In the series, the Bunker's don't own cars, but they own a house in Queens. They pay off the entire 30 year mortgage in one episode. I assume it's a 30 year mortgage anyway. On Archie's salary they can comfortably feed a family of 4, though Gloria works part time and Archie moonlights as a cabbie. They have a color TV. Archie can afford beer and cigars as well as trips to the neighborhood bar. It is hinted that occasionally they'd had to drain their savings to survive.
5.50 per hour, 40 hours a week, 52 weeks a year, $11,440 per year. That works out to 54,057.36 in 2013 dollars. According to the Tax Foundation, the tax rate at that level would be 25%. If we do the math, that means that Archie would have paid 13,910.94 in Federal income taxes. According to the New York State Department of Taxation and Finance, in 1974, only people making more than $25,000 a year paid income tax. In social security and medicare taxes,, a combined rate of 5.85% is applied for all income under $13,200, so 3162.35. This means Archie's take home pay would be 36,984.66 in 2013 dollars. The tax charts are in 2013 dollars, but the combined percentages work out to a take home of about 68%, or 7826.95 in 1974 dollars.
One could simply look at the CPI and inflation rates to get an idea. 1974 was the beginning of the oil shock and large cost increases across the board took a huge bite out of the average American's income. Let's look at specific sectors.
Medical care from 1970-1973 increased at an annual rate of 5.025%. 1974 saw an increase of 9.3%, and 1975-1980 saw an average increase of 9.95%.
Food and beverages increased from 1970-1972 at 4.02%, but in 1973 it increased 11.68%, and from 1973-1980, the average increase was 8.32% per year.
Transportation increased from 1970-1973 at 3.5%, 10% in 1974, and 9.48% from 1974-1980.
Every sector saw inflation and starting in 1973-1974 there was a sharp jump due to the 1973-1975 recession. The combination of the Nixon shock/end of the Bretton Woods/gold standard and the oil crisis took a huge toll on the economy. How would all this have affected Archie?
The rising costs across the board would have hurt, definitely. On the plus side, Archie owned his own home so the increase in housing costs would not have hurt him and the appreciation in value of his own home would have only been a benefit. Not owning a vehicle would have been a plus, but he would have still felt the pinch. 1970-1971, the fare on the NYC subway was 30 cents. From 1972-August 1975, it was 35 cents, and from September 1975 until 1980, it was 50 cents, a 60% increase over the decade. Depending on how often the family used public transportation vs. walking or carpooling, the effect could be minimal to moderate.
Finally, according to the Census Bureau, the poverty line for a non-farm, male headed family of four in 1974 was between $5,000 and $5,252 (the csv file is kind of hard to read, not sure exactly which number to use). Looking just at his income alone, we can see that he is solidly working class. Archie grosses a little more than double the poverty line and takes home about 1.5 times that from his main job. When we consider the extra income from Edith's part time job and from Archie's cash based taxi moonlighting, the numbers only look better. Finally, with Gloria and Meathead moving out in the mid 70's, the poverty line for a family of 2, head of household below 65, the poverty line is between $3,324 and $3,724. Archie and Edith were probably bringing in more than 3x that number for just the two of them.