The question is, how do you quantitatively define "purchasing power" when prices are diverging? Is it the number of cheeseburgers you can buy? The number of TVs? The number of houses? If you take some average, the average of which set, and why?
One idea is weigh by reported actual expenses in each category you're measuring. But that way, you're just measuring the trend in expenses, which should be proportional to GDP per capita.
Edit: no, not all GDP is consumer spending (there is also investment, government expenses, and net exports).