Question

1. Q = 4000 – 2P Q= - 150 +P a. Derive equilibrium price and quantity Derive point price elasticity of demand at equilibrium

Answer 1

Qd = 4000-2P

Qs = -150+P

For equllibrium price and quantity

Qd = Qs

4000-2P = -150+P

4150=3P

P= $1383.33

Approximately P = 1383

Q = 4000-2P = 4000-2*1383 = 1234

So approximate value of equillibrium price and quantity are

P = 1383

Q = 1234

point Price elasticity of demand = (-1/slope) (P/Q)

For getting slope convert the demand equation into inverse demand function

Q= 4000-2P

2P = 4000-Q

P = 2000-0.5Q

Now convert the inverse demand equation into the form of y = mx+C

m = slope

C = Constant

P = (-0.5)Q+2000

Here

m = -0.5 = slope

point Price elasticity of demand = (-1/slope)(P/Q)

Point Price elasticity of demand = (-1/-0.5)(1383/1234) = 2.241