(1) (i) Using Excel, estimate using regression analysis the linear demand equation of Qx on Px, Py, Advertising and Income. Write down this estimated equation.
(ii) Consider that in 2012 Px, Py, Advertising and Income are all 10% greater than their 2011 value. Using the estimated equation in the previous part, calculate all the point elasticities of demand (income, price, cross price, and advertising elasticities) in Year 2012. Comment on your results (e.g. is demand for X elastic or inelastic; are X and Y substitutes or complements; is X a normal or an inferior good; is X a luxury or a necessity; is X sensitive to advertising or not).
(iii) Describe how a business may utilize these elasticities to inform its decision-making process.
(2) (i) Using Excel, transform all variables into natural logarithms (ln). Then use these variables to evaluate the demand equation in log-linear form (i.e. ln(Qx) on ln(Px), ln(Py), ln(Income) and ln(Advertising). Write down this estimated equation.
(ii) Based on the evaluated log-linear model, what are the elasticities of demand ( income, price, cross price, and advertising elasticities)? Do the conclusions you have reached in Part 1(ii) still hold?
(3) (i) For each model (log-linear and linear model), investigate which of the explanatory variables are individually statistically significant at the 5% significance level.
(ii) Conduct an F-test (at the 1% significance level) for each model and comment on the results.
(iii) Based on economic theory and the statistical tests you have conducted, which model do you consider preferable (the linear or log-linear model)?
The following table provides information on the quantity demanded of commodity X (Qx), its price (Px), and the price of related good Y (Py) from 1980 to 2011.
|
Qx
|
Px
|
Py
|
Income
|
Advertising
|
|
1980
|
120.5
|
280
|
230
|
53801.16
|
100
|
|
1981
|
140.2
|
240
|
250
|
56437.504
|
120
|
|
1982
|
135.1
|
265
|
240
|
57755.075
|
115
|
|
1983
|
163.7
|
250
|
250
|
59736.251
|
140
|
|
1984
|
142.4
|
240
|
240
|
61765.159
|
125
|
|
1985
|
131.6
|
270
|
245
|
63422.59
|
111
|
|
1986
|
180.8
|
240
|
220
|
66091.16
|
160
|
|
1987
|
201.7
|
215
|
280
|
70092.659
|
180
|
|
1988
|
164.8
|
250
|
276
|
77764.084
|
141
|
|
1989
|
133.6
|
265
|
250
|
75205.738
|
113
|
|
1990
|
137.8
|
265
|
249
|
68348.947
|
116
|
|
1991
|
183.3
|
240
|
240
|
62576.636
|
165
|
|
1992
|
211.7
|
230
|
240
|
58038.468
|
200
|
|
1993
|
237.5
|
225
|
234
|
57179.301
|
270
|
|
1994
|
209.5
|
225
|
250
|
58218.893
|
195
|
|
1995
|
196.8
|
220
|
235
|
59884.088
|
175
|
|
1996
|
159.5
|
230
|
240
|
54256.702
|
135
|
|
1997
|
183.2
|
235
|
250
|
51231.436
|
164
|
|
1998
|
190.5
|
245
|
249
|
53284.208
|
170
|
|
1999
|
205.5
|
240
|
240
|
54510.731
|
185
|
|
2000
|
175.7
|
250
|
289
|
57631.999
|
150
|
|
2001
|
191.6
|
240
|
230
|
60024.551
|
174
|
|
2002
|
212.7
|
240
|
250
|
62815.812
|
205
|
|
2003
|
202.2
|
235
|
240
|
66274.054
|
190
|
|
2004
|
220.8
|
220
|
231
|
70746.422
|
240
|
|
2005
|
221.2
|
218.7
|
239
|
75244.697
|
243
|
|
2006
|
223.9
|
220
|
257
|
80143.598
|
245
|
|
2007
|
225.1
|
219
|
236
|
85311.444
|
246
|
|
2008
|
229
|
216.5
|
230
|
90592.766
|
255
|
|
2009
|
231.9
|
215.6
|
230
|
85631.577
|
260
|
|
2010
|
233
|
213
|
256
|
85967.913
|
265
|
|
2011
|
234.5
|
212.5
|
245
|
87402.494
|
270
|