Managerial Economics: A Mathematical Approach

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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 47

3.1.1 Indifference Curve 50

3.1.2 Marginal Rate of Substitution (MRS) 52

3.1.3 Nontypical Indifference Curves 55

3.2 Consumer’s Affordability 58

3.2.1 Budget Line 58

3.2.2 Slope of the Budget Line 60

3.2.3 Shift, Swing, and Kink of the Budget Line 60

The Shift 60

The Swing 63

The Kink 64

3.2.4 Three-Dimensional Budget 66

3.3 The Optimal Choice 68

3.3.1 Interior and Corner Solutions 69

3.3.2 Utility and Its Measurability 71

3.3.3 Utility Maximization 76

3.4 Effects on the Optimal Choice 81

3.4.1 Change in Income 81

Normal and Inferior Commodities 82

Income–Consumption Curve 83

Engel Curve: Nominal and Real 83

Engel Curve and Income–Consumption Curve for Homothetic and Quasi-Linear Preferences 85

Income Elasticity of Demand 86

3.4.2 Change in Prices 88

Giffen and Non-Giffen Commodities 90

Price–Consumption Curve 90

Price Change and the Demand Curve 91

Price Elasticity of Demand 91

Substitutes and Complements 93

Cross-Price Elasticity of Demand 94

3.5 Income and Substitution Effects 95

3.6 Slutsky Equation 96

Summary 98

Key Terms 99

List of Formulas 99

Exercises 101

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 QD and QS 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

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

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

8.11.2 Cash Break-Even Technique 326

8.11.3 The Break-Even Point and Target Profit 327

8.11.4 An Algebraic Approach to the Break-Even Point 329

8.11.5 Break-Even Time 330

8.11.6 The Dual Break-Even Points 334

8.12 Leverage 337

8.12.1 Operating Leverage 338

8.12.2 Operating Leverage, Fixed Cost, and Business Risk 341

Summary 342

Key Terms 344

List of Formulas 344

Exercises 347

9 Production and Cost: Estimation and Forecasting 349

9.1 Estimation of the Production Function 350

9.2 Estimation of the Cost Function 352

9.3 Forecasting Output 355

9.4 Forecasting Cost 359

9.5 Meeting Obligations through Decisions with Probabilistic Results 360

Summary 361

Key Terms 361

List of Formulas 361

Exercises 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

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

11.7.2 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

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 (β) 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

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

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