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

Y= Price per unit of 2bedroom house
X= Number of houses per year

For Demand curve; we know that (3000, 500000) is a point on the linear curve. Also the slope of the curve is change in y / change in x= 40,000/-200= -200; Thus since demand curve is a straight line, it\'s equation will be :
y-y1= slope * (x-x1); Substituting the values= Y-500,000= -200(X-3000) which upon simplifying gives:
200x+ y= 1,100,000; This is the demand curve where X and Y are both natural numbers


For supply curve: we know that y>= 100,000 which means (0,100000) is a point on the supply curve and so is (7700,1000000) so the equation of the line becomes y-100000=900000/7700 ( x) ;
which is -9000/77 * x + y= 100000;

the equilibrium is where both these curves meet; solving the 2 equations we get x= 3155 and hence y = 468766;

approx equilibrium quanitty = 3155 and approx equilibrium price = 469,000