Chapter 3

Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/IrwinManagerial Economics, 9e

Managerial Economics ThomasMauriceninth edition

Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/IrwinManagerial Economics, 9e

Managerial Economics ThomasMauriceninth edition

Chapter 3

Marginal Analysis for Optimal Decision Making

Managerial EconomicsManagerial 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


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


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


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 1,000600200

Tota

l b

en

efit

an

d t

ota

l co

st

(dolla

rs)

Panel A – Total benefit and total cost curves

A

0 1,000600200

Level of activity

Net

ben

efit

(dolla

rs)

Panel B – Net benefit curve

•G

700

•F

••

D’

D

•

•C’

C

•

•

B

B’

2,310

1,085

NB* = $1,225

•f’’

350 = A*

350 = A*

•M

1,225 •

c’’1,000

•d’’600


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


3-7

Marginal Benefit & Marginal Cost

TBMB

A

Change in total benefit

Change in activity

TCMC

A

Change in total cost

Change in activity


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


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 1,000600200

Tota

l b

en

efit

an

d t

ota

l co

st

(dolla

rs)

Panel A – Measuring slopes along TB and TC

A

0 1,000600200

Marg

inal b

en

efit

an

d

marg

inal co

st (

dolla

rs)

Panel B – Marginals give slopes of totals

800

2

4

6

8

350 = A*

100

520

100

520

350 = A*

•

•

B

B’

b•

•G

•g

100

320

100

820

•

•

d’ (600, $8.20)

d (600, $3.20)

100

640

100

340

•

•c’ (200, $3.40)

c (200, $6.40)

5.20


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


3-11

NB

Using Marginal Analysis to Find A* (Figure 3.3)

A

0 1,000

600200

Level of activity

Net

benefit

(dolla

rs)

800

•c’’

•d’’

100

300 100

500

350 = A*

MB = MC

MB > MC MB < MC

•M


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


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


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


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

A B Z

A B Z

MB MB MB...

P P P

Chapter 3

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