Question

Recall the Application​ "Smoking, Drinking, and​ Elasticity." If the number of highway deaths among young people is roughly proportional to their beer consumption and young​ peoples' elasticity of demand for beer is​ 1.5, then to decrease highway deaths of young people by 15​ percent, taxes would need to be increased enough to increase the price of beer​ by:

(A) 10%
(B) 15%
(C) 20%
(D) 25%

Answer 1

(A) 10%

Step-by-step explanation:

The price elasticity of demand measures the sensitivity of demand in the face of price change. The calculation of the price elasticity of demand consists in dividing the change in quantity by the change in price. If the result is greater than | 1 | We say that demand is elastic, that is, sensitive to changes in price. If the result is between 0 and 1 we say that demand is inelastic, not sensitive to changes in price.

Thus we already know that the demand for beer is elastic, price sensitive. By applying the formula, we get the following result:

E = ΔQ/ΔP

At where

E = elasticity

ΔQ = Change in Quantity

ΔP = Price change

Exercise gives us the data of E = 1.5% and ΔQ = 15%

So using the formula:

1,5 = 15%/ΔP

ΔP = 1,5/15 = 0,1 = 10%

Therefore, to reduce the number of student deaths in car accidents, a tax needs to raise the price of alcohol by 10%.

Note: It is given that the variation in the number of deaths is proportional to the variation in the quantity demanded for beer.