Chapter 3: Problem 31

What is consumer surplus? How is it illustrated on a demand and supply diagram?

Short Answer

Expert verified

Consumer surplus is the difference between the highest price a consumer is willing to pay for a product and the actual price they pay, indicating the benefit or value gained by consumers. It is illustrated on a demand and supply diagram as the area between the demand curve and the equilibrium price, above the supply curve and below the demand curve, forming a triangle. For example, with a demand curve equation \(Q_D = 20 - P\) and a supply curve equation \(Q_S = 2P\), we find the equilibrium price to be approximately \(6.67\) and the equilibrium quantity at \(13.33\). The consumer surplus is then calculated as the area of the triangle, which equals approximately \(88.89\) dollars.

Step by step solution

Understanding Demand Curve

The demand curve shows the relationship between the price of a good and the quantity demanded by consumers. It's downward sloping, meaning that as the price of a good decreases, the quantity demanded by consumers increases. The demand curve reflects the maximum amount a consumer is willing to pay for each unit of a good.

Understanding Supply Curve

The supply curve shows the relationship between the price of a good and the quantity supplied by producers. It is upward sloping, meaning that as the price of a good increases, the quantity supplied by producers also increases. The supply curve reflects the minimum price at which a producer is willing to sell each unit of a good.

Finding the Equilibrium Price and Quantity

The equilibrium price and quantity occur when the quantity demanded by consumers equals the quantity supplied by producers. Graphically, this is represented by the point where the demand curve and the supply curve intersect. At the equilibrium price, the market clears, meaning there is no surplus or shortage of goods.

Illustrating Consumer Surplus on the Diagram

Consumer surplus is represented by the area between the demand curve and the equilibrium price, above the supply curve, and below the demand curve. It is illustrated as a triangle in a standard demand and supply diagram. The base of the triangle is the difference in quantity demanded, and the height is the difference between the price consumers are willing to pay and the equilibrium price they actually pay.

Example: Calculating Consumer Surplus

Suppose the demand curve is represented by the equation: \(Q_D = 20 - P\), and the supply curve is represented by the equation: \(Q_S = 2P\). 1. To find the equilibrium price and quantity, set the demand equation equal to the supply equation: \(20 - P = 2P\). 2. Solving for P, we get: \(20 = 3P \Rightarrow P = \frac{20}{3} \approx 6.67\). 3. To find the equilibrium quantity, plug this value back into either the demand or supply equation: \(Q = 20 - 6.67 = 13.33\). 4. To calculate the consumer surplus, find the area of the triangle formed by the demand curve, the supply curve, and the equilibrium price. The base of the triangle is \(13.33\) units, and the height is \((20 - 6.67)\) dollars. The area (consumer surplus) is: \(\frac{1}{2} \times 13.33 \times (20 - 6.67) \approx 88.89 \) dollars.