# Managerial Economics

| May 22, 2015

you are given a data set of cost function data. The data is based on 145 U.S. Electricity Producers in 1955. The source of the original data is:

Nerlove, M. (1963) Returns to Scale in Electricity Supply. In C. Christ (ed.), Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld. Stanford University Press.

This is a classic work in cost analysis, and has been used in many managerial economics courses, starting with Harvard Business School. The original data have been revised and updated by Christensen, L. R., and Greene, W. H. The attached dataset is based on the revised data.

DATASET

Variables

TC = total cost (in 1970 Million USD)
Q = total output (Billion KwH)
PL = price of labor (wages)
PF = price of fuel
PK = price of capital

Observations

 TC Q PL PF PK 0.082 2 2.1 17.9 183 0.661 3 2.1 35.1 174 0.99 4 2.1 35.1 171 0.315 4 1.8 32.2 166 0.197 5 2.1 28.6 233 0.098 9 2.1 28.6 195 0.949 11 2 35.5 206 0.675 13 2.1 35.1 150 0.525 13 2.2 29.1 155 0.501 22 1.7 15 188 1.194 25 2.1 17.9 170 0.67 25 1.7 39.7 167 0.349 35 1.8 22.6 213 0.423 39 2.3 23.6 164 0.501 43 1.8 42.8 170 0.55 63 1.8 10.3 161 0.795 68 2 35.5 210 0.664 81 2.3 28.5 158 0.705 84 2.2 29.1 156 0.903 73 1.8 42.8 176 1.504 99 2.2 36.2 170 1.615 101 1.7 33.4 192 1.127 119 1.9 22.5 164 0.718 120 1.8 21.3 175 2.414 122 2.1 17.9 180 1.13 130 1.8 38.9 176 0.992 138 1.8 20.2 202 1.554 149 1.9 22.5 227 1.225 196 1.9 29.1 186 1.565 197 2.2 29.1 183 1.936 209 1.9 22.5 169 3.154 214 1.5 27.5 168 2.599 220 1.9 22.5 164 3.298 234 2.2 36.2 164 2.441 235 2.1 24.4 170 2.031 253 1.9 22.5 158 4.666 279 2.1 35.1 177 1.834 290 1.7 33.4 195 2.072 290 1.8 20.2 176 2.039 295 1.8 21.3 188 3.398 299 1.7 26.9 187 3.083 324 2.1 35.1 152 2.344 333 2.2 29.1 157 2.382 338 1.9 24.6 163 2.657 353 2.2 29.1 143 1.705 353 2.1 10.7 167 3.23 416 1.5 26.2 217 5.049 420 1.5 27.5 144 3.814 456 2.1 30 178 4.58 484 1.8 42.8 176 4.358 516 2.3 23.6 167 4.714 550 2.1 35.1 158 4.357 563 2.3 31.9 162 3.919 566 2.3 33.5 198 3.442 592 1.9 22.5 164 4.898 671 2.1 35.1 164 3.584 696 1.8 10.3 161 5.535 719 1.7 26.9 174 4.406 742 2 20.7 157 4.289 795 2.2 26.5 185 6.731 800 1.7 26.9 157 6.895 808 1.7 39.7 203 5.112 811 2.3 28.5 178 5.141 855 2 34.3 183 5.72 860 2.3 33.5 168 4.691 909 1.5 17.6 196 6.832 913 1.7 26.9 166 4.813 924 1.8 10.3 172 6.754 984 1.7 26.9 158 5.127 991 2.1 30 174 6.388 1000 1.6 28.2 225 4.509 1098 2.1 24.4 168 7.185 1109 2.1 35.1 177 6.8 1118 2.3 23.6 161 7.743 1122 2.2 29.1 162 7.968 1137 2 20.7 158 8.858 1156 2.3 33.5 176 8.588 1166 1.7 26.9 183 6.449 1170 2.1 35.1 166 8.488 1215 2.2 29.1 164 8.877 1279 2 34.3 207 10.274 1291 2.3 31.9 175 6.024 1290 1.6 28.2 225 8.258 1331 2.1 30 178 13.376 1373 2.2 36.2 157 10.69 1420 2.2 36.2 138 8.308 1474 1.9 24.6 163 6.082 1497 1.8 10.3 168 9.284 1545 1.8 20.2 158 10.879 1649 2.3 31.9 177 8.477 1668 1.8 20.2 170 6.877 1782 2.1 10.7 183 15.106 1831 2 35.5 162 8.031 1833 1.8 10.3 177 8.082 1838 1.5 17.6 196 10.866 1787 2.2 26.5 164 8.596 1918 1.7 12.9 158 8.673 1930 1.8 22.6 157 15.437 2028 2.1 24.4 163 8.211 2057 1.8 10.3 161 11.982 2084 1.8 21.3 156 16.674 2226 2 34.3 217 12.62 2304 2.3 23.6 161 12.905 2341 2 20.7 183 11.615 2353 1.7 12.9 167 9.321 2367 1.8 10.3 161 12.962 2451 2 20.7 163 16.932 2457 2.2 36.2 170 9.648 2507 1.8 10.3 174 18.35 2530 2.3 33.5 197 17.333 2576 1.9 22.5 162 12.015 2607 1.8 10.3 155 11.32 2870 1.8 10.3 167 22.337 2993 2.3 33.5 176 19.035 3202 2.3 23.6 170 12.205 3286 1.6 17.8 183 17.078 3312 1.7 28.8 190 25.528 3498 2.1 30 170 24.021 3538 2.1 30 176 32.197 3794 2.1 35.1 159 26.652 3841 2.3 28.5 157 20.164 4014 2.1 24.4 161 14.132 4217 1.5 18.1 172 21.41 4305 2.1 24.4 203 23.244 4494 2 20.7 167 29.845 4764 2.2 29.1 195 32.318 5277 1.9 29.1 161 21.988 5283 2 20.7 159 35.229 5668 2.1 24.4 177 17.467 5681 1.8 10.3 157 22.828 5819 1.8 18.5 196 33.154 6000 2.1 24.4 183 32.228 6119 1.5 26.2 189 34.168 6136 1.9 22.5 160 40.594 7193 2.1 28.6 162 33.354 7886 1.6 17.8 178 64.542 8419 2.3 31.9 199 41.238 8642 2.2 26.5 182 47.993 8787 2.3 33.5 190 69.878 9484 2.1 24.4 165 44.894 9956 1.7 28.8 203 67.12 11477 2.2 26.5 151 73.05 11796 2.1 28.6 148 139.422 14359 2.3 33.5 212 119.939 16719 2.3 23.6 162

Cut the data set and paste it into Excel. Then, in Excel, obtain the logarithmic transformation of all the variables using the Excel function: =LOG( . ), i.e.,

logTC = log(total cost)
logQ = log(total output)
logPL = log(price of labor)
logPF = log(price of fuel)
logPK = log(price of capital)

Run the following regression using the Excel add-in Data Analysis:
logTC=
whereis an error term, and the variables and their logarithmic transformations are defined above.

Read the Background material, run the multiple regression outlined above and then write a 3- to 4-page report (and attach the Excel printout) answering the following questions:

• What is the R-square of the regression? What does it mean?
• What is the elasticity of TC with respect to Q? Test the significance of
• What is the elasticity of TC with respect to PL? Test the significance of
• What is the elasticity of TC with respect to PF? Test the significance of
• What is the elasticity of TC with respect to PK? Test the significance of
• Can you forecast (predict) what happens to TC if PL doubles (keeping everything else constant)?
• Looking at the ANOVA table, can you conclude the independent variables jointly affect the average housing price? See the ANOVA note in Module 2 SLP.
• Do you find any anomaly in the results? That is, is there any result that does not make sense to you?
• How would inclusion of modern generation mix (Coal, Nuclear, Natural Gas) change the specification of the demand for electricity?

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