Question

Consider the following supply and demand equations: Supply: p = 10 + q Demand: p = 100 − 2q Show your work as your respond to the following questions.

(a) What is the market equilibrium price and quantity?

(b) What is the Total Surplus at equilibrium?

(c) The government enacts a price ceiling at ¯p = 50. What is the Total Surplus?

(d) Calculate the Consumer Surplus under a price ceiling of ¯p = 20.

(e) What is the Deadweight Loss under a price ceiling of ¯p = 10?

Answer 1

1)

Market equilibrium is attained where Demand = Supply:

Price = 40

Quantity = 30

2)

Total surplus at equilibrium = Area bounded by Demand and supply curves with the Y axis

Total surplus at equilibrium = (100 - 10) x 30/2 = 1350

3) price ceiling = 50 (maximum price)

This would be non-binding as equilibrium price < price ceiling

Total surplus remains the same = 1350

4)

price ceiling = 20 (maximum price)

This would be binding as equilibrium price > price ceiling

Consumer surplus = green shaded region in the graph above

CS = (100 - 80) x 10/2 = 100

5)

price ceiling = 10 (maximum price)

This would be binding as equilibrium price > price ceiling

Dead weight loss = entire total surplus calculated in part 2) , this is because no supplier would be willing to supply at a price = 10.

Quantity supplied = 0

DWL = 1350