Allocatively Efficient Quantity

Question

Demand = (-100,000/1,000,000)x +900,000 Supply =( 200,000/1,000,000)x Y-axis= price in dollars increments in100,000 X-axis= quantity of house increments in millions

equilibrium: price = 600,000 quantity = 3,000,000

The figure shows the market for new homes at the end of 2022. Virtually everyone requires a mortgage—a loan—to buy a home. In 2023, the interest rate paid on mortgages rose significantly. Consequently, at every price the quantity of new homes demand changed by 3 million. The market was in equilibrium in 2022 and 2023.

At the end of 2022, what was the allocatively efficient quantity of new homes?

Illustrate how the market (that is, the demand and supply) for new homes changed in 2023.

In 2023, what is the equilibrium price and quantity of new homes? What is the allocatively efficient quantity? What is the amount of consumer surplus? Is there a deadweight loss? Answer in an essay

Answer 1

In 2022, the allocatively efficient quantity of new homes was at the equilibrium point where the demand and supply curves intersected, with a price of $600,000 and a quantity of 3,000,000. The equations for the demand and supply curves were:

Demand: Qd = 900,000 - 100P

Supply: Qs = 200P

Here, Qd is the quantity demanded, Qs is the quantity supplied, and P is the price in hundreds of thousands of dollars.

In 2023, due to a significant rise in mortgage interest rates, the quantity of new homes demanded decreased by 3 million at every price, causing a leftward shift in the demand curve. The new demand curve can be represented by the equation:

New Demand: Qd' = -2,100,000 - 100P

This new demand equation is derived by subtracting 3,000,000 from the quantity in the original demand equation, representing the decrease in demand due to higher interest rates.

To find the new equilibrium, we set the new demand equal to supply:

-2,100,000 - 100P = 200P

Solving for P, we get:

300P = 2,100,000

P = 7,000

This means the new equilibrium price is $700,000 (as P represents price in hundreds of thousands of dollars). The new equilibrium quantity will be:

Q = 200 * 7,000 = 1,400,000

So, the new equilibrium in 2023 is a price of $700,000 and a quantity of 1.4 million homes. The allocative efficiency is at this point because it's where the new demand curve intersects the supply curve, indicating the optimal distribution of resources given the current market conditions.

However, the consumer surplus has decreased in 2023 due to the higher price and lower quantity of new homes. The consumer surplus is the area under the demand curve and above the price, up to the quantity bought. Without a specific linear demand curve or graph, we cannot calculate the exact consumer surplus.

Moreover, there is a deadweight loss in 2023 due to the shift in the demand curve caused by increased interest rates. Deadweight loss refers to the loss of economic efficiency when the market is not in allocative efficiency, meaning some consumer and producer surplus is lost. This occurs because, at the higher interest rates, fewer consumers are purchasing homes, and there's an unmet demand, leading to inefficiency in the market.

In summary, the housing market in 2023 experienced significant changes due to the rise in interest rates, leading to a new equilibrium with a higher price and a lower quantity, reduced consumer surplus, and the introduction of deadweight loss. These changes emphasize the market's sensitivity to interest rate changes and how such factors can impact market equilibrium and economic welfare.