The average monthly rent for a 1-bedroom apartment in San Francisco ranges from approximately $2500 to $3700, depending on the neighborhood. A rent control policy setting $2000 per month rent on apartments is being considered in San Francisco, where the demand for apartments is given by P = 5000 − Q and the supply of apartments is P = 1000 + Q. Here, P = dollars of monthly rent, and Q = number of apartments available for rent. For purposes of this analysis, apartments are treated as identical.

(a)  What is the current market equilibrium price and quantity before the rent control is imposed?

(b) Now impose the rent control of P = $2000. Draw a market demand and supply graph and label the equilibrium price and quantity from part (a), the rent control price, and the number of apartments actually rented under the rent control policy. What is the change in consumer surplus, comparing the market equilibrium to the market with rent control? Label consumer surplus before and after rent control is imposed and show your work

Answer:

a) Current market equilibrium before rent control is achieved when demand = supply

Demand -: P = 5000-Q

Supply -: P = 1000+Q

Equilibrium when Demand = Supply. So equating above equations , we get -:

5000-Q = 1000 + Q

2Q= 5000-1000

2Q = 4000

Q = 4000/2

Q = 2000

Therefore , equilibrium quantity = 2000

To get equilibrium price . substiture value of Q in either demand or supply equation ,

P = 5000-Q

P=5000-2000

P=3000

Therefore , equilibrium rent price = $3,000

b) Now the rent control policy is adopted and price is set at $2000. It means that now the sellers cannot charge a rent higher than $2,000 .

Let us calculate the demand at this P=$2000

P = 5000 - Q

2000 = 5000 - Q

Q = 5000-2000

Qd= 3000.

Therefore quantity demanded (of apartments) at control rent price = 3000

Let us calculate the supply of apartments at P=$2000

P= 1000 + Q

2000 = 1000 +Q

Q = 2000-1000

Qs=1000.

Therefore quantity supplied (of apartments ) at P=$2000 is = 1000.

This creates a shortage as D>S .

Shortage = 3000 - 1000 = 2000.

CONSUMER SURPLUS CALCULATION -:

- Consumer surplus prior to rent control when Market Price is $3000-:

Consumer surplus = Area of     = 1/2(base)(height)

   = 1/2(2000)(5000 - 3000 )

   = 1/2(2000)(2000)

   = $2,000,000

- Consumer Surplus after rent control when Price is $2000 -:

Consumer Surplus =1+2(shown in figure) = Area of  ABE - Area of  GCE + Area of quadrilateral BCFD

   = 1/2 (2000)(5000-3000) - 1/2 (2000-1000)(4000-3000) + 1000(3000-2000)
   = 2,000,000 - 500,000 + 1,000,000

   = 3,000,000 - 500,000

   = $2,500,000

Change in consumer surplus (Increase by) = 2500000-2000000

   = $500,000

Market equilibrium at = E

Market equilibrium Qunatity = 2000

Market equilibrium price = $3000.

Consumer surplus before Rent control =  ABE

After rent control ,

Price = $2000

Quantity demanded = 3000

Quantity supplied = 1000

Shortage = 3000 - 1000 = 2000

Consumer surplus = 1 + 2 = Quadrilateral ABCG + Quadrilateral BCFD

Dead weight loss due to rent control =  GCE +  DCE

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