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. Extract Data We have the following willingness to pay (WTP) and quantity demanded (Q) from the table:

• WTP: $202.00, Q: 120,000,000 (High Income)
• WTP: $109.90, Q: 290,000,000 (Upper Middle Income)
• WTP: $9.85, Q: 270,000,000 (Lower Middle Income)
• WTP: $3.45, Q: 600,000,000 (Low Income)

2. Create Points Using the WTP and quantity demanded, we create points in the form $(P, Q)$:

• $(202, 120,000,000)$
• $(109.9, 290,000,000)$
• $(9.85, 270,000,000)$
• $(3.45, 600,000,000)$

3. Determine Demand Function We can derive the linear equation connecting price and quantity. Generally, we use two points to find the slope ( m ): Using the points $(202, 120,000,000)$ and $(3.45, 600,000,000)$:

The slope $m$ is calculated as: $$ m = \frac{Q_2 - Q_1}{P_2 - P_1} = \frac{600,000,000 - 120,000,000}{3.45 - 202} = \frac{480,000,000}{-198.55} $$

4. Linear Equation Format The linear equation is formulated as: $$ Q = mP + b $$ Where ( b ) can be determined using one of the points.

5. Calculate Slope Calculating the slope using the formula from Step 3: $$ m \approx -2,414,730.754 $$

6. Find Intercept (b) Using one point to find ( b ). Using the point $(202, 120,000,000)$:

$$ 120,000,000 = -2,414,730.754(202) + b $$

Rearranging gives us: $$ b = 120,000,000 + 487,487,557.5 $$

Calculating ( b ): $$ b \approx 607,487,557.5 $$

7. Final Demand Equation Substituting ( m ) and ( b ) back into the equation: $$ Q = -2,414,730.754P + 607,487,557.5 $$