Question

Suppose demand and supply are given by: P = 125 - 4Qd P = 2Qs a. Find equilibrium price and quantity. b. What is the effect of a price ceiling set at P=20? c. What is the effect of a price floor set at P=20? d. What is the effect of a price ceiling set at P=60? e. What is the effect of a price floor set at P=60? e. Draw a diagram showing your answers in a, b, e.

Answer 1

a) Equilibrium is where demand = supply

Qd = (125 - P)/4

Qs = P/2

Qd = Qs

(125 - P)/4 = P/2

250 - 2P = 4P

6P = 250

P = 41.67

Q = P/2 = 41.67/2

Q = 20.83

b) At $ 20, Qd = (125 - 20)/4 = 105/4 = 26.25

Qs = 20/2 = 10 units

There is shortage of Qd - Qs = 26.25 - 10 = 16.25 units

This is binding price ceiling.

c) Price floor below equilibrium price is non binding price. It does not affect the market.

d) Price ceiling above equilibrium price is non binding price ceiling. It does not affect the market.

e) At $ 60, Qd = (125 - 60)/4 = 65/4 = 16.25

Qs = 60/2 = 30

Qs > Qd i.e. there is surplus in the market.

Surplus = Qs - Qd = 30 - 16.25 = 13.75 units