Chapter 3 - Marginal analysis for optimal decision making. In this chapter, you will learn to: Employ marginal analysis to find the optimal levels of activities in unconstrained maximization problems; explain why sunk costs, fixed costs, and average costs are irrelevant for determining the optimal levels of activities; employ marginal analysis to find the optimal levels of two or more activities in constrained maximization and minimization problems.
Managerial Economics ninth edition Thomas Maurice Chapter Marginal Analysis for Optimal Decision Making McGrawưHill/Irwin McGrawưHill/Irwin ManagerialEconomics,9e ManagerialEconomics,9e Copyrightâ2008bytheMcGrawưHillCompanies,Inc.Allrightsreserved ManagerialEconomics Optimization An optimization problem involves the specification of three things: • Objective function to be maximized or minimized • Activities or choice variables that determine the value of the objective function • Any constraints that may restrict the values of the choice variables 32 Managerial Economics Choice Variables • Choice variables determine the value of the objective function • Continuous variables • Can choose from uninterrupted span of variables • Discrete variables • Must choose from a span of variables that is interrupted by gaps 33 Managerial Economics Net Benefit • Net Benefit (NB) • Difference between total benefit (TB) and total cost (TC) for the activity • NB = TB – TC • Optimal level of the activity (A*) is the level that maximizes net benefit 34 Managerial Economics Optimal Level of Activity (Figure 3.1) TC 4,000 D • •D’ 3,000 B • 2,310 2,000 1,085 ) sr all od( t socl at ot dnatif enebl at oT 1,000 • F • • B’ •C’ 200 TB NB* = $1,225 C • G A 350 =A* 600 700 1,000 Level of activity 35 sr all od( tif enebt e N Pane l A – To tal be ne fit and to tal c o s t c urve s 1,225 1,000 M •c’’ • • 600 Pane l B – Ne t be ne fit c urve d’’ 200 350 =A* 600 A f’’ • Level of activity 1,000 NB Managerial Economics Marginal Benefit & Marginal Cost • Marginal benefit (MB) • Change in total benefit (TB) caused by an incremental change in the level of the activity • Marginal cost (MC) • Change in total cost (TC) caused by an incremental change in the level of the activity 36 Managerial Economics Marginal Benefit & Marginal Cost MB MC 37 Change in total benefit Change in activity Change in total cost Change in activity TB A TC A Managerial Economics Relating Marginals to Totals • Marginal variables measure rates of change in corresponding total variables • Marginal benefit & marginal cost are also slopes of total benefit & total cost curves, respectively 38 Managerial Economics Relating Marginals to Totals (Figure 3.2) TC 4,000 100 320 3,000 100 •B 520 100 2,000 640 •C ) sr all od( t socl at ot dnatif enebl at oT C’ • • F • TB 820 100 • B’ 1,000 •D D’• G 520 100 340 A 100 200 350 =A* 600 800 1,000 Level of activity 39 natif enebl ani gr a M ll od( t s ocl ani gr a m Pane l A – Me as uring s lo pe s alo ng TB and TC MC (= slope of TC) c (200, $6.40) 5.20 • •d’ (600, $8.20) b • •c’ (200, $3.40) d (600, $3.20) • MB (= slope of TB) g 200 350 = A* Pane l B – Marg inals g ive s lo pe s o f to tals 600 Level of activity 800 • 1,000 A Managerial Economics Using Marginal Analysis to Find Optimal Activity Levels • If marginal benefit > marginal cost • Activity should be increased to reach highest net benefit • If marginal cost > marginal benefit • Activity should be decreased to reach highest net benefit • Optimal level of activity • When no further increases in net benefit are possible • Occurs when MB = MC 3 Managerial Economics Using Marginal Analysis to Find A* (Figure 3.3) MB = MC MB > MC 100 ) sr all od( tif enebt e N 300 3 • c’’ 200 MB MC • Decrease activity if MB < MC • Optimal level of activity • Last level for which MB exceeds MC 3 Managerial Economics Irrelevance of Sunk, Fixed, & Average Costs • Sunk costs • Previously paid & cannot be recovered • Fixed costs • Constant & must be paid no matter the level of activity • Average (or unit) costs • Computed by dividing total cost by the number of units of the activity • These costs not affect marginal cost & are irrelevant for optimal decisions 3 Managerial Economics Constrained Optimization • The ratio MB/P represents the additional benefit per additional dollar spent on the activity • Ratios of marginal benefits to prices of various activities are used to allocate a fixed number of dollars among activities 3 Managerial Economics Constrained Optimization • To maximize or minimize an objective function subject to a constraint • Ratios of the marginal benefit to price must be equal for all activities • Constraint must be met MBA PA 3 MBB PB MBZ PZ ... Occurs when MB = MC 3 Managerial Economics Using Marginal Analysis to Find A* (Figure 3. 3) MB = MC MB > MC 100 ) sr all od( tif enebt e N 30 0 3 • c’’ 200 MB