Estimate the linear demand equation

Assignment Help Microeconomics
Reference no: EM131994

(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

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