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Estimation Of Production And Cost Function 45,258 views Share Like ...

Pradeep Awasare, BM at APl INDIA PVT LTD Follow Estimation of Production and Costs involves:

• 1. Data collection (time series, cross-sectional data).

1, Q increa... Technology may change over time.

• 3. Production function assumes that production takes place where input combination is most efficient.

19. 19. Estimation of Production Functions continued

• Cross-sectional

• 1. No technological change over time, but all plants in the investigation are assumed to have same technology.

• 2. Adjustments across different geographical areas must be made.

• wages and price level

• 3. No guarantee that each plant operates at the most efficient input combination for the period examined.

20. 20. Cost Estimation

• Short-run cost functions are estimated to help managers to determine optimal pricing policy for the company

• used to determine marginal cost of producing additional units of output

21. 21.

• Long-run cost functions are used in planning firm’s investment decisions

• To determine the extent of economies and diseconomies of scale in order to select the optimal plant size

22. 22. Estimation of Short-Run Cost Functions

• Techniques used:

• mostly regression analysis with time series data

• problems and adjustments

• economic vs. accounting costs

• rate changes; such as tax rates, social security contributions etc.

• output homogeneity

• timing of costs

• accounting changes (have deprecation methods changed…)

23. 23. Shapes of Short-Run Cost Functions

• Cubic cost function:

• A cubic cost function represents the normal theoretical cost function, which exhibits both decreasing marginal and average costs and increasing marginal and average costs

24. 24. Cubic cost function continued

• TC = a + bQ - cQ 2 + dQ 3

• AC = a/Q + b - cQ + dQ 2

• MC = b - 2cQ + 3dQ 2

25. 25. Cubic cost function $ TC Q 26. 26. First marginal and average costs decrease and then increase: $ MC Q AC 27. 27. Quadratic cost function

• If data does not fit to a cubic cost function, we can try to fit it to a quadratic one.

• Quadratic cost function:

• TC = a + bQ + cQ 2

• AC = a/Q + b + cQ

• MC = b + 2cQ

28. 28. Costs increasing at increasing rate $ TC Q 29. 29. No decreasing marginal cost! $ MC Q AC 30. 30. Linear cost function

• Also a linear total cost function can be fitted. Then the three functions get the following form

• TC = a + bQ

• AC = a/Q + b

• MC = b

31. 31. No Law of Diminishing Marginal Returns $ TC Q $ MC Q AC 32. 32. Note!

• Many empirical short-run cost studies have found a linear relationship between total cost and output, indicating a constant marginal cost.

Power Function continued Q L b1 33. 33. So…

• Should economist revise their view of U-shaped average and marginal cost curves?

• data employed concentrate on output levels of limited range

• capital inputs may not be fixed even in short-run

• regression is not a perfect tool

34. 34. Estimation of Long-Run Cost Functions

• Techniques used:

• Regression analysis

• Engineering cost method

• Survivor technique

35. 35. Regression analysis in L-R Cost Estimation

• Mostly with cross-sectional data

• Pluses:

• since data comes from different firms, quantity of output can vary over relatively wide ranges

• all data from same point of time, so technology will not change

• do not have to regard price changes

36. 36. Regression analysis in L-R Cost Estimation continued

• Minuses:

• interregional cost differences

• all firms not necessarily operating at optimal level of technology

• costs may be recorded differently in different firms

• different companies may pay their cost factors differently

37. 37. Engineering cost method

• Based on understanding of inputs and outputs and their relationships

• In this approach, the analysis begins with an ”engineering production function”: optimal production input combinations for producing any given level of production is identified.

• Cost can be obtained by multiplying each level of input usage by current price of the input and summing over the inputs.

38. 38. Engineering cost method continued

• Pluses:

• technology held constant

• no problem with inflation (current input prices)

• less error from measurement

• Minuses:

• cost estimates are normative

• only direct output costs are estimated

• often made based on pilot plant operations, not actual production

39. 39. Survivor technique

• This method, suggested by G. Stigler, bases its findings on the change in the proportion of total industry output produced by firms of different size categories

• look at company size that is successful in an industry!

• Used for deciding optimal plant size

40. 40. Survivor technique continued

• Pluses:

• simple

• avoids unreliable data

• Minuses:

• no help in measuring costs for planning purposes

• just tells which company size appears to be more efficient

• implicitly assumes that the industry highly competitive, so survival and prosperity are solely a function of efficient use of resources, not the market power or erection of barriers of entry

Power Function continued

• Power function is the most frequently used type of production function in empirical work... Recommended
  
  The Cobb-Douglas Production Function
  • A special case of power functions:
  • Q = aL b K 1-b ,