Studies of automobile demand suggest that unit sales of compact cars depend principally on their average price and consumers' real personal income. Consider the historical record of sales shown in the table.
|
Year
|
Sales (Millions of Cars)
|
Average Price (Thousands of Dollars)
|
Personal Income (2006 =100)
|
|
2006
|
2.00
|
20.0
|
100
|
|
2007
|
1.86
|
20.8
|
95
|
|
2008
|
1.94
|
20.0
|
97
|
|
2009
|
1.90
|
22.0
|
100
|
|
2010
|
1.90
|
24.0
|
105
|
a. Estimate the point elasticity of demand with respect to price. (Be sure to choose two years in which all other factors are constant.)
b. Estimate the income elasticity of demand.
c. Given the elasticities in parts (a) and (b), what change in sales do you expect between 2009 and 2010? How closely does your prediction match the historical record?
d. Estimate a linear demand equation that best fits the data using a regression program. Comment on the accuracy of your equation. Is this degree of accuracy realistic?