Question

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.

1. Estimate the point elasticity of demand with respect to price. (Be sure to choose two years in which all other factors are constant).

2. Estimate the income elasticity of demand.

Year	Sales (Millions of Cars)	Average Price (Thousands of Dollars)	Personal Income (2011 = 100)
2011	2.00	20.0	100
2012	1.86	20.8	95
2013	1.94	20.0	97
2014	1.90	22.0	100
2015	1.90	24.0	105

3. Given the elasticity in parts (a) and (b), what change in sales do you expect between 2014 and 2015? How closely does your prediction match the actual sales?

4. 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?

Answer 1

Q)

(a) to calculate price elasticity, years 2011 and 2014 are chosen as income is constant in these years

price elasticiy of demand = (change in quantity/ change in price)*(initial price/initial quantity)

= (1.9 -2/ 22 - 20)*(20/2)

= (-0.1/2)*(20/2)

= -0.5

(b) to calculate income elasticity, years 2011 and 2013 are chosen as price is constant in these years

income elasticiy of demand = (change in quantity/ change in income )*(initial income/initial quantity)

= (1.94-2/ 97-100)*(100/2)

= (-0.06/-3)*50

= 1

(c) % chnage in sales between 2014 and 2015

= price elasticty*percentage change in price + income elasticty*percentage change in income

= -0.5*(9.09) + 1*5

= 0.455%

The actual change in sales is = 0%

Thus there is an error of 0.455%