Question

# A shop sells 20 hats per week at \$10 each. When it increases the price to...

A shop sells 20 hats per week at \$10 each. When it increases the price to \$12, the number of hats sold falls to 15 per week. Which of the following statements are correct?

1. When the price increases from \$10 to \$12, demand increases by 25%.

2. A 20% increase in the price causes a 25% fall in demand.

3. The demand for hats is inelastic.

4. The elasticity of demand is approximately 1.25.

statement 2 is correct.
1)
the demand decreases from 20 to 15, not increase.
incorrect statement
2)
change in quantity=(15-20)/20
=-25%
the quantity decreases by 25%
increase in price=(12-10)/10=20%
the statement is correct
3) and 4)

price elasticity of demand=(change in quantity demanded/average quantity)/(change in price/average price)
change in quantity demanded=(15-20)=-5
average quantity demanded=(15+20)/2=17.5
change in price=(12-10)=2
average price=(12+10)/2=11
E=(-5/17.5)/(2/11)
=-1.57142857
second method
E=%change in quantity/%change in price
=-25/20
=-1.25
3 incorrect and 4 is correct