Question 87254
Not too sure what the equilibrium price is ie how to get it. I am assuming that it is where both equations are the same. If this is true then:


{{{ D = -200p + 35000 }}}
{{{ S = -p^2 + 400p - 20000 }}}


so when these are equal:
{{{ -200p + 35000 = -p^2 + 400p - 20000 }}}
{{{ p^2 - 600p + 55000 = 0 }}}


{{{ p = (-b +- sqrt(b^2 - 4ac) )/(2a) }}}
{{{ p = (-(-600) +- sqrt((-600)^2 - 4(1)(55000)) )/(2(1)) }}}
{{{ p = (600 +- sqrt(360000-220000) )/(2) }}}
{{{ p = (600 +- sqrt(140000) )/(2) }}}
{{{ p = (600 +- 374.17 )/(2) }}}
so {{{ p = (600 + 374.17 )/(2) }}} or {{{ p = (600 - 374.17 )/(2) }}}
so {{{ p = (974.17)/(2) }}} or {{{ p = (225.83)/(2) }}}
p = 487.1 or 112.9


Now this gives 2 valid answers so i am not too sure whether i have given you the correct method. Sorry.



cheers
Jon