Capital Furs

Thought this might be of some interest, so, posting it here. ^^

DEFINITION OF PROBLEM:
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Scenario:
I) You want to work x hours per week.
II) You want to keep commuting (ie. travel) to a minimum.
III) You want to maximize your earnings.

PROBLEM:
What is minimum pay-rate that a job that requires commuting have so that it's worth-while (from a fiscal and temporal standpoint) for you to bother commuting there?

BACKGROUND:
While some jobs can be found downtown that pay a higher than minimum wage, you may actually be able to earn more by staying around your local neighborhood, working at a minimum-wage job, than you would if you worked at the higher paying job.

Consider:
i) Commuting to your workplace can take a considerable amount of time per week.
ii) Although the wage-rages would be different, you would be working the same amount of hours if you were working locally vs at a remote location.
iii) Compare what your net weekly earnings at your local job would be if you worked extra hours there equivalent to the sum of the weekly hours commuting you would waste whilst traveling to your higher wage job.

SOLUTION:
Let p = pay-rate at local job. ($/h)
Let P = pay-rate at remote job. ($/h)
Let t = time spent commuting per week. (h)
Let x = hours worked per week. (h)
Let b = cost of transportation per week. ($)

Equation as follows:
P>=p(t/x + 1) + b/x

EXAMPLE:
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-- You currently work 18 hours/week at minimum wage ($9.50/h), 3 days a week, within walking distance to your house.
-- Your commuting time is less than 15 minutes by foot hence we assume it is effectively zero.
-- You are aware of a job downtown that pays $12/h . OC Transpo planner tells you commuting time one-way equals 1 h . Let's say you use bus tickets. Each bus ticket costs $1.15. You need 4 tickets per day to travel; 2 to get to work and 2 to get back.
-- Your weekly cost of transport will then be 4x(cost of ticket)x(number of days worked)=$13.80 fare

P>=9.5(6/18+1)+13.8/18
>=$13.43...

For this example, at 18 h/week, it is only worth your while to travel downtown if you are getting paid more than $13.43/h .

(Note: An interesting observation is that the more hours you work per week, the less the minimum wage can be to make it worth while. Eg. If you worked 30 h/week (ie. 3 8h-days), you'd need a pay of at least $11.86/h ! Hence, whether it's worthwhile really depends on how many hours you work per week! ;3 )



Supper time now!

~ Feather ~ ^^

What if the only job you can find is downtown and your stuck between no job and a down town job?

Shaedyn wrote:What if the only job you can find is downtown and your stuck between no job and a down town job?

Take the job. ^.^

This is an interesting problem.

Your equation is very good, but I think you missed one important point: if you live far away from downtown, you probably already have a bus pass. If you don't have a bus pass, investing in one will also probably make life easier outside of work. Therefore, a bus pass (as opposed to bus tickets), though a financial loss, will improve life outside of work.

Of course, if one cannot afford said bus pass, and will not travel outside of work, then your equation works perfectly.

The amount of work put into this is boggling, and I bow to your intellect and dedication.

was this an assignment or for kicks? o.o;

saberstorm wrote:was this an assignment or for kicks? o.o;

Knowing Feather he did it for fun and potential profit.

There's a lot more to take into concideration though... like I'd rather work in the market than a nowhere shithole 10 minutes away from me, even if they pay more and are closer.

Daninator wrote:This is an interesting problem.

Your equation is very good, but I think you missed one important point: if you live far away from downtown, you probably already have a bus pass. If you don't have a bus pass, investing in one will also probably make life easier outside of work. Therefore, a bus pass (as opposed to bus tickets), though a financial loss, will improve life outside of work.

Of course, if one cannot afford said bus pass, and will not travel outside of work, then your equation works perfectly.

Hi there Daninator! Pleased to make your acquaintance! =3

In response to your post, you will notice that my equation has a variable "b" that represents the cost of transportation. So, you could input the weekly cost of tickets or what the weekly cost of a monthly, semestered, or annual bus pass would be. In fact, b can be anything as long as it reflects your weekly cost of transportation--so, for instance, if you drive a car, you could imput your weekly cost of gas.

Now, everyone should keep in mind that this equation does not take into consideration any other factors except time and money. So, obviously, if one travels across the city or downtown frequently, then a bus pass is a smart investment regardless of where your work is. In my case currently, tickets are more economical since I don't take the bus often enough to warrant spending more money on bus passes. And I agree, getting out is good for the body and the soul. ^^

Indref wrote:The amount of work put into this is boggling, and I bow to your intellect and dedication.

:3 Thanks for the compliment!

saberstorm wrote:was this an assignment or for kicks? o.o;

"For Kicks" to use the vernacular. I wanted a formula to help me filter out jobs that would not meet my necessary criteria. If I'm going to work, I want to maximize my pay.

Kesslan wrote:

saberstorm wrote:was this an assignment or for kicks? o.o;

Knowing Feather he did it for fun and potential profit.

Since when did you know me so well? :P Although, it wasn't exactly 'fun', more so a necessary evil. Of course, it wasn't not fun either....so...kidnda a mix I guess. ^^

Pooshie wrote:There's a lot more to take into concideration though... like I'd rather work in the market than a nowhere shithole 10 minutes away from me, even if they pay more and are closer.

Naturally job satisfaction is a significant consideration and not to be overlooked. I didn't see the need to incorporate that into the equation as one's own judgment will suffice. You don't need a formula to tell you whether you like a job or not; you feel it in your gut. Generally speaking, my viewpoint is that most entry level jobs are on average extreme-blah to begin with anyway so it makes little difference really which one you take and whether it's near or far as long as you a) you are comfortable enough to work there to tolerate being there, b) you can do the job, c) have schedule flexibility, d) maximize your pay, e) minimize your hours, and f) preserve your sanity, g) not get hurt or maimed in the process, h) whatever else I forgot to add. So, if I'm going to be work at a job out of monetary necessity that I'd rather not be at in the first place, I'd rather earn as much pay as fast as possible so I can get out of there quickly as possible. And, since I'd be working the same number of hours per week anyway, unless I really hated all the jobs close to home, I'd rather stick with the higher pay.

Now if, for instance, you had reasonable expectation that a lower-paying job farther away would soon lead you to a promotion or aid you in your career, then that would be a significant factor that would probably be of greater importance than pay or time traveled because the short-term hardship would be offset by a significant future gain.

Personally, I find having a work-life balance goes a long way towards making you happier. "All work and no play makes Jack a dull boy" as the proverb goes.

Point is, yes, I fully acknowledge that there are other considerations beyond the scope of the equation but the equation was never designed to address those other considerations. It's purpose was simple: Determine what a reasonable pay level is to warrant the trouble and lost time incurred of going farther away to work. It's just a tool to help sort out which jobs are worth further consideration and which ones should be placed further down que list.

^^

Featheredragon wrote:Hi there Daninator! Pleased to make your acquaintance! =3

I am very pleased to make your acquaintence! By this post, you have gained my admiration and respect--this post is just awesome! I love the practical intelligence of working out a problem with equations. :D

(And, yes, I realised "b" could be changed. So, if you already spent $20 on tickets per month (as I do), you could easily shift that to the price of a pass minus your previous ticket expenses. Of course, one could also shift the values around based upon subjective considerations. If I were to take a job farther away, and had to increase my spending on travel by $55 for a bus pass, I could consider the emotional value of a bus pass as worth $20 a month, and therefore, for my equation, input "b" as $35. One of the great things about equations is that you can easily switch the variables around to suit other questions).