Ch2 Optimization Techniques Managerial Economics Notes 6thed

Managerial Economics

(Econ 4140/5140)

Professor Michael Nieswiadomy

Ch. 2. Optimization Techniques 1.

Introduction

2.

Functional Relationships

Table 2.1 Relationship between Price and Quantity Sold, Cherry Corporation Price per unit $10 $20 $30 $40

No. of units sold/day 150 100 50 0

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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Fig. 2.1: No. of units sold/day $45 $40 $35    )    t $30   n   u    / $25    $    (   e $20   c    i   r    P $15

$10 $5 $0 0

50

100

150

200

Quantity/day

3.

Marginal Analysis

Table 2.2 Relationship between Output and Profit, Roland Corporation 1 No. of units of output/day 0 1 2 3 4 5 6 7 8 9 10

2 Total Profit 0 $100.0 $250.0 $600.0 $1,000.0 $1,350.0 $1,500.0 $1,550.0 $1,500.0 $1,400.0 $1,200.0

3 Marginal Profit

4 Average Profit

$100.0 $150.0 $350.0 $400.0 $350.0 $150.0 $50.0 -$50.0 -$100.0 -$200.0

$100.0 $125.0 $200.0 $250.0 $270.0 $250.0 $221.4 $187.5 $155.6 $120.0

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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4.

Relationships between Total, Marginal, and Average Values

Fig. 2.2 Total Profit, Average Profit, and Marginal Profit, Roland Corporation 1800 1600 1400 1200 1000 800

Total Profit Marginal Profit

600 400

Average Profit

200 0 -200 0 -400

2

4

6

8

10

12

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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5.

The Concept of a Derivative

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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6.

How to Find a Derivative

a. Derivatives of Constants

Y=a

b. Derivatives of Power Functions

Y = aX

b

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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c. Derivatives of Sums and Differences

U = g(X)

W = h(X)

Y=U+W

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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Y=U-W

d. Derivatives of Products

Y = UW

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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e. Derivatives of Quotients

f.

Derivatives of a Function of a Function (Chain Rule)

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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7.

Using Derivatives to Solve Maximization and Minimization Problems

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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8.

Marginal Cost Equals Marginal Revenue and the Calculus of Optimization

9.

Partial Differentiation and the Maximizations of Multivariable Functions

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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10.

Constrained Optimization

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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11.

Lagrangian Multipliers

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12.

Comparing Incremental Costs with Incremental Revenues

Managerial Economics Econ 4140/5140 Ch. 2 Optimization Techniques

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