1. Production & Cost Estimation
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 beyond Lm units of labor •

6. MP & AP Curves for the Short-Run Cubic Production Function (Figure 10
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
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
Short-run cubic cost equations
Total variable cost
Average variable cost
Marginal cost
Average variable cost reaches minimum at
Restrictions on parameters