I know mostly about the United States, so I will limit myself to comment on that country. I'll also mostly comment on New York, then as now the center of money in the U.S.

In the United States, the period of the late nineteenth century is known as the Gilded Age for the emergence of the hyper-wealthy after the Civil War. This came about for a variety of reasons, including a huge boost to the industrial economy of the North during the Civil War, the opening of new, resource-rich territories out West, and a relatively lax federal government that included no personal income tax and little oversight of industry. From the term "Gilded Age," you might surmise that this new class of wealthy people lived ostentatiously. You would be correct in that assumption.

This is the era that defined conspicuous consumption in the United States. In earlier periods the goal of a businessman was to amass enough wealth to retire early, and then to live a comfortable but relatively mundane existence, devoting himself to family, religion, and local community organizations, or perhaps dabbling in botany or some other aspect of scientific research. This changed during this period, however, when the great fortunes of men such as Carnegie, Rockefeller, and Mellon were first amassed. These men, and those like them, made huge sums of money and spent huge sums of money. Multiple houses, European cruises and other travel, and lavish parties were the norm. Elaborate costume balls were particularly notorious affairs, complete with sexual licentiousness and other debauchery.

The other way they spent their money was on philanthropic pursuits. Many of New York's great public institutions were founded in this time, including the Metropolitan Museum of Art (1870), Metropolitan Opera (1880), and the New York Public Library (1895). These places were directly conceived of as monuments to the wealthy men who financed them, as well as spaces to develop and ensure cultural capital for wealthy New Yorkers. They were also an attempt to deflect criticism for the amassing of great wealth through a show of public-spirited philanthropy. If the wealthy spent great sums voluntarily in moral uplift for the poor, they might be spared the income taxes and other measures that had the potential to deplete that wealth even more. This worked for a time, but the Progressive Era of the early twentieth century would see a backlash and some degree of limit on personal wealth and big business.

The main source here is Sven Beckert, The Monied Metropolis