3. A number of empirical studies of automobile demand yielded the following esti

Question

3. A number of empirical studies of automobile demand yielded the following estimates of income and price elasticities: Assume that income and price effects on automobile sales are independent and additive. Assume also that the auto companies intend to increase the average price of an automobile by about 6% in the next year and that next year's disposable personal income is expected to be 4% higher than this year's. If this year's automobile sales were 11 million units, how many would you expect to be sold under each pair of price and income demand elasticity estimates? Study Chow Income Elasticity Price Elasticity 2.5 1.4 Roos and Von Szeliski Suits 2.5 3.9 Explain answer

Explanation / Answer

Suppose that the quantity demanded of autobmobiles is Q ,the price is P and the income is I. Ep and Ei is the elasticity with respect to price and income respectively.

The elasticity of demand with respect to price = % change in quantity demanded/ % change in price

Ep = (dQ/Q*100)/(dP/P*100)

The elasticity of demand with respect to income is given by Ei = (dQ/dI*100)/(dP/P*100)

Obtaining the change in total sales for CHOW,

Ei = 3 = % change in quantity due to increase in income/ % increase in income = % change in P due to income increase/ 4

% change in quantity due to increase in income = 3*4 = 12%

Ep = % change in quantity due to increase in price/ % increase in price = % change in P due to increase in price / ( 6) = -1.2

% change in quantity due to increase in price = -1.2 * 6 = - 7.2%

Therefore, the sales expected in the next year = 11 million dollars + (12 - 7.2) % of 11 million units

= 11.528 million dollars

For Atkinson,

% change in quantity due to increase in income = 2.5 * 4 = 10

% change in demand due to increase in price = -1.4 * 6 = - 8.4%

Sales in next year = 11 + (10 -8.4)% of 11 = 11.176 million units

For Roos and Von,

% change in demand due to increase income = 2.5 * 4 = 10 %

% change in demand due to increase in price = -1.5*6 = -9

Sales in next year = 11 + (10 - 9) % of 11 = 1.11 million units

For Suits,

% change in demand due to change in income = 3.9* 4 = 15.6

% change in demand due to change in price = -1.2*6 = -7.2

Sales in next year = 11 + (15.6 -7.2) % of 11 = 11.924 million units

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