Answer to Question #288175 in Microeconomics for helenabebe

Question

. The market demand and supply for the good are given as Qd = 250 - 50P and Qs = 25 + 25P; A) Find the equilibrium price and quantity respectively B) Calculate the price elasticity of demand at equilibrium point. C) Calculate the price elasticity of supply at the equilibrium point. D) What is surplus or shortage if price is Birr 5

Answer 1

Solution:

A.). At equilibrium: Qd = Qs

250 – 50P = 25 + 25P

250 – 25 = 25P + 50P

225 = 75P

P = 3

Market equilibrium price = 3

Substitute to derive market equilibrium quantity:

Qd = 250 – 50P = 250 – 50(3) = 250 – 150 = 100

Qd = 100

Market equilibrium quantity = 100

 

B.). Price elasticity of demand = $\frac{\triangle Qd}{\triangle P} \times \frac{P}{Qd}$

$\frac{\triangle Qd}{\triangle P}$ = -50

Price elasticity of demand = $-50\times \frac{3}{100} = -1.5$

Price elasticity of demand = -1.5

 

C.). Price elasticity of supply = $\frac{\triangle Qs}{\triangle P} \times \frac{P}{Qs}$

$\frac{\triangle Qs}{\triangle P}$ = 25

Price elasticity of supply = $25\times \frac{3}{100} = 0.75$

Price elasticity of supply = 0.75

 

D.). When the price is set above the equilibrium price, quantity supplied will exceed quantity demanded and excess supply will result.

Qd at the price of 5: Qd = 250 – 50(5) = 250 – 250 = 0

Qs at the price of 5: Qs = 25 + 25(5) = 25 + 125 = 150

Excess supply = 150 – 0 = 150

Excess supply = 150