Reference no: EM131994

(1)  (i) Using Excel, estimate using regression analysis the linear demand equation of Q_x on P_x, P_y, Advertising and Income. Write down this estimated equation.

(ii) Consider that in 2012 P_x, P_y, 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(Q_x) on ln(P_x), ln(P_y), 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 (Q_x), its price (P_x), and the price of related good Y (P_y) 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