It's a bidirectional relationship. The value of gold actually remained stable when the U.S. dollar was pegged to it. I view that as evidence for pegging stabilizing the value of the commodity it is pegged to. However is an simplification, because share of the dollar relative to other currencies policies has changed. I also only believe the system I depicted would work, if the exports of the commodity were restricted so that no one or only the central bank could sell it abroad.
Saying something is “pegged” is saying that the price is fixed. There doesn’t exist any volatility between pegged instruments because that’s what a peg means.
So you have to compare them to other things, which is what inflation (or deflation) measures. And gold pegged usd has volatility to other items in the economy greater than modern fiat usd.
You're near-certainly right that pegging in dollars would means some rate, let's for simplicity presume a constant ratio, between dollars and what it's begged to.
I think crux is what happens if we model two different currencies, one of which is begged, and the price of te commodity in each.
If after the conversion rate you can get cheap gold, that keeps golds value low and pegged currency's value high, I would guess.
Again I think restricting impots in the commodity is necessary to maintain supply.
