7.2 calculating producer and consumer surplus

Summary

This video explains how to calculate consumer and producer surplus using traditional supply and demand curves. It demonstrates finding equilibrium quantity and price, then calculates both surpluses using the area of a triangle formula.

Highlights

Setting Up Supply and Demand00:00:00

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.

Finding Equilibrium Quantity (Q*)00:00:24

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.

Finding Equilibrium Price (P*)00:01:28

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.

Calculating Consumer Surplus (CS)00:02:26

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.

Calculating Producer Surplus (PS)00:03:16

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.