Marginal Cost and Demand

surferbarney0729

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

Redbelly98

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?

surferbarney0729

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 in to 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

Redbelly98

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.

surferbarney0729

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?

Redbelly98

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.

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?

Matterwave

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...

Redbelly98

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.

Matterwave

Ah, my mistake, I missed the "per path" part of the question. In that case...I think the answer should be 11...

Redbelly98

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".