By: gladys

gladys — Sun, 22 Nov 2009 10:46:24 +0000

No, you are on the wrong track
The information you have gives you two points on the demand curve and two points on the supply curve. What you need to do is find the equations of the two lines and work out where they intersect. This will be the equilibrium point.
Your demand curve has the points (10, 900) and (60, 400)
where x is the price and y is the quantity.
The equation of the line is given by the formula
[y - y1]/[y2 - y1] = [x - x1]/[x2 - x1]
Substituting:
[y - 900]/[400 - 900] = [x - 10]/[60 - 10]
[y - 900]/-500 = [x- 10]/50
50[y - 900] = -500[x - 10]
You can tidy this up a bit before going any further by dividing through by 50:
y – 900 = -10[x - 10]
y – 900 = -10x + 100
y = -10x + 1000 demand function
Now do the same for the supply function:
Your points are (30,700) and (50,1400)
Substituting:
[y - 700]/[1400 - 700] = [x - 30]/[50 - 30]
[y - 700]/700 = [x- 30]/20
20[y - 700] = 700[x - 30]
You can tidy this up a bit before going any further by dividing through by 20:
y – 700 = 35[x - 30]
y – 700 = 35x – 1050
y = 35x – 350 supply curve
Now all we need to do is solve for the point where the lines intersect which means we make the two equations equal:
y = -10x + 1000
y = 35x – 350
so
35x – 350 = -10x + 1000
45x = 1350
x = 1350/45 = 30 which menas the price is $30
Substitute in either equation to get y (quantity). Both will give the same answer:
y = -10x + 1000
y = -10*30 + 1000
y = -300 + 1000 = 700 phones.
(the problem is a bit silly because this was actually one of the points given in the question).
So your equilibrium point occurs at a price of $30 where 700 phones will be sold.

Comments on: How To Solve A Market Equilibrium Problem?

By: gladys