That's what Betsey Stevenson, an economist who studies happiness, says:
What we see is that happiness rises with the log of income. I think that's where people get confused. A 10% rise in income is associated with a similar change in happiness at any income level. But when your income is $20,000 that 10% is a lot less money than when your income is $200,000. As your income goes up, the extra happiness or life satisfaction you get per dollar shrinks because it is a smaller proportion of your income. But we see that happiness rises quite steadily with the log of income.
A poor individual or a poor country is going to get a lot more happiness out of a dollar than a rich person or a rich country. But a 10% increase in income in a poor country is going to get us about the same amount of increase in happiness as a 10% rise in income in a rich country.
A lot of economists had hypothesized that relative income is what matters, so it doesn't matter if I get richer if everybody else is also getting richer. In that case my happiness isn't going to change. It only changes if my station in society changes. But, in fact, we find that richer countries are happier than poorer countries and as countries get richer, their citizens get happier. I should note, however, that there is one exception. The United States has gotten wealthier over the last 40 years and we haven't gotten any happier on average.
Lots more research on happiness here.