Ender - great topic.
As others have pointed out, there's so many things today that are different that it's hard to do an apples to apples comparison.
Also, inherent to the thread is the question "what's middle class"? IN a very basic sense you can define "middle class" as "around the median (ave)". But there are dragons here too - suppose real compensation doubles (which is has since 1950) - "middle class" is now able to afford so much more of everything then they could before. Since your question is "how much money would it take to reproduce the same standard of living as 1950" I believe we should consider what an average ("middle class") person would be able to afford in 1950.
A few other things I've encountered:
IN 1950 the laborforce participation of men 65+ was 47%. Today it's 21% This is largely due to the fact that the average retirement age is currently 62.
In 1950 about 1/4 of those 65+ were considered to be living in poverty. Today it's about 10%.
The average work week has dropped from 40 (1950) to 39 hours (2014)
In 1950 the average family spent 30% of its budget on food. Today it's about 13%
Medicare did not exist until 1965
traditional IRAs did not exist until 1974
401(k) plans did not exist until 1980
average real-adjusted SS benefits: $321 (1950) vs $1,277 (2010)
Pensions covered roughly 1/4 of workers (1960) vs 20% (2010)
Commercial air travel was basically non-existent in 1950. So was the interstate system.
Median life expectancy at birth for white males was 66.3 (1950) and 76.3 (2015)
Median life expectancy at age 60 for white males was 75.7 (1950) and 81.5 (2011).
Average new-construction home size 983sqft (1950) vs 2,521sqft (2015) - a 2.6x increase
Average family size: 3.54 (1950) vs 2.54 (2015)
Median household income (adjusted to 2015 dollars): ~$24,000 (1950) vs $51,900 (2015)
Lowest tax bracket was 17.4% (1950) vs 10% (2015) - note, i have no idea how deductions were done in 1950, and can't comment on average taxes paid.
So what can we say from this list of facts & figures pulled off the internet?
In 1950 a 'typical' family would most likely have 2 children and earn around $25,000 (in today's dollars). They would live in a 1,000sqft home and be taxed at 17.4% (but no idea about deductions). There was no medicare available. SS existed but payouts were low for someone retiring in 1950 for two reason; i) the program was still being phased in and ii) SS payouts are calculated both on wage growth and inflation, so todays payouts reflect that. There's about an even chance the breadwinner of this family would still be working after age 65, and he could expect to die 6 years sooner. They might have a car but travel more than a few hundred miles from their home would be very rare.
In contrast, a 'typical' family in 2015 would have 1 child and just over twice the income. Tax rates for median-families are lower and SS payments are higher. There's more of a social safety net in place (e.g. medicare). They probably own at least one car, if not two, and long-distance travel is affordable and available to them. Chances are they will retire before age 62, and be less likely to be in poverty when they do retire.
Note: I started referencing all the sources I used, but this got too long. Either believe me or not, but most of hte facts and figures come from my friend FRED and the Bureau of Labor Statistics.