The rationale

After having been through 7 years of school (3 undergrad, 4 grad), one already loses on 4 years of salary. To most people, this is probably negligible. However, as one ages, each year becomes arguably more valuable (we're all dying right?).

I previously did the math for a medical graduate vs. an undergraduate working in an office (approximately USD$60,000 - $100,000 salary). Very gross estimates accounting for investable income, investment returns with compounding, and a very crude tax rate - the medical graduate can finally catch up to the undergraduate after around 7-10 years (approximately age 33-36).

So how about if the medical graduate chooses to go beyond internal medicine? (Sorry surgeons, won't be calculating general surgery vs. specialty surgery).

How people usually calculate

Salary alone

"Specialists get paid more." This is likely true. The differences in internist salary and specialist salary can be pretty striking. But one needs to calculate the hours worked.

Forgetting taxes

While the salary for doctors in USA is quite generous, so are the taxes (nowhere near as obscene as the tax rate in Australia though fortunately). But taxes also remove a significant portion of money that can be invested.

Forgetting investment

"You should be making money when you're sleeping." Someone told me this. And of course that quote has probably been passed around.
Imagine working and only earning a salary. These days, this is a terrible idea. Actually, in all years, this is a terrible idea. More so now, that inflation somehow manages to equal or exceed the average real return of index funds (expect around 7-10% real return).

Forgetting compound interest

"The most powerful force in the universe is compound interest." - Albert Einstein (though somewhat questionable if he actually said this).

Assuming one wishes to be the absolute laziest defensive investor out there, expect 7-10% real return from dumping your yearly investment principal into an index fund. Per The Intelligent Investor and Security Analysis by Benjamin Graham - both must-reads I must say - this strategy is validated with decades of data, but let's not go into that here.
In 10 years of 7% real return, expect to double your money by literally doing nothing.

If you get a 3-year head start, 22% return
4-year head start, 31% return
5-year head start, 40% return
...
(n)-year head start, r% return
See where I'm going with this?

One who starts investing ahead of time, and attempting to capture the returns while perhaps getting lucky with the markets, can eventually be light-years ahead even someone who has to wait to attain a higher salary.

Forgetting a good market cycle along the way

I'm not saying this happened to me, but let's say in the 3 years during your extra degree, or fellowship, or whatever slows you down from earning a sizable salary - a market crash or opportunity comes along.
You wish to invest 10% of your income.
For someone earning $250,000: $25,000 can be invested
For someone earning $70,000: $7,000 can be invested

Assuming a 10% return, at the end of 10 years, the principals have grown to:
t = 10 _ $25,000: $65,000
t = 10 _ $7,000: $18,000
But if the return in a good opportunity is 20%...
t = 10 _ $25,000: $150,000
t = 10 _ $7,000: $43,000

The point of this basic calculation above is to demonstrate that assuming one is rather prudent in investment decision making, with a proper head-start, the gap can grow large over time thanks to compounding.

Forgetting leverage

Without going into too much detail here, with a higher income, comes higher borrowing potential.
For most peoples' purposes here, the borrowing potential will come to buying property and using leverage to augment returns.
A 3-year head-start with a $250,000 salary vs. $70,000 salary seems like a short timespan, but this time should ideally be used to consider opportunities to borrow money for larger asset purchases, particularly real estate.
Having an extra 1 or 2 properties is probably already enough to get a couple year head-start.
However, I have not actually factored this into the calculation, because it would probably get too complicated (beyond my pay grade).

Calculated with the above points in mind

At the end of everything, I of course made a spreadsheet, with variables in mind:

Salary - these were varied with around 3 sets of numbers
Tax
Investable income
Investment return
Cardiologist vs. hospitalist

The cardiologist (type below) catches up to the hospitalist by post-IM residency year...

Electrophysiologist: Year 8
Interventional cardiologist: Year 8
General cardiologist: Year 7

The differential is USD$1 million by post-IM residency year...

Electrophysiologist: Year 12
Interventional cardiologist: Year 14
General cardiologist: Year 17

USD$1 million is probably the equivalent to...1 house?
Would it be not unreasonable to just by at least 1 house during the 3 years if not choosing to pursue fellowship, to make that differential effectively $0?
Though one could argue the borrowing potential of the specialist far exceeds that of the internist once the attending physician level salaries are accounted for.

Not calculating the subjective opportunity costs

Specialists are arguably working more hours than the internist. On-call...a bit more stressed...
Then there are the things that are missed in the ages 30s-40s:

Family life
Weddings
Travel

And for the more dark people, "You never know, the next day, I could be hit by a car."

I think while I could try to factor in costs for the above, it would not be generalizable, given how each person will value each opportunity differently.

In conclusion...

We can work for money or passion, or attempt to do both. There is no one approach that is more valid than the other.

Investing money seems to be the factor that can really narrow the gaps between internists and specialists.

So what is the right answer then? I have no idea even after the above have been calculated.
The spreadsheet making was very fun though.

If you would like the spreadsheet that explains the math with the numbers, feel free to let me know. Always happy to explain the above concepts.