Calculating equilibrium elasticity

Formula:

B (P × Q)

Questions

Qd = 200 – 6P

Qs = - 400 + 34P

1.Determine the equilibrium price and output

2.Calculate the equilibrium quantity demand elasticity

3.Calculate the equilibrium quantity supply elasticity

Answers

Q1

Qd = 200 – 6P

Qs = - 400 + 34P

Qs = Qd

Determining the equilibrium price

-400 + 34P = 200 – 6P

6P + 34P = 200 + 400

40P = 600

P = 15

Now that we have the equilibrium price, we can find the equilibrium output by substituting P with it.

Determining the equilibrium quantity

Either Qs or/and Qd should have the same equilibrium, if not the equilibrium substituted must be inaccurate.

Qs = - 400 + 34P

Qs = - 400 + 34(15)

Qs = - 400 + 510

Qs = 110

For confirmation, calculate the equilibrium output of quantity demand, should it give a different from the quantity supply then something went wrong.

P = 15

Qd = 200 – 6P

Qd = 200 – 6(15)

Qd = 200 – 90

Qd = 110

Market price and output

Therefore,

Market output = 110

Market price = $15

Q2

Determining the equilibrium demand price elasticity

B (P ÷ Q)

Qd = 110

P = $15

B = - 6

Edep = - 6 ( 15 ÷ 110)

Edep = (-) 0.82 (Economists ignore the minus signs acknowledging it will always be like that because of the inverse relation)

Q3

Determining the equilibrium supply price elasticity

B (P ÷ Q)

Qs = 110

P = $15

B = 34

Esep = 34 (15 ÷ 110)

Esep = 4.64

Concluding that the quantity supplied is more elastic to price adjustments in comparison to the quantity demanded.