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1、Copyright 2008 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinManagerial Economics, 9eManagerial EconomicsThomasMauriceninth editionCopyright 2008 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinManagerial Economics, 9eManagerial EconomicsThomasMauric
2、eninth editionChapter 3Marginal Analysis for Optimal Decision MakingManagerial EconomicsManagerial EconomicsOptimizationAn optimization problem involves the specification of three things:Objective function to be maximized or minimizedActivities or choice variables that determine the value of the obj
3、ective functionAny constraints that may restrict the values of the choice variables2Managerial EconomicsManagerial EconomicsChoice VariablesChoice variables determine the value of the objective functionContinuous variablesCan choose from uninterrupted span of variablesDiscrete variablesMust choose f
4、rom a span of variables that is interrupted by gaps3Managerial EconomicsManagerial EconomicsNet BenefitNet Benefit (NB)Difference between total benefit (TB) and total cost (TC) for the activityNB = TB TCOptimal level of the activity (A*) is the level that maximizes net benefit4Managerial EconomicsMa
5、nagerial EconomicsNBTBTCOptimal Level of Activity (Figure 3.1)1,000Level of activity2,0004,0003,000A01,000600200Total benefit and total cost (dollars)Panel A Total benefit and total cost curvesA01,000600200Level of activityNet benefit (dollars)Panel B Net benefit curveG700FDDCCBB2,3101,085NB* = $1,2
6、25f350 = A*350 = A*M1,225c1,000d6005Managerial EconomicsManagerial EconomicsMarginal Benefit & Marginal CostMarginal benefit (MB)Change in total benefit (TB) caused by an incremental change in the level of the activityMarginal cost (MC)Change in total cost (TC) caused by an incremental change in the
7、 level of the activity6Managerial EconomicsManagerial EconomicsMarginal Benefit & Marginal Cost7Managerial EconomicsManagerial EconomicsRelating Marginals to TotalsMarginal variables measure rates of change in corresponding total variablesMarginal benefit & marginal cost are also slopes of total ben
8、efit & total cost curves, respectively8Managerial EconomicsManagerial EconomicsMC (= slope of TC)MB (= slope of TB)TBTCRelating Marginals to Totals (Figure 3.2)FDDCCLevel of activity8001,000Level of activity2,0004,0003,000A01,000600200Total benefit and total cost (dollars)Panel A Measuring slopes al
9、ong TB and TCA01,000600200Marginal benefit and marginal cost (dollars)Panel B Marginals give slopes of totals8002468350 = A*100520100520350 = A*BBbGg100320100820d (600, $8.20)d (600, $3.20)100640100340c (200, $3.40)c (200, $6.40)5.209Managerial EconomicsManagerial EconomicsUsing Marginal Analysis to
10、 Find Optimal Activity LevelsIf marginal benefit marginal costActivity should be increased to reach highest net benefitIf marginal cost marginal benefitActivity should be decreased to reach highest net benefitOptimal level of activityWhen no further increases in net benefit are possibleOccurs when M
11、B = MC10Managerial EconomicsManagerial EconomicsNBUsing Marginal Analysis to Find A* (Figure 3.3)A01,000600200Level of activityNet benefit (dollars)800cd100300100500350 = A*MB = MCMB MCMB MCDecrease activity if MB MCOptimal level of activityLast level for which MB exceeds MC12Managerial EconomicsMan
12、agerial EconomicsIrrelevance of Sunk, Fixed, & Average CostsSunk costsPreviously paid & cannot be recoveredFixed costsConstant & must be paid no matter the level of activityAverage (or unit) costsComputed by dividing total cost by the number of units of the activityThese costs do not affect marginal
13、 cost & are irrelevant for optimal decisions13Managerial EconomicsManagerial EconomicsConstrained OptimizationThe ratio MB/P represents the additional benefit per additional dollar spent on the activityRatios of marginal benefits to prices of various activities are used to allocate a fixed number of dollars among activities14Managerial EconomicsManagerial EconomicsConstrained OptimizationTo maximize or minimize an objective function subject to a constraintRatios of the marginal benefit to price must be equal for all activitiesConstraint must be met15
