Please help with this question:

A researched estimated that the price elasticity of demand for automobiles in the U.S. is -1.2, while the income elasticity if demand is 3.0. Next year, U.S. auto makes intend to increase the avg price of autos by 5%, and they expect consumers' disposable income will increase by 3%.

(a)If sales of domestically produced automobiles are 8 million this year, how many automobiles do you expect U.S. auto makers to sell next year?
(b)By how much should domestic auto makers increase the price of automobiles if they wish to increase sales by 5 percent next year?

take a shot, what do you think?

To answer these questions, we will need to use the price elasticity of demand and the income elasticity of demand. Let's break down the steps to find the answers:

(a) To determine the expected sales of domestically produced automobiles next year, we will use the price elasticity of demand. The price elasticity of demand measures the responsiveness of quantity demanded to a change in price.

The formula for calculating the percentage change in quantity demanded due to a percentage change in price is:

Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

Given that the price elasticity of demand is -1.2 and the average price of autos is expected to increase by 5%, we can calculate the expected change in quantity demanded.

% Change in Quantity Demanded = Price Elasticity of Demand * % Change in Price

% Change in Quantity Demanded = -1.2 * 5%

Next, we substitute the given values and calculate the expected change in quantity demanded:

% Change in Quantity Demanded = -1.2 * 0.05

% Change in Quantity Demanded = -0.06

To find the expected number of automobiles sold next year, we multiply the expected change in quantity demanded by the number of automobiles sold this year:

Expected Change in Quantity Demanded = % Change in Quantity Demanded * Number of Automobiles Sold this Year

Expected Change in Quantity Demanded = -0.06 * 8 million

Expected Change in Quantity Demanded = -480,000

Therefore, the expected number of automobiles U.S. auto makers will sell next year is:

Number of Automobiles Sold Next Year = Number of Automobiles Sold this Year + Expected Change in Quantity Demanded

Number of Automobiles Sold Next Year = 8 million + (-480,000)

Number of Automobiles Sold Next Year = 7.52 million

(b) To determine the price increase needed to increase sales by 5 percent next year, we need to consider the income elasticity of demand. The income elasticity of demand measures the responsiveness of quantity demanded to a change in income.

Using the income elasticity of demand, we can calculate the percentage change in quantity demanded due to a percentage change in income. The formula is similar to the one used for price elasticity of demand:

Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)

Given that the income elasticity of demand is 3.0 and disposable income is expected to increase by 3%, we can calculate the expected change in quantity demanded.

% Change in Quantity Demanded = Income Elasticity of Demand * % Change in Income

% Change in Quantity Demanded = 3.0 * 3%

Next, substitute the given values and calculate the expected change in quantity demanded:

% Change in Quantity Demanded = 3.0 * 0.03

% Change in Quantity Demanded = 0.09

To find the necessary price increase to achieve a 5 percent increase in sales, we divide the expected change in quantity demanded by the initial quantity:

Price Increase = % Change in Quantity Demanded / Initial Quantity

Price Increase = 0.09 / 8 million

Therefore, the necessary price increase to increase sales by 5 percent next year is:

Price Increase = 0.00001125

Price Increase = 0.001125 (approximately 0.113%)

Therefore, domestic auto makers should increase the price of automobiles by approximately 0.113% to achieve a 5 percent increase in sales next year.