The coefficient of the price of gasoline in the regression of the quantity demanded of automobiles (in millions of units) on the price of gasoline (in dollars) and other variables is -14. (a) calculate the cross price elasticity of demand between automobiles and gasoline at the gasoline $ 1 per gallon and sales of automobiles of 8 (million units).

(b) What would be the cross price elasticity of demand between automobiles and gasoline if sales of automobiles declined from 8 to 6 with an increase in the gasoline price from $ 1 to $ 1.20 per gallon?

Take a shot, what do you think.

hint: increase the price of gas by 1%, what happens to the quantity of autos (the percentage change)

To calculate the cross price elasticity of demand between automobiles and gasoline, we can use the formula:

Cross price elasticity of demand = (% change in quantity demanded of automobiles) / (% change in price of gasoline)

(a) To calculate the cross price elasticity of demand at a gasoline price of $1 per gallon and sales of automobiles of 8 million units:

First, we need to find the percentage change in quantity demanded of automobiles when the price of gasoline changes from $1 to $1 per gallon. The coefficient of the price of gasoline in the regression is -14, which means that a 1% increase in the price of gasoline is associated with a 14% decrease in quantity demanded of automobiles.

So, the percentage change in quantity demanded of automobiles is -14%.

Next, we need to find the percentage change in the price of gasoline. Since the price is constant at $1 per gallon, the percentage change is 0%.

Using these values in the formula:

Cross price elasticity of demand = (-14%) / (0%) = undefined (since there is no change in price)

So, the cross price elasticity of demand between automobiles and gasoline at a gasoline price of $1 per gallon is undefined.

(b) To calculate the cross price elasticity of demand when sales of automobiles declined from 8 to 6 million units and the price of gasoline increased from $1 to $1.20 per gallon:

First, we need to find the percentage change in quantity demanded of automobiles. The quantity demanded decreased from 8 to 6 million units, which is a decrease of 2 million units. The percentage change is therefore (-2 million units / 8 million units) x 100% = -25%.

Next, we need to find the percentage change in the price of gasoline. The price increased from $1 to $1.20 per gallon, which is an increase of $0.20. The percentage change is therefore ($0.20 / $1) x 100% = 20%.

Using these values in the formula:

Cross price elasticity of demand = (-25%) / (20%) = -1.25

So, the cross price elasticity of demand between automobiles and gasoline when sales of automobiles declined from 8 to 6 million units and the price of gasoline increased from $1 to $1.20 per gallon is -1.25.

To calculate the cross price elasticity of demand, we need the formula:

Cross Price Elasticity of Demand = (% change in quantity demanded of automobiles) / (% change in price of gasoline)

(a) At a gasoline price of $1 per gallon and sales of automobiles of 8 million units, we first need to calculate the percentage change in quantity demanded and the percentage change in price.

To calculate the percentage change in quantity demanded:
% change in quantity demanded = (change in quantity demanded / initial quantity demanded) * 100%

Since the initial sales of automobiles are 8 million units and there is no change in quantity demanded, the percentage change in quantity demanded will be 0.

To calculate the percentage change in price:
% change in price = (change in price / initial price) * 100%

Since the initial price of gasoline is $1 per gallon and there is no change in price, the percentage change in price will also be 0.

Therefore, the cross price elasticity of demand at a gasoline price of $1 per gallon and sales of automobiles of 8 million units is 0/0, which is undefined.

(b) If sales of automobiles decline from 8 to 6 million units and the gasoline price increases from $1 to $1.20 per gallon, we can calculate the percentage change in quantity demanded and the percentage change in price.

Percentage change in quantity demanded:
% change in quantity demanded = ((final quantity demanded - initial quantity demanded) / initial quantity demanded) * 100%
% change in quantity demanded = ((6 - 8) / 8) * 100%
% change in quantity demanded = (-2 / 8) * 100%
% change in quantity demanded = -25%

Percentage change in price:
% change in price = ((final price - initial price) / initial price) * 100%
% change in price = (($1.20 - $1) / $1) * 100%
% change in price = ($0.20 / $1) * 100%
% change in price = 20%

Now, we can calculate the cross price elasticity of demand:
Cross Price Elasticity of Demand = (% change in quantity demanded of automobiles) / (% change in price of gasoline)
Cross Price Elasticity of Demand = -25% / 20%
Cross Price Elasticity of Demand = -1.25

Therefore, the cross price elasticity of demand between automobiles and gasoline, when sales of automobiles decline from 8 to 6 million units and the gasoline price increases from $1 to $1.20 per gallon, is -1.25.