7.2 calculating producer and consumer surplus

The video introduces the equations for the demand curve (P = 40 - 0.1Q) and the supply curve (P = 10 + 0.2Q) and sets the goal of finding consumer and producer surplus.

To find the equilibrium quantity (Q*), the supply and demand equations are set equal to each other: 10 + 0.2Q = 40 - 0.1Q. Solving this equation yields Q* = 100.

The equilibrium quantity (Q*=100) is plugged back into either the supply or demand equation to find the equilibrium price (P*). Using the supply equation (P = 10 + 0.2 * 100), P* is calculated as 30. Verifying with the demand equation also gives P* = 30.

Consumer surplus is calculated as the area of the triangle above the equilibrium price and below the demand curve. Using the formula 0.5 * base * height, where base is Q* (100) and height is the difference between the demand curve's y-intercept (40) and P* (30), CS is found to be 500.

Producer surplus is calculated as the area of the triangle below the equilibrium price and above the supply curve. Using the formula 0.5 * base * height, where base is Q* (100) and height is the difference between P* (30) and the supply curve's y-intercept (10), PS is found to be 1000.