Anonymous
Anonymous asked in Education & ReferenceHomework Help · 1 month ago

MATH HELP ??

If the supply and demand functions for a commodity are given by 

4p − q = 46

 and 

(p + 2)q = 2,170,

 respectively, find the price and quantity that will result in market equilibrium.

equilibrium price $ 

equilibrium quantity 

1 Answer

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  • 1 month ago
    Favourite answer

    Supply

    4p − q = 46 

    Solving for q

    q = 4p - 46

    Demand

    (p + 2)q = 2,170

    Solving for q

    q = 2,170/(p + 2)

    ------------------------

    At equilibrium quantity

    4p - 46 = 2,170/(p + 2)

    Multiply both sides by p + 2

    (4p - 46)(p + 2) = 2170

    4p² - 38p - 92 = 2170

    4p² - 38p - 2262 = 0

    Apply quadratic formula 

    (work not shown)

    p = {-39/2, 29}

    The negative price is extraneous

    p = 29 <––––– equilibrium price

    q = 4p - 46

    p = 4(29) - 46

    q = 70 <––––– equilibrium quantity

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