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Applied Economics for Business Management

Applied Economics for Business Management. Lecture #8. Review Homework Set #6 Continue Production Economic Theory. Lecture Outline. Distinguish between cost equation and cost function. Cost function: C = f(z). Cost Function. Cost Function.

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Applied Economics for Business Management

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  1. Applied Economics for Business Management Lecture #8

  2. Review • Homework Set #6 • Continue Production Economic Theory Lecture Outline

  3. Distinguish between cost equation and cost function Cost function: C = f(z) Cost Function

  4. Cost Function

  5. How do we derive the cost function for a competitive firm given only production information and market prices? To derive the cost function, you need the following information: i. production function ii. cost equation • iii. equation of the expansion path Case of 2 or more inputs

  6. (production function) (cost equation) Example

  7. How do we derive the equation of the expansion path? Recall the expansion path is the locus of least cost combinations. A least cost combination is where the isoquant is tangent to the isocost line. Slope of isoquant = slope of isocost Example

  8. Example Equation of the expansion path

  9. Now use the 3 pieces of information: Example

  10. Now use the cost equation: Example

  11. ┌Total Fixed Cost └Total Variable Cost Example

  12. Using the previous example: Example

  13. Marginal Cost

  14. Profit Maximization (using output formulation rather than input formulation) Previously, we examined profit maximization as finding the value ofinputs where profits are maximized. Now consider profits in terms of output: └cost function Profit Maximization

  15. 1st order condition: So profits are maximized for the output level where Profit Maximization

  16. 2nd order condition: Profit Maximization

  17. What does this mean? C″(y) is the slope of the MC function C″(y) > 0  slope of MC function is positive or MC function is upward sloping. Profit Maximization

  18. What does this mean? Graphically, Profit Maximization

  19. If the market price for this commodity is p0, then equating p0 to MC yields the profit maximizing level of output y0. Note p = MC on the upward sloping portion of the MC curve (satisfying the 2nd order condition). Profit Maximization

  20. A familiar example: We solved earlier: Profit Maximization: Input Formulation Method

  21. 1st order conditions: Profit Maximization: Input Formulation Method

  22. 2nd order conditions: Profit Maximization: Input Formulation Method

  23. Let’s now check this solution using the input formulation. 1st order conditions: Profit Maximization: Input Formulation Method

  24. Profit Maximization: Input Formulation Method

  25. Profit Maximization: Input Formulation Method

  26. So the input formulation method finds a profit maximizing output level to be: found with the output formulation Profit Maximization: Input Formulation Method

  27. Beginning and intermediate microeconomics courses state that the supply curve for the firm is that portion of the MC curve above minimum AVC. Supply Curve

  28. Recall also that the second order conditions for profit maximization states that the critical values must lie on the upward sloping portion of the MC curve. Supply Curve

  29. Why isn’t the supply curve of the firm the entire MC function? • 2 reasons: • 2nd order conditions for profit max eliminates the • negatively sloped portion of the MC curve • (ii) if p < min AVC  the firm chooses not to produce • since cannot cover all of fixed costs and a portion of • variable costs Supply Curve

  30. What is the supply function of the firm? The supply function expresses a relationship between the price of the product and the quantity supplied of that product by the firm. Note that input or factor demand or derived demand is derived from profit maximization (using the input formulation in the profit function). For the firm’s supply function, this too is derived from profit maximization however by using the output formulation for profit. Supply Curve

  31. So we can derived the firm’s supply function from profit maximization as follows: From this equation, we solve for y in terms of p Supply Function

  32. From the firm’s supply function we can derive the  as p increases, y increases and as p decreases, y decreases. (These are movements along the firm’s supply curve.). Supply Function

  33. Recall we derived the following cost function: Example

  34. supply function of the firm Example

  35. What is the elasticity of supply evaluated at the profit maximizing level? So if p increases by 10%, the firm is expected to increases quantities supplied by 40%. Example

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