To solve for the consumer and producer surplus in this scenario, let's break down the process step by step.

1. Identify Equilibrium Price and Quantity

The table shows the price of the book, the quantity demanded, and the quantity supplied. To find the equilibrium price and quantity, we need to find the point where the quantity demanded equals the quantity supplied.

By examining the table, we can see that at a price of $42, both the quantity demanded and quantity supplied are 10. Therefore, the equilibrium price is $42, and the equilibrium quantity is 10 books.

2. Consumer Surplus

Consumer surplus is the area below the demand curve and above the equilibrium price, up to the equilibrium quantity. To calculate this, we:

• Identify the highest price a consumer is willing to pay and subtract the equilibrium price.

• Multiply by the corresponding quantity and take the sum of these areas.

• From the table:

  • At $30, consumers are willing to buy 50 books.
  • At $42, the quantity demanded is 10.

We need to calculate the area between these points, which is essentially a triangle.

$\text{Consumer Surplus} = \frac{1}{2} \times \text{Base} \times \text{Height}$

• Base is the change in quantity from 50 to 10, so 40.
• Height is the difference between the highest price ($42) and the lowest ($30), which is $12.

$\text{Consumer Surplus} = \frac{1}{2} \times 40 \times 12 = 240$

3. Producer Surplus

Producer surplus is the area above the supply curve and below the equilibrium price, up to the equilibrium quantity.

• At $42, producers are willing to supply 10 books.
• At $30, producers are willing to supply 0 books.

Again, this forms a triangle:

$\text{Producer Surplus} = \frac{1}{2} \times \text{Base} \times \text{Height}$

• Base is the change in quantity from 0 to 10, so 10.
• Height is the change in price from $30 to $42, which is $12.

$\text{Producer Surplus} = \frac{1}{2} \times 10 \times 12 = 60$

Final Answers:

• Consumer Surplus: $240
• Producer Surplus: $60

Would you like more details or have any questions?

5 Related Questions:

1. How does a shift in demand or supply affect consumer and producer surplus?
2. What happens to the surplus values if the price floor is set above the equilibrium price?
3. How would the surpluses change if the equilibrium price was lower?
4. Can consumer and producer surplus be negative? If so, under what circumstances?
5. How do government interventions like taxes affect consumer and producer surplus?

Tip:

Understanding the relationship between equilibrium price and surplus can help in visualizing shifts in the market due to changes in demand or supply.