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