Lecture Managerial economics (Ninth edition): Chapter 3 – Thomas, Maurice

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.

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McGrawHill/Irwin

Managerial Economics, 9e

Managerial Economics Thomas

Maurice

ninth edition

McGrawHill/Irwin

Managerial Economics, 9e

Managerial Economics Thomas

Maurice

ninth edition

Chapter 3

Marginal Analysis for Optimal Decision Making

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Managerial Economics Managerial Economics

32

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

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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

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Net Benefit

• Difference between total benefit (TB) and total cost (TC) for the activity

• NB = TB – TC

the level that maximizes net benefit

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NB

TB TC

Optimal Level of Activity (Figure 3.1)

1,000

Level of activity

2,000

4,000 3,000

A

0 200 600 1,000

Panel A – Total benefit and total cos t curves

A

0 200 600 1,000

Level of activity

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

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Marginal Benefit & Marginal Cost

• Change in total benefit (TB) caused by an incremental change in the level of the activity

• Change in total cost (TC) caused by an incremental change in the level of the activity

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Marginal Benefit & Marginal Cost

TB MB

A

Change in total benefit

Change in activity

TC MC

A

Change in total cost Change in activity

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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

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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

0 200 600 1,000

Panel A – Meas uring s lopes along TB and TC

A

0 200 600 1,000

Panel B – Marginals give s lopes 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

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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

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3

11

NB

(Figure 3.3)

A

0 200 600 1,000

Level of activity

800

•

c’’

•

d’’

100

300 100

500

350 = A*

MB = MC

MB > MC MB < MC

•

M

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12

Unconstrained Maximization with Discrete Choice Variables

• Optimal level of activity

• Last level for which MB exceeds MC

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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

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14

Constrained Optimization

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

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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

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