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cost_analysis.docx

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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?