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Chapter 10

Chapter 10. Production & Cost Estimation. Empirical Production Function. Cubic empirical specification for a short-run production function is derived from a long-run cubic production function Cubic form of the long-run production function is expressed as.

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Chapter 10

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  1. Chapter 10 Production & Cost Estimation

  2. Empirical Production Function • Cubic empirical specification for a short-run production function is derived from a long-run cubic production function • Cubic form of the long-run production function is expressed as

  3. Properties of a Short-Run Cubic Production Function • Holding capital constant, short-run cubic production function is derived as follows:

  4. Properties of a Short-Run Cubic Production Function • The average & marginal products of labor are, respectively:

  5. • Properties of a Short-Run Cubic Production Function • Marginal product of labor begins to diminish beyondLmunits of labor

  6. MP & AP Curves for the Short-Run Cubic Production Function(Figure 10.1) Q = AL3 + BL2

  7. Properties of a Short-Run Cubic Production Function • To have necessary properties of a production function, parameters must satisfy the following restrictions:

  8. Estimation of a Short-Run Production Function • To use linear regression analysis, the cubic equation must be transformed into linear form • Q = AX + BW • Where X = L3 and W = L2 • Estimated regression line must pass through the origin • Specify in computer routine

  9. Estimation of a Short-Run Cost Function • Estimate using data for which the level of usage of one or more inputs is fixed • Usually time series data are used • Data collection may be complicated by the fact that accounting data do not include firm’s opportunity costs • Capital costs should reflect not only acquisition cost but any foregone rental income, depreciation, & capital gains/losses • Must eliminate effects of inflation • Divide by appropriate price index

  10. Properties of a Short-Run Cubic Cost Function • Average variable cost & marginal cost functions are, respectively:

  11. • Properties of a Short-Run Cubic Cost Function • Average variable cost reaches its minimum value at:

  12. Properties of a Short-Run Cost Function • Cubic specification produces S-shaped TVC curve & -shaped AVC & SMC curves • All three cost curves employ the same parameters • Only necessary to estimate one of these functions to obtain estimates of all three • In the short-run cubic specification, input prices are assumed constant • Not explicitly included in cost equation

  13. Summary of Short-Run Empirical Production Functions

  14. Summary of Short-Run Empirical Cost Functions

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