Question

Given below are the demand and supply functions for three interdependant.

Qd=110-4p+3p-4p: Qs=2p-20

Determine the equilibrium price and quantity for the commodity market model.Then compute the price and cross elasticities of demand for the market and interpreted it's coefficient

Answer 1

Solution:

At equilibrium: Qd = Qs

110 – 4p + 3p – 4p = 2p – 20

110 + 20 = 2p + 4p + 4p – 3p

130 = 7p

P = 18.57

Equilibrium price = 18.57

Substitute to derive equilibrium quantity:

Qd = 110 – 4p + 3p – 4p = 110 – 4(18.57) + 3(18.57) – 4(18.57) = 110 – 74.28 + 55.71 – 74.28 = 17

Qd = 17 units

Equilibrium quantity = 17 units

 

 

Price elasticity of demand = $\frac{ \triangle Q} {\triangle P} \times \frac{P} {Q}$

$\frac{ \triangle Q} {\triangle P} =$ -4

= $-4 \times \frac{18.57} {17} = -4.37$

Price elasticity of demand = 4.37