Maximization 3.4 Effects on the Optimal Choice 3.4.1 Change in Income Normal and Inferior Commodities Income-Consumption Curve Engel Curve: Nominal and Real Engel Curve and Income-Consumption Curve for Homothetic and Quasi-Linear Preferences Income Elasticity of Demand 3.4.2 Change in Prices Giffen and Non-Giffen Commodities Price-Consumption Curve Price Change and the Demand Curve Price Elasticity of Demand Substitutes and Complements Cross-Price Elasticity of Demand 3.5 Income and Substitution Effects 3.6 Slutsky Equation Summary Key Terms List of Formulas Exercises 47 50 52 55 58 58 60 60 60 63 64 66 68 69 71 76 81 81 82 83 83 85 86 88 90 90 91 91 93 94 95 96 98 99 99 101
xi 4 Consumer Demand: Theoretical Analysis 103 4.1 Demand and Supply: Functions and Laws 103 4.2 Deriving a Demand Function from Utility Maximization 105 4.3 Homogeneity and the Numeraire 109 4.4 Inverse Demand Function 111 4.5 Demand and Supply: Table and Curves 111 4.6 Market Equilibrium 114 4.7 From Individual to Market Demand 120 4.8 Demand and Network Externalities 122 4.8.1 The Case of the Bandwagon Effect 122 4.8.2 The Case of the Snob Effect 124 4.9 Deriving a Market Demand Function under Externalities 126 4.10 Changes in Q D and Q s versus Changes in D and S 129 4.11 Changes in Equilibrium 131 4.11.1 The Case of Thanksgiving Turkey 132 4.11.2 The Case of Sales and Excise Taxes 134 4.12 Market Disequilibrium 138 4.12.1 The Case of a Price Ceiling 139 4.12.2 The Case of a Price Floor 142 4.13 Marshallian versus Hicksian Demand Curves 144 4.13.1 Shephard Lemma and the Expenditure Function 145 4.14 Deriving the Hicksian (Compensated) Demand Curve 147 4.15 Revealed Preferences 149 4.16 Interdependent Demand 152 Summary 155 Key Terms 157 List of Formulas 157 Exercises 157 5 Consumer Demand: Empirical Estimation 160 5.1 Simple Market Experimentation 160 5.2 Linearity of the Demand Function: From Visual to Regression 163 5.3 Reliability of the Estimation 168 5.4 Quality of Fitting 170 5.5 Fitting by Computerized Regression 172 5.6 Demand Estimation by the Multiple Regression Method 174 5.6.1 Results and Interpretation 179 5.6.2 Goodness of Fit 181 5.6.3 The Overall Explanatory Power of the Model 182 5.6.4 Major Problems to Check On 183 Multicollinearity 183 Autocorrelation 184 Heteroscedasticity 185 5.7 Nonregression Approaches to Estimation 186 5.7.1 Market Experimentation 186
xii CONTENTS 5.7.2 Observational Studies 187 5.7.3 Micromarketing and Virtual Shopping 187 5.8 Advanced Demand Estimation: The Pad Model 188 5.8.1 Model Specification 188 Desired Demand 188 Adjustment Equation 188 Estimating Equation 189 5.8.2 Graph of the Linear PAD Model 189 Summary 196 Key Terms 196 List of Formulas 196 Exercises 198 6 Consumer Demand: Economic Forecasting 200 6.1 Forecasting Models 201 6.1.1 Quantitative Models 201 6.1.2 Qualitative Models 202 6.2 Time Series Analysis 202 6.2.1 Secular Trends 202 6.2.2 Seasonal Variations 202 6.2.3 Cyclical Fluctuations 203 6.2.4 Random Changes 203 6.3 From Symbolic to Numeric Fitting 203 6.4 Adjusting for Seasonality 207 6.4.1 The Simple Average of Errors Method 208 6.4.2 The Actual-to-Forecast (A/F) Ratio Method 210 6.4.3 The Dummy Variables Method 212 6.5 Smoothed Forecasts 214 6.5.1 Simple Moving Average Method 214 The RMSE Check 217 6.5.2 The Weighted Moving Average 218 6.5.3 Exponential Smoothing 219 Mean Absolute Deviation (MAD) 223 6.6 Barometric Forecasting 224 6.7 Econometric Models 226 6.7.1 Single-Equation Model 227 6.7.2 Multiple-Equation Model 229 6.8 Input-Output Matrix 231 6.9 Judgmental Models 233 6.9.1 Opinions and Polls 233 6.9.2 Surveys and Market Research 233 6.10 Forecasting Accuracy and Reliability 234 Summary 235 Key Terms 236 List of Formulas 236 Exercises 238
xiii UNIT III MANAGERIAL DECISIONS AT THE FIRM LEVEL 7 Production Theory 243 7.1 Variability of Inputs throughout Time 243 7.2 Production Function 244 7.3 Graphical Representation of the Production Function 246 7.4 Short-Run, One Variable Input Function 250 7.5 Dynamic Relations among Production Curves 252 7.6 Law of Diminishing Marginal Returns 260 7.7 Long-Run, Two Variable Input Function 261 Isoquants 261 7.8 Marginal Rate of Technical Substitution (MRTS) 263 7.9 The Economically Efficient Region of Production 266 7.10 Returns to Scale 267 7.11 Elasticity of Substitution 269 7.11.1 Elasticity of the Cobb-Douglas Production Function 270 7.11.2 Elasticity of the Leontief Production Function 271 7.11.3 Leontief Technology and Linear Programming 272 7.11.4 Elasticity of the Linear Production Function 273 7.11.5 Elasticity of the CES Production Function 274 7.11.6 Graphical Representation of CES 275 7.12 Optimal Employment of an Input 277 7.13 Technological Progress, Invention, and Innovation 278 7.14 Technological Progress and Production Function 280 Summary 282 Key Terms 283 List of Formulas 283 Exercises 285 8 Cost Theory 287 8.1 Cost Concepts and Categories 287 8.2 Short-Run Costs 289 8.3 The Optimal Combination of Inputs 297 8.3.1 Isocost 297 8.4 Minimizing Input Cost and Maximizing Output 298 8.5 Long-Run Costs 301 8.6 Short-Run and Long-Run Average Costs: Economies of Scale 303 8.7 Derivation of the Cost Function 306 8.8 Economies of Scope: Basic Concept and Cost Complementarities 311 8.9 Economies of Scope: Synergy and Input Indivisibility 313 8.10 The Learning Curve 316 8.11 Cost-Volume-Profit Analysis and Operating Leverage 321 8.11.1 Break-Even Quantity and Break-Even Revenue 322 Fixed Cost 323 Variable Cost 323 Contribution Margin 324
xiv CONTENTS 8.11.2 Cash Break-Even Technique 8.11.3 The Break-Even Point and Target Profit 8.11.4 An Algebraic Approach to the Break-Even Point 8.11.5 Break-Even Time 8.11.6 The Dual Break-Even Points 8.12 Leverage 8.12.1 Operating Leverage 8.12.2 Operating Leverage, Fixed Cost, and Business Risk Summary Key Terms List of Formulas Exercises Production and Cost: Estimation and Forecasting 9.1 Estimation of the Production Function 9.2 Estimation of the Cost Function 9.3 Forecasting Output 9.4 Forecasting Cost 9.5 Meeting Obligations through Decisions with Probabilistic Results Summary Key Terms List of Formulas Exercises 326 327 329 330 334 337 338 341 342 344 344 347 349 350 352 355 359 360 361 361 361 363 UNIT IV MANAGERIAL DECISIONS AT THE MARKET LEVEL 10 Market Structure and Business Organization 367 10.1 Perfect Competition 368 10.1.1 Characteristics of Perfect Competition 368 10.1.2 Profit Maximization for Competitive Firms 369 10.1.3 The Decision to Shut Down 373 10.1.4 The Competitive Firm in the Long Run 377 10.2 Monopoly 381 10.2.1 Monopoly's Equilibrium in the Short Run 381 10.2.2 Monopoly's Equilibrium in the Long Run 385 10.2.3 Monopoly Power and the Lerner Index 388 10.3 Monopolistic Competition 389 10.3.1 Monopolistic Competition Equilibrium in the Short Run 390 10.3.2 Monopolistic Competition Equilibrium in the Long Run 391 10.4 Oligopoly 393 10.4.1 The Concentration Ratio and the Herfindahl Index 394 10.4.2 Models of Oligopoly 395 Cournot Model 395 Stackelberg Model 399 Bertrand Model 403 Sweezy Model 407
XV Summary 410 Key Terms 411 List of Formulas 411 Exercises 412 11 Pricing Decisions and Practices 414 11.1 Basics of Price Setting 414 11.2 The Markup Rule 415 11.3 Multiproduct Pricing Strategies 418 11.4 Joint Products with Independent Demands 419 11.4.1 Product Set of Fixed Proportions 419 11.4.2 Product Set of Variable Proportions 421 11.5 Transfer Pricing 423 11.5.1 The Intermediate Product in a Perfectly Competitive Market 424 11.5.2 The Intermediate Product in an Imperfectly Competitive Market 429 11.6 Pricing Strategies and Practices 430 11.7 Price Discrimination 433 11.7.1 First-Degree Price Discrimination 434 W.I.2 Second-Degree Price Discrimination 436 11.7.3 Third-Degree Price Discrimination 437 Summary 445 Key Terms 446 List of Formulas 446 Exercises 447 UNIT V MANAGERIAL DECISIONS IN THE LONG RUN 12 Capital Budgeting and Investment Project Evaluation 451 12.1 What is Capital Budgeting? 451 12.2 Basic Model of Capital Budgeting 453 12.3 Selection Process and Project Evaluation 454 12.4 Methods of Evaluation for Proposed Investment Projects 455 12.4.1 Net Present Value 455 12.4.2 Internal Rate of Return 459 12.4.3 NPV versus IRR for Mutually Exclusive Projects 462 12.4.4 NPV Profile, Crossover Rate, and the Ranking Reversal 465 12.5 Profitability Index and Capital Rationing 467 12.6 Payback Method 469 12.7 Cost of Capital 471 12.7.1 Cost of Debt Capital 472 12.7.2 Cost of Equity Capital 473 The CAPM Estimation 473 The Dividend Valuation Estimation 474 12.7.3 The Weighted Marginal Cost of Capital 476 12.7.4 Capitalization and Capitalized Cost 478 12.7.5 Last Words on the Cost of Capital 481
xvi CONTENTS Summary 481 Key Terms 483 List of Formulas 483 Exercises 485 13 Risk Analysis and Managerial Decisions under Uncertainty 487 13.1 Risk and Uncertainty 487 13.2 Sources of Risk 488 13.2.1 Economic Sources 488 13.2.2 Political Sources 488 13.2.3 Social Sources 489 13.2.4 International Sources 489 13.3 Measurement of Risk 489 13.3.1 The Absolute Measure 490 13.3.2 The Relative Measure 495 13.4 Risk Aversion 495 13.5 Risk Attitudes and Utility of Money 496 13.6 Expected Utility of Money versus Expected Monetary Return 498 13.7 Risk Discount and Certainty Equivalent 501 13.8 Risk Impact on the Valuation Model 503 13.8.1 Risk Premium Adjustment 503 13.8.2 Certainty-Equivalent Adjustment 506 13.9 Diversifiable versus Nondiversifiable Risk 509 13.10 Portfolio Risk 510 13.11 Risk of Two-Asset Portfolio 518 13.12 Lending and Borrowing at the Risk-Free Rate of Return 520 13.13 Measuring the Systematic Risk by Beta (P) 522 13.14 The CAPM Model 525 13.15 The Security Market Line (SML) 526 13.15.1 SML Shift by Inflation 527 13.15.2 SML Swing by Risk Aversion 528 13.16 Managerial Decision Tree 532 13.17 Mathematical Simulation and Sensitivity Analysis 533 13.18 Advanced Choice under Risk, Ambiguity, and Uncertainty 536 13.18.1 Stochastic Dominance. 536 Assumptions 537 Expected Utility 537 First-Degree Stochastic Dominance 537 Interpretation of FSD Conditions 538 Second-Degree Stochastic Dominance 538 Interpretation of FSD Conditions 538 Applications of SSD Conditions 539 13.18.2 Choice under Ambiguity 539 13.18.3 Choice under Uncertainty 539 Summary 541 Key Terms 542
xvii List of Formulas 543 Exercises 544 14 Management Consultants and Information 546 14.1 Measuring Information and Its Impact on Uncertainty 546 14.2 Perfect Management Information 548 14.3 Valuing Perfect Management Information 549 14.4 Valuing Less-than-Perfect Management Information 549 Summary 556 Key Terms 557 List of Formulas 557 Exercises 558 APPENDIX 560 FURTHER READING 569 INDEX 573