Question

Consider the following supply and demand equations, in the market for laddus: Supply:p= (1/5)q, Demand:p= 30−q. The government wants people to enjoy laddus at a reasonable price, and so enacts a price ceiling of ̄p= 1. What is the deadweight loss under this price ceiling?

Answer 1

We have the following information

Supply: p = (1/5)q

Demand: p = 30 – q

Equilibrium is achieved at the intersection of demand and supply curves

30 – q = (1/5)q

30 = (1/5)q + q

30 = (6/5)q

Equilibrium quantity (q) = 25

p = 30 – q

p = 30 – 25

Equilibrium price (p) = 5

The equilibrium is signified by point e in the diagram below

Now, it is given that government has introduced a price ceiling of p = 1. At this price, the quantity demanded is

p = 30 – q

1 = 30 – q   

Quantity demanded at price 1 = 29

However, at the price of 1 the quantity that the sellers are ready to sell is

p = (1/5)q

1 = (1/5)q

Quantity supplied at price 1 = 5

So, the shortage is of 24 units

For the 5 units that the suppliers are ready to sell at price 1, the consumer is willing to pay

p = 30 – q

p = 30 – 5

Price consumers are willing to pay for 5 units is 25.

The Deadweight loss generated by the price ceiling is signified by the shaded area of triangle def.

Area of a triangle =   (1/2) × Base × Height

Deadweight loss = (1/2) × 24 × 20

Deadweight loss = 240