Question 919211


 Supply and demand are in equilibrium when {{{Qd=Qs}}}. In your case:

1. to find the equilibrium price, solve the two equations simultaneously:

{{{Qs = 100+ 3p}}}
{{{Qd= 400 – 2p}}}

{{{Qd=Qs}}}=>

{{{100+ 3p= 400 – 2p}}}
{{{3p+2p =400-100}}}
{{{5p= 300}}}
{{{p= 300/5}}}
{{{p= 60}}}

Equilibrium price is ${{{60}}}

To find the equilibrium quantity, substitute equilibrium price into the equations:

{{{Qs = 100+ 3*60=100+180=280}}}
{{{Qd= 400 – 2*60=400-120=280}}}

You'll know if your answer is correct if both equilibrium quantities for supply and demand are the same, which in this case is {{{280}}}.

2) Now suppose that a tax is placed on buyers so that the {{{Qd  =400-(2p+T)}}}  where T is taxes. If {{{T = 15}}}, solve for the equilibrium new price and quantity. 


{{{100+3P = 400-2(P+15)}}}
{{{100+3P = 400-2P - 30}}}
{{{5P = 270}}}
{{{P = 54}}} (receive sellers)
{{{Pd = 54+15 = 69}}} (pay buyers)
{{{Q = 262}}}
{{{Tax_ Revenue = 262*15 = 3930 }}}