Answer to Question #175089 in Microeconomics for taha

Question

Q1.(A) Find equilibrium Price and quantity from the following demand and supply functions

        I.           D=40-4P                                                  S= 10+2P

(B)The demand function is Q= 20-5P estimate the elasticity of demand at P=2 and P=3

Equilibrium in market 

Answer 1

Solution:

A.). Equilibrium price and quantity:

At equilibrium: D = S

40 – 4P = 10 + 2P

40 – 10 = 2P + 4P

30 = 6P

P = $\frac{30}{6} = 5$

Substitute for Q:

Q = 40 – 4P = 40 – 4(5) = 40 – 20 = 20

Equilibrium price = 5

Equilibrium quantity = 20

B.). Point price elasticity of demand:

At equilibrium: D = S

40 – 4P = 10 + 2P

40 – 10 = 2P + 4P

30 = 6P

P = 30/6 = 5

Substitute for Q:

Q = 40 – 4P = 40 – 4(5) = 40 – 20 = 20

Equilibrium price = 5

Equilibrium quantity = 20

B.). Elasticity of demand:

Q = 20 – 5P

When P = 2

Q_d = 20 – 5 (2) = 20 – 10 = 10

When P = 3

Q_d = 20 – 5 (3) = 20 – 15 = 5

Point price elasticity of demand (PED) = $\frac{ P}{ Q} \times\frac{\% \triangle Q}{ \%\triangle P} = \frac{ P}{ Q}\times\frac{ \triangle Q}{ \triangle P}$

Point price elasticity when P = 2,

First derive: Elasticity of demand

Elasticity of demand (E_d) = $\frac{ \triangle Q}{ \triangle P}$ from the demand function:

Elasticity of demand (E_d) = $\frac{-5}{1} = - 5$

At P = 2, Q = 10

Point Price Elasticity of demand (PED) = $\frac{2}{10}\times - 5 = - 1$

PED = $-1$

At P = 3, Q = 5

Point Price Elasticity of demand (PED) = $\frac{3}{5}\times - 5 = - 3$

PED = $-3$

Point price elasticity for P = 2: = -1 and P = 3: = -3