The dataset below contains information on the input of production data and on the output (in natural logarithms) for 30 hypothetical companies. Your textbook uses logarithm of base 10 which is different from natural logarithm which has base e. With the data, the parameters of a Cobb-Douglas Production Function can be estimated. I converted the data into natural logs trying to make your life easier and also prevent you from following your textbook's use of log of base 10, that takes more steps to find the answers for the questions below. Make sure you read my special lecture note and watch the Panopto lecture.

lnK        lnL          lnQ   
3.6889  3.6889  3.4675 
3.6889  4.7875  3.8069 
3.6889  5.2983  3.7564 
3.6889  5.7683  4.0918 
4.382  3.6889  3.5946 
4.382  4.382  3.5149 
4.382  5.0752  4.1281 
4.382  5.6348  4.4534 
4.7875  4.7875  4.0031 
4.7875  5.2983  4.1896 
4.7875  5.7683  4.5463 
5.0752  3.6889  3.643 
5.0752  4.382  4.1242 
5.0752  5.0752  4.4723 
5.0752  5.4806  4.3563 
5.2983  4.7875  4.3965 
5.2983  5.2983  4.3934 
5.2983  5.7683  4.7487 
5.4806  3.6889  3.6726 
5.4806  5.0752  4.4991 
5.4806  5.4806  4.5027 
5.4806  5.6348  4.6062 
5.6348  4.382  4.219 
5.6348  4.7875  4.0904 
5.6348  5.4806  4.7451 
5.6348  5.7683  4.7228 
5.7683  3.6889  3.9925 
5.7683  4.7875  4.7719 
5.7683  5.2983  4.9012 
5.7683  5.7683  4.8305

A multiplicative Cobb-Douglas Production Function is written as Q = AKαLβ. We cannot use the Ordinary Least Squares method (OLS) in Excel to estimate the above multiplicative Cobb-Douglas Production Function since the independent variables are not linear. Hence, by transforming the above Cobb-Douglas production function into natural logs, we make the independent variables into linear. Then we can use the OLS technique.1. After estimating the transformed Cobb-Douglas production function using the data, write the estimated Cobb-Douglas production equation in natural logarithms. Make sure you use the proper variable names used in the data preparation.

2. Test whether coefficients of capital and labor are statistically significant.

3. What are the labor production elasticity and the capital production elasticity from the regression output.

4. Using information from Question 3, how much does output increase if L increases by 2%?

5. Determine whether this production function exhibits increasing, decreasing, or constant returns to scale. (Ignore statistical significance of the variables). Then explain your finding.

6. What's the MPL at L = 50, K = 100, & Q = 741?