Question

Given the following market demand and supply functions;
Qd = 20 – 2P; Qs = -40 + 6P.
.
i. What are the equilibrium conditions (5 marks)
ii. Find the equilibrium price (5 Marks)
iii. Find the equilibrium quantity (5 Marks)
iv. Calculate the own price elasticity of demand

Answer 1

Solution:

i.). The equilibrium conditions are; the quantity demanded must be equal to the quantity supplied at a particular price; the market will be at equilibrium at the point where the demand curve intersect the supply curve.

 

ii.). At equilibrium: Qd = Qs

20 – 2P = -40 + 6P

20 + 40 = 6P + 2P

60 = 8P

P = 7.5

The equilibrium price = 7.5

 

iii.). Substitute the equilibrium price in either the demand or supply equation to derive the quantity:

Qd = 20 – 2P

Qd = 20 – 2(7.5) = 20 – 15 = 5

Qd = 5

Qs = -40 + 6P

Qs = -40 + 6(7.5) = -40 + 45 = 5

Qs = 5

Therefore, the equilibrium quantity = 5 units

 

iv.). Own price elasticity of demand = $\frac{\%\triangle Qd}{\%\triangle P} \times \frac{P}{Q}$

$\frac{\%\triangle Qd}{\%\triangle P} =$ -2

P = 7.5

Q = 5

PEd = $-2 \times \frac{5}{7.5} = -2\times1.5 = -3$

Own price elasticity of demand = -3