Question 1161515


The demand curve for a certain product is given by {{{p(q)=574-q^2 }}}
The supply curve is given by {{{p(q)=1.4q^2}}}

The intersection of the supply and demand curves is the point at which the market is at equilibrium.
the consumer surplus at equilibrium:

{{{574-q^2 =1.4q^2}}}

{{{574 =q^2+1.4q^2}}}

{{{574 =2.4q^2}}}

{{{q^2=574 /2.4}}}

{{{q^2=239.16666666666669}}}

{{{q=sqrt(239.16666666666669)}}}
{{{q=15.465 }}}

{{{p(q)=574-15.465 ^2 }}}

{{{p(q)=334.833 }}}


The intersection point of the supply and demand curves,  the point at which the market is at equilibrium is:

({{{15.465 }}},{{{334.833 }}})