Question

Given the following supply and demand equations, solve the following

supply: p=q

Demand: p=200-p

a) What is the market equilibrium price and quantity?

b) What is the Consumer surplus and the producer surplus?

c) The government enacts a price ceiling of $120. What is the new consumer surplus?

d) Assume now the government enacts a price ceiling of $20. What is the new consumer surplus?

e) When the price ceiling is $20, consumer surplus declines, compared to the market equilibrium. Why? (this question gives answer options)

1. The lower prices do not overcome reduced quantity

2.The lower quantity does compensate for higher prices

3. Both 1 and 2

4. The lower prices create a marginal elasticity of demand

f) What is the deadweight loss from the price ceiling of $20?

g) What is the Producer Surplus under a price ceiling of $20?

Thank-you in advance for the help!!!

Answer 1

a) Supply: p = q

Demand: p = 200 - q

At equilibrium, q = 200 - q

=> q + q = 200

=> 2q = 200

=> q = 100

p = q = $100

Equilibrium price = $100

Equilibrium quantity = 100 units

b)

Consumer Surplus = Area below the demand curve but above the equilibrium price = Area of the triangle as shown in the graph above = 0.5 * Base * Height = 0.5 * 100 * ($200 - $100) = 0.5 * 100 * $100 = $5,000

Producer Surplus = Area above the supply curve but below the equilibrium price = Area of triangle = 0.5 * Base * Height = 0.5 * 100 * $100 = $5,000

c) A price ceiling of $120 is not binding on the market equilibrium as the equilibrium price is below the price ceiling of $120. Hence, the consumer surplus would remain the same as in the case of market equilibrium.

Consumer surplus = $5,000

d)

When a price ceiling of $20 is imposed, it is binding on the market as the market equilibrium price is above the price ceiling.

When p = $20, q = p = 20 units

Consumer Surplus = Area of the trapezium as shown in the graph above = 0.5 * (Sum of the lengths of the parallel sides) * (Perpendicular distance between the parallel sides)

= 0.5 * ($180 + $160) * 20

= 0.5 * $340 * 20

= $3,400