Let's solve this problem step-by-step.

(a) Equation of the Demand Curve:

The graph shows a linear demand curve. To find the equation of the line, we need to use the slope-intercept form of a line:

$P = mQ + b$

Where:

• $P$ is the price on the y-axis (in dollars),
• $Q$ is the quantity on the x-axis (in units),
• $m$ is the slope of the demand curve,
• $b$ is the y-intercept (where the curve crosses the y-axis).

Step 1: Identify two points from the graph: From the graph, two clear points are:

• Point 1: $(Q = 0, P = 4)$ — This is the y-intercept where the curve touches the price axis.
• Point 2: $(Q = 20, P = 0)$ — This is the x-intercept where the curve touches the quantity axis.

Step 2: Calculate the slope: The slope $m$ is calculated as:

$m = \frac{{P_2 - P_1}}{{Q_2 - Q_1}} = \frac{0 - 4}{20 - 0} = -\frac{4}{20} = -\frac{1}{5}$

Step 3: Write the equation of the line: Now, using the slope-intercept form and the y-intercept $b = 4$, the equation of the demand curve is:

$P = -\frac{1}{5}Q + 4$

(b) Quantity demanded when the price is $2.5:

To find the quantity demanded when the price $P = 2.5$, substitute $P = 2.5$ into the demand curve equation:

$2.5 = -\frac{1}{5}Q + 4$

Now, solve for $Q$:

$2.5 - 4 = -\frac{1}{5}Q$ $-1.5 = -\frac{1}{5}Q$ $Q = \frac{1.5 \times 5}{1} = 7.5$

So, the quantity demanded when the price is $2.5 is 7.5 units.

(c) Total benefits when 11 units are consumed:

Total benefits (or consumer surplus) can be found by calculating the area under the demand curve up to 11 units. This area is a triangle formed between the price axis, the demand curve, and the vertical line at $Q = 11$.

Step 1: Find the price at $Q = 11$: Substitute $Q = 11$ into the demand curve equation:

$P = -\frac{1}{5}(11) + 4 = -\frac{11}{5} + 4 = 2.8$

So, the price when $Q = 11$ is $2.8.

Step 2: Calculate the area under the curve: The total benefits are the area of the triangle with:

• Base = $Q = 11$ units,
• Height = Price when $Q = 0$ (which is $4).

The area $A$ of the triangle is:

$A = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 11 \times 4 = 22$

Thus, the total benefits for consuming 11 units is $22.

Summary:

• (a) The equation of the demand curve is $P = -\frac{1}{5}Q + 4$.
• (b) The quantity demanded when the price is $2.5 is 7.5 units.
• (c) The total benefits of consuming 11 units is $22.

Would you like more details on any part of the solution?

Here are 5 related questions to explore further:

1. What happens to the total benefits if the price drops to $1?
2. How would the demand curve change if the maximum price consumers are willing to pay increases to $5?
3. What is the elasticity of demand at $Q = 11$?
4. How would a subsidy of $1 per unit affect the quantity demanded?
5. How does consumer surplus change when the price is $3?

Tip: When calculating areas under demand curves, remember that triangles represent consumer surplus when dealing with linear demand curves!