Does Increasing Prices Increase Revenue Given Q = 30 – 3P?

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Discussion Overview

The discussion revolves around the relationship between price and revenue in the context of a linear demand equation given by Q = 30 – 3P. Participants explore whether increasing prices leads to increased revenue, focusing on the implications of demand and price on revenue calculations.

Discussion Character

  • Homework-related
  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to approach the problem of determining the relationship between price increases and revenue.
  • Another participant emphasizes the need to understand how revenue relates to demand and price, suggesting that assumptions may be necessary for this relationship.
  • A participant questions the demand at specific price points (P=1, P=2, P=3) and notes that increasing price leads to decreasing demand.
  • One participant calculates demand at various price points, confirming that demand decreases as price increases, but notes that this does not clarify the effect on revenue.
  • A participant points out that the demand equation is linear and suggests plotting Q vs. P to find the point where demand becomes zero, indicating no revenue.
  • Another participant clarifies that revenue is the product of demand and price, raising concerns about interpreting demand as synonymous with revenue.
  • One participant notes that while the relationship between demand and price has been established, revenue has not yet been calculated for specific price points.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether increasing prices increases revenue, as there are multiple viewpoints regarding the relationship between demand, price, and revenue. The discussion remains unresolved.

Contextual Notes

Participants have not yet calculated revenue based on the demand equation, and there are assumptions regarding stock availability and the interpretation of demand in relation to revenue.

chickenlips
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Homework Statement


Here is the question:

Suppose demand is given by Q = 30 – 3P. Does this indicate increasing prices increases revenue?

Homework Equations





The Attempt at a Solution


I'm not sure how to go about figuring this out...what should I look for?
 
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ACcording to our guidelines (see link below), we can't help you until you show us your effort first.

How is revenue related to demand and price? Do you have to make an assumption for this relationship to work?
 
What is the demand when P= 1? What is the demand when P= 2? Does increasing the price increase the demand?
 
Thanks very much Halls! That is exactly what I was looking for!

So, if we let p=1, we get 30-3(1)=27. if we let p=2, we get 30-3(2)=24, and if we let p=3, we get 30-3(3)=21. The price is obviously decreasing...

Thanks again!
 
chickenlips said:
Thanks very much Halls! That is exactly what I was looking for!

So, if we let p=1, we get 30-3(1)=27. if we let p=2, we get 30-3(2)=24, and if we let p=3, we get 30-3(3)=21. The price is obviously decreasing...
I think you mean to say the demand is decreasing. But this does not tell you what the revenue is doing.
 
The equation of Demand (Q) is linear. Plot Q vs. P and see at what point Q will become zero (no demand = no revenue).

I assume that your instructor interprets demand as a euphemism for revenue in this example.
 
chemisttree said:
I assume that your instructor interprets demand as a euphemism for revenue in this example.
I sure hope not. Revenue is the product of demand and price (in the limit of infinite supply).
 
So far the link between Demand (Q) and Price (P) has been determined as it is the linear plot Q= 30-3P, but Revenue (R) has not been calculated at all.

Assuming you have enough stock such that you will always meet demand. How much revenue would you make if P=1, P=2?
 

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