Write the demand function (equation) showing the relationship between the quantity of vaccine demanded (Q) and the price (P). Using the data above.
Understand the Problem
The question is asking to derive a demand function (equation) that represents the relationship between the quantity of vaccine doses demanded (Q) and the price (P) based on the provided data.
Answer
The demand function is $$ Q = -446103P + 12090191006 $$.
Answer for screen readers
The demand function is given by: $$ Q = -446103P + 12090191006 $$
Steps to Solve
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Identify the Variables Here, let ( Q ) represent the quantity demanded of vaccine doses, and ( P ) represent the price of the vaccine. The slope of the demand curve is given as -446103.
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Determine the Demand Equation Structure The standard form of a linear demand function is given by: $$ Q = mP + b $$ Where ( m ) is the slope and ( b ) is the y-intercept.
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Substitute the Slope into the Equation Substituting the slope into the equation: $$ Q = -446103P + b $$
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Determine the Intercept (b) Using Data Points We can find the intercept ( b ) using one of the given data points. For example, using the point where $P = 202$ and $Q = 12000000000$ (high-income group): $$ 12000000000 = -446103(202) + b $$ Calculate: $$ b = 12000000000 + 446103 \times 202 $$
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Calculate the y-intercept (b) Computing this gives: $$ b = 12000000000 + 90191006 = 12090191006 $$
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Write the Final Demand Function Substitute ( b ) back into the demand equation: $$ Q = -446103P + 12090191006 $$
The demand function is given by: $$ Q = -446103P + 12090191006 $$
More Information
This demand function indicates how the quantity of vaccine doses demanded decreases as the price increases, as reflected by the negative slope. Additionally, the y-intercept represents the quantity demanded when the price is zero.
Tips
- Neglecting the slope: Sometimes, the negative slope is ignored, leading to incorrect demand equations.
- Incorrectly calculating the intercept: Errors can occur when substituting data points and calculating ( b ). Carefully ensure the arithmetic is accurate.
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