Y= Price per unit of 2bedroom house X= Number of houses per year For Demand curv
ID: 2857466 • Letter: Y
Question
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
Comment
Explanation / Answer
Demand :
This is the equation that links together price and the quantity demanded. And this is a linear curve which can be found if we have the slope and a single point. That was what was done with y - y1 =m(x - x1) to get 200x + y = 1100000.
Supply :
This is the equation that links together price and the quantity supplied. And this is a linear curve also.
The equilibrium(as one might have guessed from the word equilibrium) is simply the point at which demand and supply are equal at the price, y.
The equations were solved and answers obtained for x and y...
And since these have got to be natural numbers, they were rounded appropriately to get the final solution.
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