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Homework answers / question archive / 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? 

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? 

Economics

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? 

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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