Write the demand function (equation) showing the relationship between the quantity of vaccine demanded (Q) and the price (P). Using the data above.

Steps to Solve

1. Identify the Data Points From the provided table, we have the following points for willingness to pay (WTP) and quantity demanded (Q):

• WTP: $202.00, Q: 120,000,000
• WTP: $109.90, Q: 290,000,000
• WTP: $9.85, Q: 270,000,000
• WTP: $3.45, Q: 60,000,000

2. Convert WTP into Price (P) The willingness to pay (WTP) represents the price. We can denote:

• $P_1 = 202.00$
• $Q_1 = 120,000,000$
• $P_2 = 109.90$
• $Q_2 = 290,000,000$
• $P_3 = 9.85$
• $Q_3 = 270,000,000$
• $P_4 = 3.45$
• $Q_4 = 60,000,000$

3. Calculate the Slope of the Demand Curve Using the slope formula:

$$ \text{slope} = \frac{\Delta Q}{\Delta P} $$

Using two points, for example, $(P_1, Q_1)$ and $(P_2, Q_2)$:

$$ \text{slope} = \frac{Q_2 - Q_1}{P_2 - P_1} = \frac{290,000,000 - 120,000,000}{109.90 - 202.00} $$

Calculating gives:

$$ \text{slope} = \frac{170,000,000}{-92.10} \approx -1,846,144.14 $$

4. Formulate the Demand Function The demand function can be written in the standard linear form:

$$ Q = mP + b $$

Where $m$ is the slope we calculated. To find $b$, use one of the points, for instance, $(P_1, Q_1)$:

$$ 120,000,000 = (-1,846,144.14)(202.00) + b $$

Solving for $b$ gives:

$$ b = 120,000,000 + 1,846,144.14 \cdot 202.00 $$ Calculate the specific value of $b$.

5. Final Demand Function Substituting both $m$ (slope) and $b$ into the demand function form results in:

$$ Q = -1,846,144.14P + b $$