Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Managerial Economics, 9e Managerial Economics Thomas Maurice ninth edition Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Managerial Economics, 9e Managerial Economics Thomas Maurice ninth edition Chapter 3 Marginal Analysis for Optimal Decision Making

Managerial Economics 3-2 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

Managerial Economics 3-3 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

Managerial Economics 3-4 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

Managerial Economics 3-5 NB TB TC Optimal Level of Activity (Figure 3.1) 1,000 Level of activity 2,000 4,000 3,000 A 0 1, Total benefit and total cost (dollars) Panel A – Total benefit and total cost curves A 0 1, Level of activity Net benefit (dollars) Panel B – Net benefit curve G 700 F D’ D C’ C B B’ 2,310 1,085 NB* = $1,225 f’’ 350 = A* M 1,225 c’’ 1,000 d’’ 600

Managerial Economics 3-6 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

Managerial Economics 3-7 Marginal Benefit & Marginal Cost

Managerial Economics 3-8 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

Managerial Economics 3-9 MC (= slope of TC) MB (= slope of TB) TB TC Relating Marginals to Totals (Figure 3.2) F D’ D C’ C Level of activity 800 1,000 Level of activity 2,000 4,000 3,000 A 0 1, Total benefit and total cost (dollars) Panel A – Measuring slopes along TB and TC A 0 1, Marginal benefit andmarginal cost (dollars) Panel B – Marginals give slopes of totals = A* = A* B B’ b G g d’ (600, $8.20) d (600, $3.20) c’ (200, $3.40) c (200, $6.40) 5.20

Managerial Economics 3-10 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

Managerial Economics 3-11 NB Using Marginal Analysis to Find A* (Figure 3.3) A 0 1, Level of activity Net benefit (dollars) 800 c’’ d’’ = A* MB = MC MB > MCMB < MC M

Managerial Economics 3-12 Unconstrained Maximization with Discrete Choice Variables Increase activity if MB > MC Decrease activity if MB < MC Optimal level of activity Last level for which MB exceeds MC

Managerial Economics 3-13 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 do not affect marginal cost & are irrelevant for optimal decisions

Managerial Economics 3-14 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

Managerial Economics 3-15 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