If 3000 two-bedroom houses are demanded per year, at a price of $500,000 per uni

Question

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.

Explanation / Answer

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

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