Normally, in an economy that is growing in productivity, your purchasing power should be growing, not merely staying the same. If your productivity increases by 3% per year, then you should be able to buy 3% more goods and services every year (assuming you work the same hours).

If the supply of money does not change, then increases in productivity will be reflected in lower prices. If you made 100 widgets last year for $100 ($1/widget), and this year you made 103 widgets because you got better at it (productivity increase), the price of your widgets would be $100/103widgets = $.97/widget if people spent the same amount of money or portion of their income on widgets. Your goods would be cheaper for customers, or, put another way, your customers would be a little richer in widgets. If others in the economy experienced the same productivity growth, you would also be richer. The $100 you made producing widgets would buy you more of other people's goods. Your standard of living depends on your own productivity and everyone else's. If your productivity is average, and the average is growing, then your standard of living should be growing too.

Thus, if the money supply were relatively constant as it would be under a gold standard, prices should naturally fall as productivity increases, while wages should be constant (assuming no population change).

When the money supply is growing, it is a lot harder to make these calculations and know what your money should be worth. This is an irritation at the personal, consumer level, you don't know exactly how much the government is screwing you, but at the macro level, it causes bubbles. When people don't know the value of money, they spend unwisely, paying too much for a thing. The housing bubble was caused because people thought that money was worth less than it was. (They can be forgiven for this mistake because it was reasonable. If money were worth more, why were the banks selling it so cheaply?) As a result, they overpaid for houses and builders built too many of them. By the time the mistake was discovered, there were too many houses on the market and their prices dropped suddenly.

...which would be a bad thing, because if the purchasing power of your money grows even when it's parked under your mattress, it's a lot harder for entrepreneurs to attract investment.

I would agree that the Fed has been too loose with the money supply over the past twenty years or so, and that this appears to be a structural problem with the central banks; George Cooper makes a good case in The Origin of Financial Crises. But I don't think the solution lies in a return to the gold standard.

A gold standard also solves inflation, but fundamentally and non-policically, by limiting money to the supply of gold.

The purpose of the Fed is to inflate the money supply for the benefit of the government, the banks, and borrowers who want artificially low interest rates at the expense of everyone else who uses money. If the Fed did not inflate, it would be no different from a gold standard, and in fact, when the Fed corrects inflation, it does so by reducing the production of new money as under a gold standard.

That’s not how I define inflation, and I don’t think it’s how most people (even economists) define it. I define inflation as stuff getting more expensive.

If you define “inflation” as “increase in the money supply” and “value” as “value denominated in the mass of shiny rocks”, then yes, a gold standard prevents inflation and stabilizes the value of money. But this is a tautology, not an argument.