Question

Suppose that the demand curve for Game of Thrones episodes is given by QD = 30 − 2P. The supply curve for Game of Thones episodes is fixed at QS = 10.

1. Write down the corresponding inverse demand function.

2. At what price will the quantity demanded of Game of Thrones episodes become zero?

3. Draw the demand curve and find a set of prices (3) where the demand curve is elastic, inelastic, and unit elastic.

4. Following season 8, consumer preferences for Game of Thrones episodes fell sharply and is now only Q = 20 − 2P. What is the new equilibrium price? How does it compare to the old equilibrium price?

Answer 1

1. Qd=30-2P

Inverse demand function:

P= 15-0.5Qd

2. Qd=0=30-2P

P= 30/2=15

At Price=15, Qd= 0

3. When demand is unit elastic, total revenue is maximum.

TR=P*Q= (15-.5Qd)*Qd= 15Qd-0.5Qd^2

dTR/dQ= 15-Qd=0

Qd=15 or TR is maximum when Qd=15.

P= 15-.5*15= $7.5

So demand is elastic when 15≤P<7.5

Demand is unit elastic when p=7.5

Demand is inelastic when 7.5<p≤0

4. Old equilibrium exist where Qd=Qs

30-2p=10

20=2p

Equilibrium price= $10

New equilibrium price is where Q=Qs

20-2p=10

10=2p

New Equilibrium price = $5

New equilibrium price is less than old equilibrium price due to fall in demand.

Answer 3. Demand curve.