If an inverse demand function (demand curve) is P= 110 - 2Q and supply is P = 40+30, what is the value of Consumer Surplus and Producer Surplus at the market equilibrium? 

First we need to find equilibrium price and quantity.

Equilibrium price and quantity is where demand and supply are equal.

Qd =Qs

110-2Q=40+3Q

110-40=3Q+2Q

70=5Q

70/5=Q

14=Q.

Price can be find by putting Q=14 in demand function.

P=110-2Q

=110-2(14)

=110-28

=82

Now we will find,

Price at quantity demanded is zero

P=110-2Q

=110-2(0)

=110

Price at quantity supplied is zero.

P=40+3Q

=40+3(0)

=40.

Now consumer surplus =1/2(price at quantity 0- equilibrium quantity) *(equilibrium quantity - 0)

=1/2*(110-82)*(14-0)

=1/2*28*14

=196

Producer surplus =1/2*(equilibrium price - price at 0 quantity supplied) *(equilibrium quantity - 0)

=1/2*(82-40)*(14-0)

=1/2*42*14

=294