Question

Suppose the housing market is characterized by supply constraints, such that the supply is fixed in the short-run: X _S=100. The market demand function for housing is D(X)=1000-4X, where X is the number of houses in the market.

1. Which side, demand or supply, is less price elastic in the housing market? {Enter D for demand, or enter S for supply, or enter E if you think that they are equally price elastic}

2) What is equilibrium number of houses in this market? X ₀=

3) What is the equilibrium price in the housing market? p ₀=

The government is thinking of introducing a home-buyers' grant of $150. The grant would be given to buyers once they purchase a property. As an economist working at the Treasury you are asked to determine the effects of this grant.

4) What would be the new equilibrium quantity according to the model? X ₁=

5) What is the new equilibrium price in the housing market? p ₁=

6) What fraction of the grant is shifted from the buyers to the sellers? {Enter a number between 0 and 1}

7) What fraction of the grant would be shifted from the buyers to the sellers if the $150 grant was replaced by a grant equal to 25\% of the value of the house sold? {Enter a number between 0 and 1}

8) If we write the housing supply as S(X)=γ X, for what value of γ would we reach the conclusion that the economic incidence of the $150 grant is equally split between the buyer and seller? γ=

Answer 1

Answer 1:

Since Supply is constant at 100 units, the supply is perfectly inelastic as any change in the price will not affect the supply. Hence Supply is less Price Elastic. I.e S

Answer 2

SInce supply is fixed at 100 units, Equilibrium Quantity will be X0 =100

Answer 3

D(X) = 1000-4X

Price at Equilibrium will be given by D(X) at X= 100,

Hence D(100) = 1000-4*100 = 1000-400 = 600

Hence Price at Equilibrium, P0 = $600

Answer 4

New Equilibrium Quantity will still be X1= 100 units as Supply is Fixed

Answer 5

In new Demand Function, Price for buyer will be (P-150) since $150 grant will reduce the price

Hence now, D(X) -150 = 1000 - 4X

or, D(X) = 1000-4X+150

or, D(X) = 1150-4X

So, New Equilibrium Price will be D(100) = 1150-4*100 = 1150-400 = 750

Hence New Equilibrium Price, P1 = $750

Answer 6

Earlier Price for Buyer was $600

After Grant Buyer had to Pay $750 but $150 he received as Grant, hence Buyer paid 750-150 = $600.

Since the New Price paid by Buyer is equal to Old Price, Buyer got no benefit from the Grant and entire Grant actually is shared by Supplier.

Hence the answer is 1

Answer 7

Since supply is perfectly inelastic, irrespective of the value of grant, the buyer will have to shift the entire Grant amount to Supplier. Hence answer is 1

Answer 8

Before Grant,

S= yX , D = 1000-4X,

at equilibrium S=D, hence yX = 1000-4X

yX+4X = 1000

X0 = 1000/(4+y) units

Hence Equilibrium Price, P0 = y * 1000 /(4+y) = 1000y / (4+y)

After Grant,

Before Grant,

S= yX will remain same

D = 1000-4X will change to D-150 = 1000-4X

or, D = 1150-4X

at equilibrium S=D, hence yX = 1150-4X

yX+4X = 1150

X1 = 1150/(4+y) units

Hence New Equilibrium Price, P1 = y * 1150 /(4+y) = 1150y / (4+y)

New Equilibrium Price for Buyer, P1D = P1- 150 = 1150y/(4+y) -150

For equal sharing Buyer should have received a benefit of 150/2 = $75

Hence For Buyer, New Equilibrium Price = old equilibrium Price -75 (Since Buyer saved $75 due to grant,

Hence, 1150y / (4+y) -150 = 1000y/(4+y) -75

or, 1150y / (4+y) - 1000y/(4+y)= 150 -75

or, (1150y - 1000y)/ (4+y) =75

or, 150y/(4+y) =75

or, 150y = 75 *(4+y)

or 150y = 300 +75y

or, 150y-75y =300

or, 75y = 300

or, y =300/75

or, y=4

Hence for Equal distribution of Grant y =4.