Question

1. Assuming the underlying demand for cases of O Be Joyful beverages is a linear function of O Be Joyful per-case price and state income (000s), use the data to obtain least squares estimates for each state's beverage demand function (three separate regressions). Report each estimated demand function in your memo. Please feel free to attach summary results to your memo. Your memo should stand alone, however, as communication. Do not ask the reader to go to attachments to justify any argument.
   1. Estimate own-price and income elasticities for each state and interpret the results. (Please see three tables below)

Wisconsin

Quantity	Price	Income
309	29.77	25.59
341	26.49	28.16
600	28.56	54.66
298	32.38	26.15
241	26.15	17.63
202	30.37	14.63
654	27.29	60.42
459	29.44	40.15
490	32.83	44.4
399	36.68	36.91
351	27.39	29.81
157	29.46	10.93
457	28.49	40.72
322	29.16	27.29
306	29.91	25.48
536	32.3	48.43
416	26.44	36.27
411	32.12	35.94
628	29.84	57.61
393	32.37	33.75
446	28.59	39.46
288	32.14	24.19
432	32.22	38.45
350	31.52	29.52
423	31.81	38.05
316	33.36	27.18
275	33.44	24.07
342	28.14	29
454	26.04	40.16
239	30.37	19.74
368	32.19	32.02
407	30.84	35.43
252	31.56	20.19
151	33.11	10.8
314	31.42	26.46
451	34.14	40.69
395	30.52	34.81
229	25.32	17.36
340	28.66	28.36
415	32.2	37.04
476	32.52	43.47
285	26.36	22.97
345	30.79	29.52
420	35.14	38.4
394	34.1	35.73
443	28.5	38.81
393	25.72	33.23
269	30.64	22.66
565	31.27	51.13
515	26.23	46.6

  

Answer 1

1. In order to find the own elasticity and income elasticity first we need to convert the data to log form as below using function = log() in excel

Quantity	Price	Income
2.49	1.47	1.41
2.53	1.42	1.45
2.78	1.46	1.74
2.47	1.51	1.42
2.38	1.42	1.25
2.31	1.48	1.17
2.82	1.44	1.78
2.66	1.47	1.60
2.69	1.52	1.65
2.60	1.56	1.57
2.55	1.44	1.47
2.20	1.47	1.04
2.66	1.45	1.61
2.51	1.46	1.44
2.49	1.48	1.41
2.73	1.51	1.69
2.62	1.42	1.56
2.61	1.51	1.56
2.80	1.47	1.76
2.59	1.51	1.53
2.65	1.46	1.60
2.46	1.51	1.38
2.64	1.51	1.58
2.54	1.50	1.47
2.63	1.50	1.58
2.50	1.52	1.43
2.44	1.52	1.38
2.53	1.45	1.46
2.66	1.42	1.60
2.38	1.48	1.30
2.57	1.51	1.51
2.61	1.49	1.55
2.40	1.50	1.31
2.18	1.52	1.03
2.50	1.50	1.42
2.65	1.53	1.61
2.60	1.48	1.54
2.36	1.40	1.24
2.53	1.46	1.45
2.62	1.51	1.57
2.68	1.51	1.64
2.45	1.42	1.36
2.54	1.49	1.47
2.62	1.55	1.58
2.60	1.53	1.55
2.65	1.45	1.59
2.59	1.41	1.52
2.43	1.49	1.36
2.75	1.50	1.71
2.71	1.42	1.67

2. Using data analysis run regression, keeping Y as Q, and Price, Income as X

3. The results is expressed as below

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9981
R Square	0.9961
Adjusted R Square	0.9960
Standard Error	0.0088
Observations	50.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	2.0000	0.9287	0.4644	6049.3363	0.0000
Residual	47.0000	0.0036	0.0001
Total	49.0000	0.9324
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.5665	0.0486	32.2614	0.0000	1.4688	1.6641
Price	-0.1742	0.0322	-5.4054	0.0000	-0.2391	-0.1094
Income	0.8385	0.0076	109.9932	0.0000	0.8232	0.8539

  4. The expression is log(Q) = 1.57-0.1742*log(P)+0.84*log(Income)

Where Own price elasticity = -0.1742, means for one percent increase in price the quantity decreases by -0.1742 percent

Income elasticity  = 0.84, means for one percent increase in price the quantity increases by 0.84 percent