5. You have been asked to estimate your company\'s production function. You asse

Question

5. You have been asked to estimate your company's production function. You assembled the following data over the last 20 months. 22.61 26.79 31.2 35.83 0.63 45.59 50.66 55.83 61.07 66.35 71.64 76.91 82.13 87.29 92.33 97.25 12 13 15 16 17 18 12 13 21 15 16 26 27 18 106.60 110.90 115.10 a. Copy the above data into an excel spreadsheet. (2 pts.) b. Create the data table that you will use in order to estimate the company's production function if it takes the form of Q AL^3-BL12. (4 pts.) function of the Run the regression that will allow you to estimate the company's production form Q = AL^3-BL^2. Be careful: intercept?) Show the regression output. (3 pts.) c. d. What is the general estimating equation for the company's production function? (2 pts.) What level of laborers produce the maximum average production? (2 pts.) (Calculate a specific number e.

Explanation / Answer

d. Q = 0.27*L^2 - 0.0047*L^3

e. AP = Q/L = 0.27*L - 0.0047*L^2

max. AP: 0.27 - 0.0047*2*L = 0

0.27 / 0.0047*2 = L

L = 28.72

L = 29

time L Q L^3 L^2 1 10 22.61 1000 100 2 11 26.79 1331 121 3 12 31.2 1728 144 4 13 35.83 2197 169 5 14 40.63 2744 196 6 15 45.59 3375 225 7 16 50.66 4096 256 8 17 55.83 4913 289 9 18 61.07 5832 324 10 19 66.35 6859 361 11 20 71.64 8000 400 12 21 76.91 9261 441 13 22 82.13 10648 484 14 23 87.29 12167 529 15 24 92.33 13824 576 16 25 97.25 15625 625 17 26 102 17576 676 18 27 106.6 19683 729 19 28 110.9 21952 784 20 29 115.1 24389 841 SUMMARY OUTPUT Regression Statistics Multiple R 1 R Square 1 Adjusted R Square 0.944444 Standard Error 0.015229 Observations 20 ANOVA df SS MS F Significance F Regression 2 111739.8 55869.88 2.41E+08 4.51E-64 Residual 18 0.004175 0.000232 Total 20 111739.8 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A L^3 -0.0047 1.79E-06 -2625.35 1.05E-51 -0.0047 -0.00469 -0.0047 -0.00469 L^2 0.273055 4.47E-05 6114.015 2.58E-58 0.272961 0.273148 0.272961 0.273148 RESIDUAL OUTPUT Observation Predicted Q Residuals 1 22.60747 0.002527 2 26.78659 0.003413 3 31.20174 -0.00174 4 35.82475 0.005246 5 40.62743 0.002568 6 45.58159 0.008411 7 50.65904 0.000964 8 55.83159 -0.00159 9 61.07105 -0.00105 10 66.34925 0.000754 11 71.63798 0.002021 12 76.90906 0.000937 13 82.13431 -0.00431 14 87.28554 0.004464 15 92.33455 -0.00455 16 97.25316 -0.00316 17 102.0132 -0.01318 18 106.5864 0.013567 19 110.9447 -0.04472 20 115.0599 0.040147

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