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).

Here is an example:

The price of a tonne of wheat last year was £20. At this price 200,000 tonnes were sold. An economist firm calculated that the PED of wheat was -0.2 and that the PES was 0.6. Calculate the demand and supply functions based on this information.

First we substitute the information into PED = -b(P/Q):

-0.2 = -b(20/200,000)

-0.2 = -b(0.0001)

b = 2000

This can then be substituted into the demand function (QD = a – bP):

200,000 = a – 2000(20)

200,000 = a – 40,000

a = 240,000

Therefore QD = 240,000 – 2000P which can be simplified to:

QD = 240 – 2P

We now apply the same process to find out the supply function

PES = d(P/Q)

0.6 = d(20/200,000)

d = 6000

QS = c + dP

200,000 = c + 6000(20)

200,000 = c + 12,000

188000 = c

We can then substitute and simply to get QS = 188 + 12P