# Maths with Price Elasticity

Below is an example of how to use the formulae for PED and PES to work out the supply and demand functions.

Firstly we have to be able to re-arrange PED (the same applies for the respective formula for PES):

PED = ΔQD / ΔP (where Δ is change, QD is quantity demanded, and P is price)

We know that the formula for percentage change is:

((Change/Original)*100)

Therefore the formula for nominal change (a change in numbers, not percentages) is (Change / Original)

Hence, using this, we can change the PED formula to:

PED = ΔQD/QD ÷ ΔP/P

We can change the division symbol to a multiplication symbol by flipping the term on the right hand side:

PED = ΔQD/QD x P/ΔP

PED = ΔQD/ΔP x P/QD

A change in QD divided by a change in P can be written as the differential of QD in terms of P:

PED = dQD/dP x P/Q

We can then work out dQD/dP by differentiating the demand function and substituting this value in:

QD = a – bP

dQD/dP = -b (differentiate a – bP)

Substitute:

PED = -b(P/Q)

We can now use this formula to find out demand functions (and if you use the same process with PES, supply functions). [...]

# Everyday Economics – Why are consumer prices generally higher in urban areas than in rural areas?

In condensed urban areas there are many (potential) consumers and many firms operating to produce and sell to these consumers. The retail industry could be seen as operating between perfect competition and monopolistic competition, most retail establishments (including corner shops and the larger chains who sell branded goods; not including own brands) sell homogeneous goods and don’t usually have monopolies (however shop locations can be seen as effective local monopolies, as areas may be restricted as to the number of shops they can have). Therefore we would expect strong competition in this market and hence the driving down of prices for consumers. [...]