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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