1. Chapter 10: Production and Cost Estimation McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

2. 10-2 Empirical Production Function An empirical production function is the mathematical form of the production function to be estimated

3. 10-3 Empirical Production Function Long-run production function A production function in which all inputs are variable Short-run production function A production function in which at least one input is fixed

4. 10-4 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

5. 10-5 Properties of a Short-Run Cubic Production Function Holding capital constant, short-run cubic production function is derived as follows:

6. 10-6 The average & marginal products of labor are, respectively: Properties of a Short-Run Cubic Production Function

7. 10-7 Marginal product of labor begins to diminish beyond L m units of labor Average product of labor begins to diminish beyond L a units of labor Properties of a Short-Run Cubic Production Function

8. 10-8 MP & AP Curves for the Short-Run Cubic Production Function (Figure 10.1) Q = AL 3 + BL 2

9. 10-9 To have necessary properties of a production function, parameters must satisfy the following restrictions: A 0 Properties of a Short-Run Cubic Production Function

10. 10-10 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

11. 10-11 Estimate using data for which the level of usage of one or more inputs is fixed Usually time series data are used Estimation of a Short-Run Production Function

12. 10-12 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 Estimation of a Short-Run Production Function

13. 10-13 Nominal cost data Data that have not been corrected for the effects of inflation Must eliminate effects of inflation Correct for the influence of inflation by dividing nominal cost data by an appropriate price index (or implicit price deflator) Estimation of a Short-Run Production Function

14. 10-14 Average variable cost & marginal cost functions are, respectively: Properties of a Short-Run Cubic Cost Function

15. 10-15 Average variable cost reaches its minimum value at: Properties of a Short-Run Cubic Cost Function

16. 10-16 To conform to theoretical properties, parameters must satisfy the following restrictions: a > 0, b 0 Properties of a Short-Run Cubic Cost Function

17. 10-17 Cubic specification produces S-shaped TVC curve & U-shaped AVC & SMC curves Properties of a Short-Run Cubic Cost Function

18. 10-18 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 Properties of a Short-Run Cubic Cost Function

19. 10-19 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 A 0

20. 10-20 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 a > 0, b 0

21. 10-21 Problem Mercantile Metalworks, Inc. manufactures wire carts for grocery stores. The production manager at Mercantile wishes to estimate an empirical production function for the assembly of carts using time-series data for the last 22 days of assembly. L is the daily number of assembly workers employed and Q is the number of carts assembled (completely) for that day. Mercantile pays its assembly workers $160 per day in wages and benefits.

22. 10-22 1.Use Excel to estimate the following short run cubic production function: Do the parameter estimates have the appropriate algebraic signs? Are they statistically significant at the 1 percent level? 2.What are the estimated total, average, and marginal product functions from your regression results? 3.At what level of labor usage does average product reach its maximum value? In a day, how many carts are assembled when average product is at its maximum? What is average variable cost when average product is maximized?