https://file.aiquickdraw.com/mathbot/file/1727047870495phvr9vqe.jpg

how would this look: Calculate and shade the consumer surplus and producer surplus at the equilibrium point. You must show your work to get full points.

The graph you uploaded represents a standard supply and demand curve with price on the vertical axis and quantity on the horizontal axis. The intersection of the supply curve $ S $ and the demand curve $ D $ represents the equilibrium point. 

### Step-by-Step Breakdown:

#### 1. **Equilibrium Point:**
   - **Price**: The equilibrium price occurs where the supply and demand curves intersect. From the graph, the intersection happens at **\$30**.
   - **Quantity**: At the equilibrium price of \$30, the equilibrium quantity is **500 units**.

#### 2. **Consumer Surplus:**
   Consumer surplus is the area above the price level but below the demand curve, up to the equilibrium quantity.

   - The demand curve shows the maximum price consumers are willing to pay for various quantities. At a quantity of 0, the price consumers are willing to pay is **\$45** (the intercept of the demand curve on the price axis).
   - The equilibrium price is **\$30**, so the consumer surplus is the triangular area between the price level of \$30 and \$45.
   - The base of this triangle is the quantity, from 0 to 500 units.
   - The height of the triangle is from **\$30** to **\$45**, which is a difference of **\$15**.

   The formula for the area of a triangle is:
   \[
   \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   - Base = 500 units (the equilibrium quantity)
   - Height = \$15 (the difference between \$45 and \$30)

   \[
   \text{Consumer Surplus} = \frac{1}{2} \times 500 \times 15 = 3750
   \]
   So, the consumer surplus is **\$3,750**.

#### 3. **Producer Surplus:**
   Producer surplus is the area below the price level but above the supply curve, up to the equilibrium quantity.

   - The supply curve shows the minimum price producers are willing to accept for various quantities. At a quantity of 0, the price producers are willing to accept is **\$5** (the intercept of the supply curve on the price axis).
   - The equilibrium price is **\$30**, so the producer surplus is the triangular area between the price level of \$5 and \$30.
   - The base of this triangle is the quantity, from 0 to 500 units.
   - The height of the triangle is from **\$5** to **\$30**, which is a difference of **\$25**.

   The formula for the area of a triangle is the same as for consumer surplus:
   \[
   \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   - Base = 500 units (the equilibrium quantity)
   - Height = \$25 (the difference between \$30 and \$5)

   \[
   \text{Producer Surplus} = \frac{1}{2} \times 500 \times 25 = 6250
   \]
   So, the producer surplus is **\$6,250**.

#### 4. **Shading on the Graph:**
   - **Consumer Surplus**: This is the area of the triangle between the demand curve and the price line at \$30, shaded above the price and below the demand curve.
   - **Producer Surplus**: This is the area of the triangle between the supply curve and the price line at \$30, shaded below the price and above the supply curve.

Let me know if you'd like an image with the shaded areas drawn.

Would you like further details or have any questions about this process?

Here are some related questions to explore:
1. How does a shift in demand affect consumer surplus and producer surplus?
2. What happens to the equilibrium price and quantity when the supply curve shifts?
3. Can consumer surplus be negative? Why or why not?
4. How does a price ceiling affect the areas of consumer and producer surplus?
5. How does a subsidy impact the equilibrium and the surplus areas?

**Tip**: The area of consumer and producer surplus can help in analyzing market efficiency and the effects of policies like taxes or subsidies.

Calculate and shade the consumer surplus and producer surplus at the equilibrium point. You must show your work to get full points.

Learn how to calculate and shade consumer and producer surplus at the equilibrium point with a detailed breakdown. This example explains how to find the equilibrium price and quantity using supply and demand curves, and how to apply the formula for triangular areas to determine surplus values.

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