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25 July, 01:49

In the pair of supply and demand equations below, where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price. p = - x2 - 3x + 80 and p = 7x + 5

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  1. 25 July, 02:07
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    Equilibrium quantity = 5

    Equilibrium price = 40

    Explanation:

    given:

    p = - x²-3x+80

    p = 7x+5

    For the equilibrium quantity the price from both the functions will be equal

    thus, we have

    -x² - 3x + 80 = 7x+5

    ⇒ x² + 3x + 7x + 5 - 80 = 0

    ⇒x² + 10x - 75 = 0

    now solving for x

    x² - 5x + 15x - 75 = 0

    x (x-5) + 15 (x-5) = 0

    therefore, the two roots of the equation are

    x = 5 and x = - 15

    since the quantity cannot be in negative

    therefore, the equilibrium quantity will be = 5

    now the equilibrium price can be found out by substituting the equilibrium quantity in any of the equation

    thus,

    p = - (5) ² - 3 (5) + 80 = 40

    or

    p = 7 (5) + 5 = 40
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