I'm not sure that anyone here knows the context or terminology of your problem.

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Discussion Overview

The discussion revolves around a problem involving the demand for bike paths in a town, focusing on the calculations related to individual demand functions, marginal costs, and tax distribution among residents. Participants explore the implications of different marginal cost values and how they affect the number of paths built, as well as the tax rates applied to each resident.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how the answers 0, 11, and 2.67 were derived, particularly in relation to the marginal cost being stated as 7.
  • Another participant points out a contradiction in the problem statement regarding the marginal cost, questioning whether both MC=21 and MC=7 are correct.
  • A participant suggests that if the tax rates are shared equally among the three residents, then they should all be equal to 7, leading to confusion about the demand calculations.
  • One participant clarifies that the marginal cost is indeed 21, not 7, and agrees with a demand calculation that yields 5.67 for one resident, while noting a discrepancy with the provided answer of 2.67.
  • Another participant argues that the problem seems flawed, questioning how the town can fund more than one bike path given the stated marginal cost of 21 dollars.
  • A different viewpoint suggests that if the tax is set at 7 per path and 11 paths are built, the total tax collected would cover the costs, drawing an analogy to public funding for services.
  • One participant acknowledges a misunderstanding regarding the "per path" aspect of the tax, leading to a revised belief that the answer should be 11 paths.
  • Another participant notes that since this is a homework question, the original poster should ideally provide the answer first.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the marginal cost and the implications for the number of paths built. There is no consensus on the correct number of paths or the validity of the calculations presented.

Contextual Notes

There are unresolved issues regarding the assumptions made about the marginal cost and the distribution of tax rates. The problem statement's clarity is questioned, particularly concerning the values of MC and the implications for demand calculations.

surferbarney0729
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confused

Andrew, Beth, and Cathy live in Lindhville. Andrew’s demand for bike paths, a public
good, is given by Q = 12 – 2P. Beth’s demand is Q = 18 – P, and Cathy’s is Q = 8 – P/3.
The marginal cost of building a bike path is MC = 21. The town government decides to
use the following procedure for deciding how many paths to build. It asks each resident how many paths they want, and it builds the largest number asked for by any
resident. To pay for these paths, it then taxes Andrew, Beth, and Cathy the prices a, b,
and c per path, respectively, where a + b + c = MC. (The residents know these tax
rates before stating how many paths they want.)

Can anyone help me on how the answers 0,11, and 2.67 where found using the MC being equal to 7?

I am missing something simple and am looking for some help.

Thanks
 
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Not sure how much I can help. However:

You have not stated what the question is.
The problem statement, as you posted it, contains the contradictory statements MC=21 and MC=7. Does the actual problem statement really have both statements -- or is it supposed to be something other than MC in one of those statements?
 
The tax rates are shared equaly among the three residents. So in an a=b=c format the three residents all share the MC of 7.

I simply did plugging into figure out the demand, but in no way can see how to get 2.67

for example,

Q=12-2(7) = no demand for paths
Q=18-7 = 11 paths demanded
Q= 8-(7/3) = ...I see it as 5.67, but the answer is 2.67. This is where I become confused
 
Where do you get a=b=c from? The problem statement suggests they are not necessarily equal.

What is the actual question? What is it you are supposed to find? It's best if you can copy and paste or quote the complete problem statement in it's exact original words.
 
Andrew, Beth, and Cathy live in Lindhville. Andrew’s demand for bike paths, a public
good, is given by Q = 12 – 2P. Beth’s demand is Q = 18 – P, and Cathy’s is Q = 8 – P/3.
The marginal cost of building a bike path is MC = 21. The town government decides to
use the following procedure for deciding how many paths to build. It asks each resident how many paths they want, and it builds the largest number asked for by any
resident. To pay for these paths, it then taxes Andrew, Beth, and Cathy the prices a, b,
and c per path, respectively, where a + b + c = MC. (The residents know these tax
rates before stating how many paths they want.)

a. If the taxes are set so that each resident shares the cost evenly (a = b = c), how
many paths will get built?
 
Okay, this makes a lot more sense now.

In your work, you have correctly set a, b, and c all equal to 7=21/3=MC/3. It was confusing me that you started referring to MC as equal to 7 -- it is not 7, it is 21 as stated in the problem.

swoodward said:
Q=12-2(7) = no demand for paths
Q=18-7 = 11 paths demanded
Q= 8-(7/3) = ...I see it as 5.67, but the answer is 2.67. This is where I become confused
Looks like you have it worked out correctly, and I agree with the 5.67 number. Apparently whoever posted the solution made an error.

So, based on this, did you come up with the number of bike paths that the town builds?
 
This problem seems flawed to me...the marginal cost of 21 dollars is for building one bike path, so how can the town pay for any number of paths (other than one) if it only taxes a total of 21 dollars?

If a=b=c=7 and that's it (presumably the town will just pay from reserve funds or something), then there should be 11 paths built since Beth would demand 11 paths and the government wants to build the maximum number of paths asked for...
 
I thought it meant a=b=c=$7 per path. If they build 11 paths, they tax each person 11x$7 or $77. The town then collects 3x$77 = $231 total from the 3 citizens, just the amount needed to pay for 11 paths (11x$21 is $231).

From Andrew's standpoint, it is similar to my town taxing me to pay for the school system, even though I have no children and so do not benefit from the school system.
 
Ah, my mistake, I missed the "per path" part of the question. In that case...I think the answer should be 11...
 
  • #10
Okay, though technically this is a homework question so we should let the OP provide the answer first.

I have moved this thread to Homework & Coursework Questions, "Other Sciences".
 
Last edited:

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