To find the total demand by each consumer at the price $p = 3$, we need to evaluate the individual demand functions for Buick and Dodge owners at this price. Let's break down the steps:

Step 1: Demand by Each Individual Buick Owner

The demand function for a Buick owner is:

$D_B(p) = 20 - 5p \quad \text{for} \quad p \leq 4, \quad D_B(p) = 0 \quad \text{if} \quad p > 4.$

For $p = 3$:

$D_B(3) = 20 - 5(3) = 20 - 15 = 5 \quad \text{gallons per week}.$

Each Buick owner demands 5 gallons of gasoline when the price is $3.

Step 2: Demand by Each Individual Dodge Owner

The demand function for a Dodge owner is:

$D_D(p) = 15 - 3p \quad \text{for} \quad p \leq 5, \quad D_D(p) = 0 \quad \text{if} \quad p > 5.$

For $p = 3$:

$D_D(3) = 15 - 3(3) = 15 - 9 = 6 \quad \text{gallons per week}.$

Each Dodge owner demands 6 gallons of gasoline when the price is $3.

Step 3: Graphing the Demand Curves

Next, we'll represent the demand curves graphically.

1. Buick Owners' Total Demand Curve (Blue Ink):

Since there are 100 Buick owners, the total demand for gasoline by all Buick owners at price $p$ is $100 \times D_B(p)$. The equation for the total demand of Buick owners is:

$Q_B(p) = 100 \times (20 - 5p) = 2000 - 500p \quad \text{for} \quad p \leq 4.$

For $p > 4$, total demand is zero.

This curve should start at $p = 0$ with a demand of 2000 gallons and slope downwards at a rate of 500 gallons per dollar until it hits zero demand at $p = 4$.

2. Dodge Owners' Total Demand Curve (Black Ink):

For Dodge owners, there are 50 consumers, so the total demand is $50 \times D_D(p)$. The equation for the total demand of Dodge owners is:

$Q_D(p) = 50 \times (15 - 3p) = 750 - 150p \quad \text{for} \quad p \leq 5.$

For $p > 5$, total demand is zero.

This curve starts at $p = 0$ with a demand of 750 gallons and slopes downwards at a rate of 150 gallons per dollar until it hits zero demand at $p = 5$.

3. Market Demand Curve for the Whole Town (Red Ink):

The market demand is the sum of the total demand from both Buick and Dodge owners. Therefore, the market demand is:

$Q_{\text{market}}(p) = Q_B(p) + Q_D(p) = (2000 - 500p) + (750 - 150p) = 2750 - 650p \quad \text{for} \quad p \leq 4.$

For $4 < p \leq 5$, only Dodge owners are demanding gas, so:

$Q_{\text{market}}(p) = 750 - 150p.$

For $p > 5$, no one demands gasoline, so:

$Q_{\text{market}}(p) = 0.$

This curve will start at $p = 0$ with a total demand of 2750 gallons and slope downwards until $p = 4$, after which only the Dodge owners contribute to the demand until $p = 5$, where total demand becomes zero.

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Do you want me to sketch these curves for you?

Relative Questions:

1. How would the demand curves change if gasoline prices increased to $4?
2. What is the total amount of gasoline demanded by both Buick and Dodge owners when the price is $2?
3. What happens to the market demand if the number of Dodge owners increases?
4. How does the price elasticity of demand differ between Buick and Dodge owners?
5. How would the demand curves shift if both Buick and Dodge owners received a gasoline subsidy?

Tip:

When graphing demand curves, remember that the slope of the curve reflects the rate at which demand decreases as price increases.