How To Solve A Market Equilibrium Problem?

By b2b on November 22nd, 2009

A retail chain will buy 900 cordless phones if the price is 10$ each and 400 if the price is 60$. So I was thinking:
p = 900 -10q
p = 400 – 60q
Am I right so far? Then it asks:
A whollsaler will supply 700 phones at 30$ each and 1400 phones at 50$ each. Assuming supply and demand are linear find the market equilibrium point.
This is where I get lost. Any help would be greatly appreciated.

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One Comment

  • gladys says:
    November 22, 2009 at 10:46 am

    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.

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