Question

Find the equilibrium price and equilibrium quantity for the following functions. 

Demand: x = 100 – 2p and supply: x = 3p – 50.

Answer 1

Demand x = 100 – 2p 

Supply x = 3p – 50 

At equilibrium, demand = supply

100 – 2p = 3p – 50 

-2p – 3p = -100 – 50 

-5p = -150 

p = \(\frac{-150}{-5}\) = 30 

∴ Equilibrium price p_E = 30 

Supply, x = 3p – 50 

Put p = 30, we get 

x = 3(30) – 50 = 90 – 50 = 40 

∴ Equilibrium quantity x_E = 40