Answer to Question #159061 in Macroeconomics for Desalegn Beyene

Question

Qs=150+14P and demand function P= 16.875-0.0625Q with 10 number of sellers and buyers.

Find equilibrium price and quantity

Find price elasticity of demand and and supply at equilibrium price and quantity

Answer 1

a)Let's first rearrange our demand function:

$0.0625Q=16.875-P,$ $Q_d=270-16P.$

Let's find the equilibrium price and quantity. In the equilibrium, $Q_d=Q_s$ and we can find the equilibrium price:

$270-16P_E =150+14P_E,$ $30P_E=120,$ $P_E=\$4.$

Then, we can find the equilibrium quantity by substituting $P_E$ into the equation for $Q_d$:

$Q_d=Q_s=Q_E=270-16\cdot4=206.$

b) Let's rewrite our equations for $Q_d$ and $Q_s$ in slope-intercept form:

$P=16.875-0.0625Q_d,$ $P=0.071Q_s-10.71.$

The price elasticity of demand can be found as follows:

$E_d=(\dfrac{-1}{slope})(\dfrac{P}{Q_d})=(\dfrac{-1}{(-0.0625)})(\dfrac{4}{206})=0.31$

The price elasticity of supply can be found as follows:

$E_s=(\dfrac{1}{slope})(\dfrac{P}{Q_s})=(\dfrac{1}{0.071})(\dfrac{4}{206})=0.27$