"Lower than most people suspect" is not the same thing as low, even if it were true. It is in only in developed countries where the children of people who didn't graduate high school can become billionaires without using force to do it,  and a billionaire can lose his fortunes the next day if he makes a mistake. You won't find that in a buraeucratic system where there are legal protections for the powerful. 

Also, many Western countries have tons of redistribution (more than nominal "socialist" places like China or India.) Many U.S states also invest heavily in poor, urban areas through special state funding of the schools and business grants, and it just doesn't work (mostly because the poverty is an effect of the drug war.) 

It is quite obvious to anyone that the standards of living and opportunity of social mobility for the (relatively) poor in developed countries  is excellent when compared to the rest of the world. That the rest of the world has the opportunity to do the same (like China, Brazil, etc) is quite nice, and the historical trend has shown that people are indeed leaving poverty, without needing social ownership of the means of production.

It is also important to note, that there is a high correlation between per-capita income and economic freedom. Much more noteworth than the one between per-capita income and personal freedom (linear vs. square-root.) 

The bolded is the answer for why it is only $2 /day. The majority of places making less than $2 /day have lower costs of living than places where the wages are much higher. Nevertheless, you can't ignore that just two centuries ago 80% of the world made less than this, and the cost of living (on average) was mostly the same. 

I think it is a combination of hard work and smart work. One shouldn't be paid more because they dig ditches and fill them up. They need to help produce a social good that others demand. That is why there are different wages/salaries for different jobs. Not all work is equally valueable. 

I would like to know where you get your tables from.

The academic sources I consulted and my classes of sociology painted a very different picture. For example: social mobility in Belgium is really not high (aside from succes stories that exist in any country). You also have the situation that the government here and the bureaucracy are often on bad terms with each other.

(I would also like to point out India isn't socialist at all, and while China is ruled by a "Communist Party", social security is really lacking)

This is actually incorrect but you are on the right path.  Labor, like any other good is what is sold to an empolyer.  So basically, when you get a job, your employers is purchasing labor from you.  The idea of social good has NOTHING to do with anything.  There are different things that affect prices (in this case the price you can charge your employer for your labor) but the most basic is supply and demand.  There are more people avalible who can fulfil the job of the ditch digger so the cost of that labor is substancially lower than the cost of labor for a computer engineer who labor isn't natural more valibable, but is more scare and therefore you can demand a higher price for your labor.   There is no moral highground when it comes to labor, only scarity.  Therefore to look down on someone who works hard in a lower paying job is really shitty.  

Now you try to damage controll with something irrelevant and ignore inflation. 10,000 gbp could buy you everything this is correct but compare the same amount of money what you could buy today with the same money, 10k british pounds wont buy you even a mordern car these day. Back then 10k pounds would buy you probably an entire factory or mid size company.

The inequality has increased this is a fact. Back then 10% of the world population owned the same amount like 50%, today its 1% from i can remember.

And now you show decade old gdp per capita numbers before the worldbank adjusted ppp conversation rates.

And look where you so called first world econmic freedom loving countries are leading

http://www.globaltradealert.org/

Does this look like economic freedom?

"Social good" in this context (one in which the market is efficient at maximizing utility) means "good demanded by consumers." An employer (unless they are a government) isn't going to hire people unless they know there is a social good to be made, from which they can make a profit. What I was stating was the same principle you are describing, the problem of scarcity. Nobody demands a person to dig ditches and fill them up, therefore it is not a social good. Now if one believes in market failures that can be solved by government, then social good does not mean what I said it means (in the general context it means a good  which maximizes utility for the most people.) 

India's preamble says: 

WE, THE PEOPLE OF INDIA, having solemnly resolved to constitute India into a SOVEREIGN SOCIALIST SECULAR DEMOCRATIC REPUBLIC 

India followed the Soviet planned economic model until 1991 after the Soviet Union collapsed. While the economy is much freer today, due to some liberalization, there is still a lot of central planning going on, much more than in Western Countries, and yes that includes European social democracies. 

You are fine to provide your academic sources by the way, rather than just mention them. ;) 

Here is one of my sources; 

https://books.google.com/books?id=jIBac4n5vU8C&pg=PA16&lpg=PA16&dq=intergenerational+elasticity+coefficient+third+world&source=bl&ots=35Y5yiueVU&sig=iScJxo5xwjJzNHqalcVmXiHjnLM&hl=en&sa=X&ved=0ahUKEwjUsc-rjf3MAhVOTFIKHatUDpcQ6AEIOTAD#v=onepage&q=intergenerational%20elasticity%20coefficient%20third%20world&f=false

Africa, Latin America, and Asia have base intergenerational elasticities between parents and children's income of about 0.66, 0.66, 0.5 respectively. Europe of .4, and the Nordic countries of .2. Lower is better here. 

I didn't ignore inflation, it isn't relevant to the argument I made besides showing you that the nominal value in the mid 1800's for the poverty rate was much lower than $2. You were saying $2 /day was poverty in the 1800's, not today. Which is not true. $2/day in the early 1800's was a decent wage, and in the late 1800's a livable one. Since the $2 /day is adjusted for inflation, what is meant is that it is $2 in today's money that is the poverty level of both time periods. This is a measure of absolute, not relative poverty. 

But if  you care so much, 10,000 GBP in 1850 is only equal to around 964,400 GBP today, and that was what the richest people in the world had. Considering the richest people in Britain have on the order of billions GBP, that is a measly amount, still. 

The top might not have owned as much, but the lowest bottom 10% had a much lower share of the world's wealth than today.  I'd call that less equal. 

The following is for the 20th century, but it illustrates the point quite well. Income inequality right after the Gilded Age was higher than today in Anglo-Saxon countries. 

So you think the trend just changed suddently in the pass 10 years? I'll answer that for you, nope! 

2012

Let's also look at other measures of good living