Short run price elasticity of demand?

Question

Economists from the University of Chicago estimate that the short run price elasticity of demand for cigarettes is 0.4. Based on this figure how much does a 10 percent hike in the price of cigarettes curtail the quantity demanded? How large a price hike is required to achieve a 10 percent reduction in quantity demanded?

can anybody help me with this question?

i feel as if there is not enough information

Answer 1

I would interpret the 0.4 number as indicating that demand drops only 0.4 times the percent of the cost increase. In other words, a 10% increase in the cost would result in only a 4% drop in demand.

To achieve a 10% drop in demand, a 25% increase in cost would be required (since 0.4 times 25% = 10%).

Answer 2

Ignore the other answer, it's wrong.

A PED measures how sensitive we are to prices.  So a PED of .4 (inelastic) means that as price increases 1%, quantity demanded drops .4.  So a 10% increase in the price would let to a 4% reduction in sales.  Notice that the reduction in quantity is less than the increase in price.  Thats because it is inelastic (people need their cigarettes) and people are not that sensitive to price changes.

If you want a 10% reduction in quantity, you would:

.4*x=10, so x=25% increase in price.

The previous poster had the right answer but an incorrect reasoning.  There is no 'drop in demand'.  The drop is in quantity demanded.  A drop in demand is an actual shift in the demand curve.  A drop in quantity demanded is a movement along the demand curve.  People often confuse the two