Chapter 2 Economic
optimization
OVERVIEW
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Economic Optimization Process
Expressing Economic Relations
Marginal Analysis in Decision Making
Incremental Concept in Economic
Analysis
一. Economic relationship
1.Ways to show economic relationship
(variables)
Table. Graph. Equation
2.Totals , marginals and averages
formula
P3 fig.2.2
• Marginal and total
• Marginal and average
• ** Marginal and average derived from
total a----b
• ** tatal from marginal and average
• b----a
• Slope : steepness of a line
• Tangent: straight line
intersection point
3.Marginals and the Derivatives
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Y= f(x)
• ** small △X → △Y
• △Y/ △X = Marginal Y
• TR= f(Q); TC=f(Q); T∏=f(Q)
• Derivative = the “limit” of a function
• Derivative : the change in the dependent
variable (Y) when the change in the
independent variable (X) approaches zero.
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**Derivative/marginal relation/ slope
Derivative of total revenue is marginal revenue.
Derivative of total cost is marginal cost.
Derivative of total profit is marginal profit.
Rule 1. the derivative of a constant
y= f(x)= n
Rule 2. the derivative of a term containing
the independent variable (x)
Y=f(x)=aX
Rule 3. the derivative of a sum (or
b
difference)
二. Marginal Analysis in
Decision Making
1. To find maximum or minimum y
• objective y: Maximums or Minimums
If marginal is zero.
Optimum x if marginal is zero
Example: TR= f(Q)= 20Q-0.1QQ
TC=f(Q)=50+9Q+0.1QQ
??Q=? To max profit
• 2.to distinguish Maximums from
Minimums
**Maximum or minimum if first derivative= 0,
** maximum when second derivative < 0.
** Minimum where second derivative >0
positive.
3. To Maximize the Difference
Between Two Functions
– Maximum profit requires MR = MC.
Incremental Concept in
Economic Analysis
• Marginal versus Incremental Concept
Marginal---- one unit change
Incremental------ one managerial decision.
• Multiple units of output is possible.
• Incremental Profits
– Profits tied to a managerial decision.
• Incremental Concept Example
• P39 summary
Chapter 2
KEY CONCEPTS
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optimal decision
table
spreadsheet
graph
equation
dependent variable
independent variable
marginal
marginal revenue
marginal cost
marginal profit
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derivative
inflection point
second derivative
profit maximization
breakeven point
revenue maximization
average cost
minimization
• multivariate
optimization
• constrained
optimization
• Lagrangian technique