Question

Suppose the Madison city government imposes a price ceiling on the rental price of apartments.The demand for rental apartments is given by the equationP= 1500−0.2Q, and the supply is given by the equationP= 0.2Q+ 300.

(a) Without a price ceiling, what would be the equilibrium quantity and price? Calculate the consumer surplus (CS) and producer surplus (PS). Graph the demand and supply curves and shade the areas for CS and PS on the graph.

(b) Suppose the price ceiling is $700. How large a shortage will this create?

(c) Draw a graph representing the market outcome with the price ceiling. Calculate CS andPS.

(d) How does total surplus change due to the price ceiling?

(e) Suppose the government decided to instead implement a price ceiling that only created a shortage of 500 apartments. What price ceiling would accomplish this?

Answer 1

a. Without price ceiling, Equilibrium occurs where demand equals supply.

1500-0.2Q=0.2Q+300

1200=0.4Q

Equilibrium quantity Q*= 1200/0.4= 3000

Equilibrium Price P*= 1500-0.2*3000= $900

Consumer surplus=0.5*(1500-900)3000= $900000

Producer surplus=0.5*(900-300)3000=$900000

b. Price ceiling= $700

Shortage= Qd-Qs

700=1500-0.2Qd

Qd=4000

700=0.2Qs+300

Qs=2000

SHORTAGE= Qd-Qs=2000

c.

Consumer surplus=0.5(1500-1100)2000+(1100-700)(2000)=400000+800000=$1200000

Producer surplus=0.5(700-300)2000= $400000

d. Total surplus change due to price ceiling= Deadweight loss=0.5(1100-700)(3000-2000)= $200000

e. SHORTAGE of 500 apartmemts is when Price ceiling=$850

When Price Ceiling=$850,

Qd=3250, Qs=2750

SHORTAGE= Qd-Qs= 3250-2750=500 apartments.

If it helps kindly upvote