If 3000 twobedroom houses are demanded per year at a price o

If 3000 two-bedroom houses are demanded per year, at a price of $500,000 per unit. However, for every $40,000 increase in the price per unit, the quantity of units demanded falls by 200. Contractors are unwilling to build and sell any two-bedroom houses for any price less than $100,000 but are willing to sell as much as 7700 unit per year at a price of $1 million. If the demand and supply curves are assumed to be linear.

(i) Find the demand curve.

(ii) Find the supply curve.

(iii) Find the approximate equilibrium quantity and price.

Solution

i) Demand: we need to find two points to fderive demand equation:

3000 houses -----$ 500, 000 per unit ----> ( 3000, 500,000)

3000 -200 ------$500, 000 - $40,000

2800 houses ---- $ 460, 000 per unit ----> ( 2800, 460,000)

Demand equation can be modelled by a linear equation: D = a - bP

( 500,000, 3000) and ( 460,000, 2800)

3000 = a - 500,000b ----(1)

2800 = a - 460,000b ----(2)

a = 500 ; b= -1/200

So, D = 500 + P/200

ii) Similarly for Supply:

(0 units, $100,000) and ( 7700 units , $ 1000,000)

Supply equation can be given as: S = c +dP

0 = c+d*100,000 -----(1)

7700 = c +d*1000,000 -----(2)

solve these two equations to get value of c, d:

c = -7700/9 and d= 77/9000

S = -7700/9 +77P/9000

iii) Eqiulibrium when supply = demand

-7700/9 +77P/9000 = 500 + P/200

P( 77/9000 - 1/200) = 1355.55

P( 0.0355) =1355.55

P = $38184.66 per unit