%ΔQ = elasticity %ΔP; %Δ (PQ) = %ΔP+%ΔQ
The price elasticity of supply is defined as %ΔQ/%ΔP when moving along a supply curve. It is typically a positive number. (That is, supply curves slope up.)
The price elasticity of demand is defined as %ΔQ/%ΔP when moving along a demand curve. It is typically a negative number. Economists often talk about price elasticities of demand in terms of their absolute value, so that you have to supply the negative sign yourself from your general knowledge that increases in price reduce the quantity demanded. (That is, demand curves slope down.)
In the exercise below, the last four problems are more difficult, but for the rest, here is the procedure:
- Figure out whether the elasticity should have a negative sign because it is a demand elasticity or a positive sign because it is a supply elasticity. Together with the absolute value of the elasticity in the second column, that will give you the elasticity with a + or a - in the third column.
- Multiply the (Platonic) percent change in the price by the elasticity to find the percent change in the quantity.
- Add the percent change in the price and the percent change in the quantity to get the percent change in revenue PQ.
Of the harder questions, some are missing %ΔP but have %ΔQ. All you need to do there is to divide %ΔQ by the signed elasticity to get %ΔP. Then you can add %ΔP to %ΔQ to get the percent change in PQ. The last two questions are the hardest. There you need to do a bit of algebra:
%Δ (PQ) = (1 + elasticity) %ΔP
You can solve for %ΔP, and then multiply by the elasticity to get %ΔQ.
The answers are below as a filled-in table.
