The document discusses empirical models for short-run production and cost functions using cubic specifications. It describes how a cubic long-run production function can be used to derive a short-run cubic production function by holding capital constant. It also outlines the properties of average and marginal products and costs for such short-run cubic specifications, including how they are estimated and restrictions on the parameters.

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 10-

3. Properties of a Short-Run Cubic Production Function Holding capital constant, short-run cubic production function is derived as follows: 10-

4. Properties of a Short-Run Cubic Production Function The average & marginal products of labor are, respectively: 10-

5. Properties of a Short-Run Cubic Production Function Marginal product of labor begins to diminish beyond L m units of labor 10- •

6. MP & AP Curves for the Short-Run Cubic Production Function (Figure 10.1) 10- Q = AL 3 + BL 2

7. Properties of a Short-Run Cubic Production Function To have necessary properties of a production function, parameters must satisfy the following restrictions: 10-

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 = L 3 and W = L 2 Estimated regression line must pass through the origin Specify in computer routine 10-

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-

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

11. Properties of a Short-Run Cubic Cost Function Average variable cost reaches its minimum value at: 10- To conform to theoretical properties, parameters must satisfy the following restrictions:

12. Properties of a Short-Run Cost Function Cubic specification produces S -shaped TVC curve & U -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 10-

13. Summary of Short-Run Empirical Production Functions 10- Short-run cubic production equations Total product Average product of labor Marginal product of labor Diminishing marginal returns Restrictions on parameters

14. Summary of Short-Run Empirical Cost Functions 10- Short-run cubic cost equations Total variable cost Average variable cost Marginal cost Average variable cost reaches minimum at Restrictions on parameters