To find the demand function, we typically assume that the relationship between price $p$ and quantity demanded $q$ follows a linear form, which is a common starting point unless more specific information is given. This relationship is often expressed as:

$q = a - bp$

Where:

• $q$ is the quantity demanded.
• $p$ is the price.
• $a$ and $b$ are constants that we need to determine.

However, in this case, we only have one price point: the vendor charges $50 for the jacket. Without additional data points or assumptions about the behavior of demand at other price levels, we cannot fully determine the demand function. Typically, more information, like how the quantity demanded changes with price (e.g., a second price point or elasticity data), is required to calculate $a$ and $b$.

With just one price point ($p = 50$), we can conclude that:

1. If more details are provided (e.g., what the quantity demanded is when $p = 50$), the demand function can be better specified.
2. If you assume a specific number of jackets sold at $p = 50$, you could fit the model accordingly.

Would you like to provide more information or assumptions, or should I guide you further on estimating a demand function?

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Here are 5 questions to deepen understanding:

1. How many jackets are sold at the price of $50?
2. Do you have another price point with its corresponding quantity demanded?
3. Are you familiar with linear demand functions?
4. Have you considered elasticity in this scenario?
5. What would you assume about the market size?

Tip: To fully determine a demand function, it's often helpful to have at least two price-quantity pairs.