Economics - Production Function Projects

a. Estimate the Cobb-Douglas production function Q=αL β1 K β2 , where Q=output; L = labor input; K = capital

Question 1

a.
Estimate the Cobb-Douglas production function Q=αL ^β1 K ^β2 , where Q=output; L = labor input; K = capital input; and α, β1, and β2 are the parameters to be estimated.

b.
Test whether the coefficients of capital and labor are statistically significant. Describe.

c.
Determine the percentage of the variation in output that is "explained" by the regression equation.

d.
Determine whether this production function exhibits increasing, decreasing or constant returns to scale. (Ignore the issue of statistical significance)

Production Function for Wilson Company Data
Plant	Output (000 Tons)	Capital ($000)	Labor (000 Worker Hours)
1	605.3	18,891	700.2
2	566.1	19,201	651.8
3	647.1	20,655	822.9
4	523.7	15,082	650.3
5	712.3	20,300	859
6	487.5	16,079	613
7	761.6	24,194	851.3
8	442.5	11,504	655.4
9	821.1	25,970	900.6
10	397.8	10,127	550.4
11	896.7	25,622	842.2
12	359.3	12,477	540.5
13	979.1	24,002	949.4
14	331.7	8,042	575.7
15	1064.9	23,972	925.8

QUESTION 2

a.
Estimate the demand for soft drinks using a multiple regression program available on your computer. Show the result.

b.
Interpret the coefficients and calculate the price elasticity of soft drink demand.

c.
Omit price from the regression equation and observe the bias introduced into the parameter estimate for income. Also describe the bias.

d.
Now omit both price and temperature from the regression equation. Should a marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighborhoods? Why or why not?

EXPERIMENTAL DATA FOR 50 STATES
	Annual Cans per Capita	Price per six pack	Income per Capita	Mean Temp.
Alabama	200	2.19	13	66
Arizona	150	1.99	17	62
Arkansas	237	1.93	11	63
California	135	2.59	25	56
Colorado	121	2.29	19	52
Connecticut	118	2.49	27	50
Delaware	217	1.99	28	52
Florida	242	2.29	18	72
Georgia	295	1.89	14	64
Idaho	85	2.39	16	46
Illinois	114	2.35	24	52
Indiana	184	2.19	20	52
Iowa	104	2.21	16	50
Kansas	143	2.17	17	56
Kentucky	230	2.05	13	56
Louisiana	269	1.97	15	69
Maine	111	2.19	16	41
Maryland	217	2.11	21	54
Massachusetts	114	2.29	22	47
Michigan	108	2.25	21	47
Minnesota	108	2.31	18	41
Mississippi	248	1.98	10	65
Missouri	203	1.94	19	57
Montana	77	2.31	19	44
Nebraska	97	2.28	16	49
Nevada	166	2.19	24	48
new Hampshire	177	2.27	18	35
New Jersey	143	2.31	24	54
New Mexico	157	2.17	15	56
New York	111	2.43	25	48
North Carolina	330	1.89	13	59
North Dakota	63	2.33	14	39
Ohio	165	2.21	22	51
Oklahoma	184	2.19	16	82
Oregon	68	2.25	19	51
Pennsylvania	121	2.31	20	50
Rhode Island	138	2.23	20	50
South Carolina	237	1.93	12	65
South Dakota	95	2.34	13	45
Tennessee	236	2.19	13	60
Texas	222	2.08	17	69
Utah	100	2.37	16	50
Vermont	64	2.36	16	44
Virginia	270	2.04	16	58
Washington	77	2.19	20	49
West Virginia	144	2.11	15	55
Wisconsin	97	2.38	19	46
Wyoming	102	2.31	19	46