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Gillespie: Foundations of Economics

Demand, Supply and Equilibrium - Mathematically

The demand curve can be expressed mathematically. For example,
Qd = 50 - 5P
where Qd is the quantity demanded and P is the price. Notice that this is a downward sloping demand curve because a higher price leads to a fall in quantity demanded.

When the price is £3 the Qd = 50- (5*3) = 50 - 15 = 35 units
When the price increases to £5 the Qd = 50 - (5*5) = 50 - 25 = 25 units

The supply curve can also be expressed mathematically. For example,
Qs = 2 + 3P. This is an upward sloping supply curve; a higher price increases the quantity supplied.
When the price is £10 the quantity supplied = 2 + (3*10) = 32 units
When price increases to £20 the quantity supplied = 2 + (3*20) = 63

Equilbrium occurs where supply equals demand. This means:
50 - 5P = 2 + 3P

Rearranging the equation:
50 - 2 = 3P + 5P
48 = 8P
P = £6
This means the equilibrium price is £6
To find the equilibrium quantity we put the value for the price in either the supply or demand equation.
For example: Qs = 2 + (3*6) = 2 + 18 = 20 units