How to find equilibrium price and quantity and consumer surp

How to find equilibrium price and quantity, and consumer surplus when:

Demand: Q^d= 400 - 100P

and

Supply: Q^s= 280 + 20P (for P>0)

Demand equation is as follows -

Qd = 400 - 100P

Supply equation is as follows -

Qs = 280 + 20P

Equilibrium is attained when demand equals supply.

Equating demand and supply equations -

400 - 100P = 280 + 20P

400 - 280 = 100P + 20P

120P = 120

P = 1

The equilibrium price is $1 per unit.

Equilibrium quantity can be ascertained by putting this value of equilibrium price in either demand or supply equation.

Putting value of P in demand equation -

Equilibrium quantity = 400 - 100P = 400 - 100*1 = 300

The equilibrium quantity is 300 units.

Calculate Consumer Surplus -

Step 1 - Calculate price at which zero quantity is demanded -

Qd = 400 - 100P

0 = 400 - 100P

100P = 400

P = 4

The price at which zero quantity is demanded is $4 per unit.

Step 2 - Calculate Consumer Surplus -

CS = 1/2 * ( Price at which zero quantity is demanded - Equilibrium price) * Equilibrium quantity

= 1/2 * ($4 - $1) * 300

= 450

The consumer surplus is 450.