Chapter 2 Economic optimization

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Chapter 2 Economic optimization
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OVERVIEW

• Economic Optimization Process
• Expressing Economic Relations
• Marginal Analysis in Decision Making
• Incremental Concept in Economic Analysis

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?. Economic relationship

• 1.Ways to show economic relationship (variables)
• Table. Graph. Equation
• 2.Totals , marginals and averages
• formula

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P3 fig.2.2

• Marginal and total
• Marginal and average

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• Marginal and average derived from total a----b
• tatal from marginal and average
• b----a

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• Slope steepness of a line
• Tangent straight line
• intersection point

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3.Marginals and the Derivatives

• Y f(x)
• small ?X ? ?Y
• ?Y/ ?X Marginal Y
• TR f(Q) TCf(Q) T?f(Q)

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• Derivative the limit of a function
• Derivative the change in the dependent variable
  (Y) when the change in the independent variable
  (X) approaches zero.
• 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.

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• Rule 1. the derivative of a constant
• y f(x) n
• Rule 2. the derivative of a term containing the
  independent variable (x)
• Yf(x)aX
• Rule 3. the derivative of a sum (or difference)

b
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?. 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
• TCf(Q)509Q0.1QQ
• ??Q? To max profit

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• 2.to distinguish Maximums from Minimums
• Maximum or minimum if first derivative 0,
• maximum when second derivative lt 0.
• Minimum where second derivative gt0 positive.

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• 3. To Maximize the Difference Between Two
  Functions
• Maximum profit requires MR MC.

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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

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• P39 summary

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Chapter 2KEY CONCEPTS

• optimal decision
• table
• spreadsheet
• graph
• equation
• dependent variable
• independent variable
• marginal
• marginal revenue
• marginal cost
• marginal profit

• derivative
• inflection point
• second derivative
• profit maximization
• breakeven point
• revenue maximization
• average cost minimization
• multivariate optimization
• constrained optimization
• Lagrangian technique
• Lagrangian multiplier, ?