In a competitive market, the demand and supply functions

Solution

To find the consumer surplus, we must follow three primary steps: find the equilibrium point, determine the "choke price" (the price where demand is zero), and calculate the area of the surplus triangle. Find the Market Equilibrium At equilibrium, the quantity demanded equals the quantity supplied (Qd = Qs), and the price is the same for both. We set the two equations equal to each other: 120 - 2Q = 30 + Q 120 - 30 = Q + 2Q 90 = 3Q Q* = 30 Now, substitute Q = 30 back into either equation to find the equilibrium price (P*): P* = 120 - 2(30) = 120 - 60 = 60 So, the equilibrium is at P = 60 and Q = 30. Find the Maximum Willingness to Pay (Choke Price) Consumer surplus is the area below the demand curve but above the market price. The "height" of this triangle starts at the price where Q = 0 on the demand curve. Pmax = 120 - 2(0) = 120 Calculate Consumer Surplus (CS) Graphically, consumer surplus is a triangle. The formula for the area of a triangle is: Consumer Surplus = ½ (Base)(Height) Base = Equilibrium Quantity (Q*) = 30 Height = Pmax - P* = 120 - 60 = 60 CS = ½ (30)(60) = 900