Question

10. Exercise 3.10

The Reliable Aircraft Company manufactures small, pleasure-use aircraft. Based on past experience, sales volume appears to be affected by changes in the price of the planes and by the state of the economy as measured by consumers' disposable personal income. The following data pertaining to Reliable's aircraft sales, selling prices, and consumers' personal income were collected:

Year	Aircraft Sales	Average Price	Disposable Constant Income
		(Dollars)	(In constant 2006 dollars, billions)
2006	525	16,800	610
2007	450	8,000	610
2008	400	8,000	580

The arc price elasticity of demand between 2006 and 2007 is:

0.38

0.22

0

–0.22

The arc income elasticity of demand between 2007 and 2008 is:

0

2.33

5.36

–2.33

Assume that these estimates are expected to remain stable during 2009. Forecast 2009 sales for Reliable assuming that its aircraft prices remain constant at 2007 levels and that disposable personal income will increase by 7%. Also assume that the arc income elasticity you just computed is the best available estimate of income elasticity.

Aircraft Sales 2009 Forecast:

Forecast 2009 sales for Reliable given that its aircraft prices will increase by 6% from 2008 levels and that disposable personal income will increase by 7%. Assume that the price and income effects are independent and additive and that the arc income and price elasticities you just computed are the best available estimates of these elasticities to be used in making the forecast.

Aircraft Sales 2009 Forecast:

Answer 1

(1) Arc elasticity of demand = (Change in Sales / Average sales) / (Change in price / Average price)

= [(450 - 525) / (450 + 525)] / [(8,000 - 16,800) / (8,000 + 16,800)]

= (-75 / 975) / (-8,800 / 24,800)

= 0.22

(2) Arc income elasticity = (Change in Sales / Average sales) / (Change in Income / Average income)

= [(400 - 450) / (400 + 450)] / [(580 - 610) / (580 + 610)]

= (-50 / 850) / (-30 / 1,190)

= 2.33

(3) Income elasticity = % Change in Sales / % Change in disposable income

2.33 = % Change in Sales / 7%

% Change in Sales = 7% x 2.33 = 16.31%

New value of sales = 400 x 1.1631 = 465.24

(4) Price elasticity = % Change in Sales / % Change in price

0.22 = % Change in Sales / 6%

% Change in Sales = 6% x 0.22 = 1.32%

Change in sales caused by price effect = 400 x 1.32% = 5.28

Change in sales caused by income effect = 400 x 16.31% = 65.24

Net change in sales = Change in sales caused by price effect + Change in sales caused by income effect = 5.28 + 65.24

= 70.52 (increase)

New value of sales = 400 + 70.52 = 470.52