A researcher estimated the Ep for autos in the U.S. is –1.2, while the Ei is 3.0. Next year, U.S. automakers intend to increase the average price of autos by 5%, and they expect consumers’ disposable income to rise by 3%.
A) If sales of domestically produced autos are 8 million this year, how many autos do you expect U.S. automakers to sell next year?
B)Byy how much should domestic automakers increase the price of autos if they wish to increase sales by 5%?
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To answer these questions, we need to first understand the concepts of the price elasticity of demand (Ep) and the income elasticity of demand (Ei).
Ep measures the responsiveness of quantity demanded to a change in price, while Ei measures the responsiveness of quantity demanded to a change in income.
A) To estimate the number of autos U.S. automakers are expected to sell next year, we can use the formula:
% Change in Sales = % Change in Price + (% Change in Income x Ei)
Given that the estimated Ep is -1.2, the % Change in Price is 5%, and the % Change in Income is 3%, we can plug these values into the formula:
% Change in Sales = 5 + (3 x -1.2)
% Change in Sales = 5 - 3.6
% Change in Sales = -1.6
To calculate the number of autos U.S. automakers are expected to sell next year, we multiply the % Change in Sales by the original sales figure:
Expected Sales = (1 + % Change in Sales) x Current Sales
Expected Sales = (1 - 0.016) x 8 million
Expected Sales = 7.968 million
Therefore, U.S. automakers are expected to sell approximately 7.968 million autos next year.
B) To determine the increase in price required to achieve a 5% increase in sales, we need to calculate the price elasticity of demand (Ep) using the formula:
Ep = % Change in Quantity Demanded / % Change in Price
Given that the desired increase in sales is 5% and the current Ep is -1.2, we can rearrange the formula to solve for the % Change in Price:
% Change in Price = % Change in Quantity Demanded / Ep
% Change in Price = 0.05 / -1.2
% Change in Price = -0.0417
To calculate the increase in price, we multiply the % Change in Price by the current price:
Increase in Price = Current Price x % Change in Price
Increase in Price = Current Price x (-0.0417)
Therefore, the domestic automakers should increase the price of autos by -0.0417 (approximately -4.17%) if they wish to increase sales by 5%.