A firm estimates its cubic production function of the form Q = AL^3 + BL^2 and obtains the following estimation results: A. What are the estimated total, average, and marginal product functions? B. At what level of labor usage is average product at its maximum?
A firm estimates its cubic production function of the form Q = AL^3 + BL^2 and obtains the following estimation results: A. What are the estimated total, average, and marginal product functions? B. At what level of labor usage is average product at its maximum?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
- A firm estimates its cubic production function of the form
Q = AL^3 + BL^2
and obtains the following estimation results:
A. What are the estimated total, average, and marginal product functions?
B. At what level of labor usage is average product at its maximum?
Transcribed Image Text:**Statistical Analysis Summary**
**Dependent Variable:** Q
**Observations:** 27
- **R-Square:** 0.7972
- **F-Ratio:** 98.256
- **P-Value on F:** 0.0001
**Variable Analysis:**
1. **Variable: L3**
- **Parameter Estimate:** -0.00160
- **Standard Error:** 0.000750
- **T-Ratio:** -2.13
- **P-Value:** 0.0429
2. **Variable: L2**
- **Parameter Estimate:** 0.480
- **Standard Error:** 0.37510
- **T-Ratio:** 1.28
- **P-Value:** 0.2124
**Interpretation:**
- The model explains approximately 79.72% of the variability in the dependent variable Q, as indicated by the R-Square value.
- The overall model is statistically significant, given the F-Ratio of 98.256 and a P-Value on F of 0.0001.
- For variable L3, the parameter estimate is negative and statistically significant at the 5% level.
- The variable L2 has a positive parameter estimate but is not statistically significant at the 5% level.
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