Math Problem Statement

At the equilibrium price in the graph, producer surplus is calculated.

Solution

In this graph, we are asked to find the producer surplus at the equilibrium price. Let's go step-by-step to calculate it:

Key information from the graph:

  1. Equilibrium price is where the supply (S) and demand (D) curves intersect. From the graph, this is at a price of $100 and a quantity of 15 units.
  2. The producer surplus is the area above the supply curve and below the equilibrium price line (a triangle).

Producer surplus is calculated as the area of a triangle:

The formula for the area of a triangle is: Area=12×Base×Height\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}

  • Base: The base is the quantity at equilibrium, which is 15 units.
  • Height: The height is the difference between the equilibrium price and the lowest price at which producers are willing to supply the product. From the graph, the supply curve starts at a price of $20, so the height is 10020=80100 - 20 = 80.

Calculation:

Producer Surplus=12×15×80=12×1200=600\text{Producer Surplus} = \frac{1}{2} \times 15 \times 80 = \frac{1}{2} \times 1200 = 600

However, this value is not exactly one of the options provided, but $800 seems to be the closest.

Would you like to discuss why the option is closest, or have any other questions on this?


Here are some follow-up questions related to the concept:

  1. How does a change in demand affect the producer surplus?
  2. What would happen to producer surplus if the supply curve shifts right?
  3. Can producer surplus be negative, and under what conditions?
  4. How do taxes affect the producer surplus?
  5. How would you calculate consumer surplus from the same graph?

Tip: Producer surplus is a good measure of producer welfare, representing the extra benefit producers receive for selling at a market price higher than their minimum acceptable price.

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Math Problem Analysis

Mathematical Concepts

Microeconomics
Producer Surplus
Geometry (area of a triangle)

Formulas

Producer Surplus = (1/2) * Base * Height

Theorems

Producer surplus in microeconomics

Suitable Grade Level

Grades 10-12 (Economics)