The government, through its Department of Trade, is analyzing the market for a new product. The demand and supply curves for the product are linear. At a price of $71
per unit, the quantity demanded is 710
units, and the quantity supplied is 344
units. At a price of $92
per unit, the quantity demanded is 626
units, and the quantity supplied is 470
units.

Given this information, calculate the consumer surplus (in $) at a market price of $60
per unit.

To calculate the consumer surplus at a market price of $60 per unit, we need to follow these steps:

### 1. Determine the Demand Curve:
The demand curve is typically linear and can be expressed as:

\[
Q_d = a - bP
\]

Where:
- $Q_d$ is the quantity demanded,
- $P$ is the price,
- $a$ and $b$ are constants.

Using the two points given:
- At $P = 71$, $Q_d = 710$
- At $P = 92$, $Q_d = 626$

We can set up the equations:
\[
710 = a - 71b
\]
\[
626 = a - 92b
\]

Subtract the second equation from the first to eliminate $a$ and solve for $b$:

\[
710 - 626 = (a - 71b) - (a - 92b)
\]
\[
84 = 21b \implies b = 4
\]

Now, substitute $b = 4$ back into one of the original equations to solve for $a$:

\[
710 = a - 71 \times 4
\]
\[
710 = a - 284 \implies a = 994
\]

Thus, the demand curve equation is:
\[
Q_d = 994 - 4P
\]

### 2. Determine the Quantity Demanded at $P = 60$:

Substitute $P = 60$ into the demand equation:

\[
Q_d = 994 - 4(60) = 994 - 240 = 754
\]

### 3. Find the Intercept of the Demand Curve (Maximum Price Consumers are Willing to Pay):
Set $Q_d = 0$ to find the intercept:

\[
0 = 994 - 4P \implies P = \frac{994}{4} = 248.5
\]

This is the maximum price consumers are willing to pay when quantity demanded is zero.

### 4. Calculate the Consumer Surplus:

Consumer surplus is the area between the demand curve and the market price line. Since this area forms a triangle, we can calculate the area using the formula for the area of a triangle:

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

Here:
- The base is the difference in quantity demanded at the intercept and at $P = 60$: $754 - 0 = 754$
- The height is the difference in price: $248.5 - 60 = 188.5$

\[
\text{Consumer Surplus} = \frac{1}{2} \times 754 \times 188.5 = 71009.5
\]

Thus, the consumer surplus at a market price of $60 per unit is **$71,009.5**.

Would you like further details or have any questions about the calculation? Here are some related questions you might consider:

1. How does consumer surplus change with different market prices?
2. What is the significance of the demand curve's slope in determining consumer behavior?
3. How would changes in the supply curve affect consumer surplus?
4. Can consumer surplus be negative, and what does that imply?
5. What other factors might influence the calculation of consumer surplus in a real-world scenario?

**Tip:** Understanding the relationship between price and quantity is key in economics—supply and demand curves reflect consumer behavior and producer response, which are central to market dynamics.

Learn how to calculate consumer surplus using the demand curve equation and specific market price data. Understand the significance of consumer behavior and market dynamics in economics.

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