Managerial Economics
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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Category: Economics