Answer in Microeconomics for taha #175089
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
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
Qd = 20 – 5 (2) = 20 – 10 = 10
When P = 3
Qd = 20 – 5 (3) = 20 – 15 = 5
Point price elasticity of demand (PED) = “frac{ P}{ Q} timesfrac{% triangle Q}{ %triangle P} = frac{ P}{ Q}timesfrac{ triangle Q}{ triangle P}”
Point price elasticity when P = 2,
First derive: Elasticity of demand
Elasticity of demand (Ed) = “frac{ triangle Q}{ triangle P}” from the demand function:
Elasticity of demand (Ed) = “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
