Question

Find equilibrium Price and Quantity and Price Elasticity of Demand from the following demand and supply functions

         i.       Q=10-2P²                      Q=5+3P

         ii.      Qd= 200-40P                Qs= -40+80P

Answer 1

i) The market equilibrium occurs when $Q_d=Q_s$:

$$10-2P_E=5+3P_E,$$ $$5=5P_E,$$ $$P_E=\$1.$$

Then, we can find the equilibrium quantity:

$$Q_E=10-2\cdot1=8.$$

Let's write the inverse-demand function:

$$P=5-0.5Q.$$

The price elasticity of demand can be found as follows:

$$E_d=(\dfrac{-1}{slope})\dfrac{P}{Q_d},$$ $$E_d=(\dfrac{-1}{-0.5})\cdot\dfrac{1}{8}=0.25.$$

ii) The market equilibrium occurs when $Q_d=Q_s$:

$$200-40P_E=-40+80P_E,$$ $$240=120P_E,$$ $$P_E=\$2.$$

Then, we can find the equilibrium quantity:

$$Q_E=200-40\cdot2=120.$$

Let's write the inverse-demand function:

$$P=5-0.025Q.$$

The price elasticity of demand can be found as follows:

$$E_d=(\dfrac{-1}{slope})\dfrac{P}{Q_d},$$ $$E_d=(\dfrac{-1}{-0.025})\cdot\dfrac{2}{120}=0.67.$$