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Chapter 2 Economic optimization

Chapter 2 Economic optimization. OVERVIEW. 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

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Chapter 2 Economic optimization

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  1. Chapter 2 Economic optimization

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

  3. 一. Economic relationship 1.Ways to show economic relationship (variables) Table. Graph. Equation 2.Totals , marginals and averages formula

  4. P3 fig.2.2 • Marginal and total • Marginal and average

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

  6. Slope : steepness of a line • Tangent: straight line intersection point

  7. 3.Marginals and the Derivatives • Y= f(x) • ** small △X → △Y • △Y/ △X = Marginal Y • TR= f(Q); TC=f(Q); T∏=f(Q)

  8. 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.

  9. 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 difference) b

  10. 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

  11. 2.to distinguish Maximums from Minimums **Maximum or minimum if first derivative= 0, ** maximum when second derivative < 0. ** Minimum where second derivative >0 positive.

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

  13. 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

  14. P39 summary

  15. 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, λ Chapter 2KEY CONCEPTS

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