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Math Help - Equilbrium Equation Help

  1. #1
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    Equilbrium Equation Help

    When price is 0.8, the supply is 450 and the demand is 550. But when the price is 1, the supply is 600 and demand is 475.Demand and supply are linear so find the equilibrium??

    So first how to make the equations>?
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  2. #2
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    Quote Originally Posted by someone21 View Post
    When price is 0.8, the supply is 450 and the demand is 550. But when the price is 1, the supply is 600 and demand is 475.Demand and supply are linear so find the equilibrium??

    So first how to make the equations>?
    We had very basic , one semester only, "business" subject in college, so I searched the web for your question.
    As I first thought, the solution should involve two linear functions and their intersection point.
    The website I read says the vertical axis is for price while the horizontal axis is for quantity (supply or demand), which means the the price is dependent on the quantity. (I thought it was the reverse.)
    Anyway, so we will use a cartesian (rectangular) set of axes, (q,p), for the graphs.

    The equilibrium is the intersection point of th Supply-curve and the Demand-curve.

    The supply-curve:
    The two points are: (450,0.8) and (600,1.0)
    Slope, m1 = (1.0 -0.8) / (600 -450) = 0.2 / 150 = 0.001333333
    Using the point-slope form of the equation of the line, with point (600,1.0):
    (p -1.0) = (0.0013333)(q -600)
    p = (0.0013333)(q -600) +1 -------------(1)


    The demand-curve:
    The two points are: (550,0.8) and (475,1.0)
    Slope, m2 = (1.0 -0.8) / (475 -550) = 0.2 / (-75) = -0.002666666
    Using the pont-slope form of the equation of the line, with point (475,1.0):
    (p -1.0) = (0.00266666)(q -475)
    p = (0.00266666)(q -475) +1 -------------(2)

    At the intersectiom, p from (1) is the same as the p from (2), so,
    (0.00133333)(q -600) +1 = (0.00266666)(q -475) +1
    (0.00133333)(q -600) = -(0.00266666)(q -475)
    q -600 = -2q +950
    q +2q = 950 +600
    3q = 1550
    q = 1550 / 3 = 516.66666 .......not a whole number??

    And so, p = (0.00133333)(516.66666 -600) +1 = 0.8888

    Therefore, equilibrium is when the demand equals supply equals 516.667 units. --------answer.
    (if you want a whole number answer, pick 516 or 517. I'd say 517 if we follow rounding off.)

    (...and the price at equlibrium is about 0.889 monetary units.)
    Last edited by ticbol; September 16th 2008 at 03:21 PM.
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