Math Problem Statement

Consider the accompanying supply and demand graph. What is the value of consumer surplus? What is the value of producer surplus? What is the value of total surplus, also known as the social or economic surplus?

Solution

To solve the problem based on the given supply and demand graph, we need to calculate the consumer surplus, producer surplus, and total surplus.

Step 1: Identify the equilibrium point

The graph shows that the equilibrium quantity is 5, and the equilibrium price is $4.5. This is where the supply and demand curves intersect.

Step 2: Consumer Surplus Calculation

  • Consumer surplus is the area between the demand curve and the price, up to the equilibrium quantity.
  • The formula for the area of a triangle is: Area of triangle=12×base×height\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
  • In this case, the height is the difference between the maximum price on the demand curve ($9) and the equilibrium price ($4.5): [ \text{Height} = 9

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Math Problem Analysis

Mathematical Concepts

Consumer Surplus
Producer Surplus
Total Surplus
Supply and Demand

Formulas

Consumer Surplus = 0.5 * Base * Height
Producer Surplus = 0.5 * Base * Height
Total Surplus = Consumer Surplus + Producer Surplus

Theorems

Basic Supply and Demand Theorem

Suitable Grade Level

Grades 10-12