Problem : If supply is unit elastic and demand is inelastic, a shift in which curve would affect quantity more? Price more?
Shifting the demand curve would affect quantity more, and shifting the supply curve would affect price more.
Problem : Katherine advertises to sell cookies for $4 a dozen. She sells 50 dozen, and decides that she can charge more. She raises the price to $6 a dozen and sells 40 dozen. What is the elasticity of demand? Assuming that the elasticity of demand is constant, how many would she sell if the price were $10 a box?
To find the elasticity of demand, we need to divide the percent change in quantity by the percent change in price.
% Change in Quantity = (40 - 50)/(50) = -0.20 = -20%
% Change in Price = (6.00 - 4.00)/(4.00) = 0.50 = 50%
Elasticity = |(-20%)/(50%)| = |-0.4| = 0.4
The elasticity of demand is 0.4 (elastic).
To find the quantity when the price is $10 a box, we use the same formula:
Elasticity = 0.4 = |(% Change in Quantity)/(% Change in Price)|
% Change in Price = (10.00 - 4.00)/(4.00) = 1.5 = 150%
Remember that before taking the absolute value, elasticity was -0.4, so use -0.4 to calculate the changes in quantity, or you will end up with a big increase in consumption, instead of a decrease!
-0.4 = |(% Change in Quantity)/(150%)|
|(%Change in Quantity)| = -60% = -0.6
-0.6 = (X - 50)/50
X = 20
The new demand at $10 a dozen will be 20 dozen cookies.