Gold is not money in our day and age. It is a commodity. And like other commodities, people invest in gold to earn a rate of return. The rate of return on gold, or investment in anything, conforms to the general time preference rate of interest. Rates of return in the various lines of investment conform by changes in the prices paid to buy into the investment relative to the anticipations of future prices to be realized when selling out of the investment.
Of course, there is consumer demand also for commodities as well as investor demand. But that doesn’t change the basic incentive of the investor, which is to earn a rate of return on investment. An investor thinks that the rate of return on buying gold now and selling it a some point in the future will be at least the same as any other investment of the same maturity and in the same risk class. If investors didn’t think this, they would invest in other lines which would lower the price of gold and raise the price of assets in the other lines. This arbitrage will cease when the anticipated rates of return are the same.
When the Fed pushes short-term interest rate down through monetary inflation and credit expansion, it sets in motion the arbitrage process across the different lines of investment. Then rates of return will also decline in these lines as investors move to buy their assets. Asset price inflation is the result.
How investors see the variations in changing demands across the different lines into the future will determine how asset prices will change relative to each other over time. Since gold is a traditional hedge against price inflation, investors are sensitive to changes in the purchasing power of money overall when assessing investment in gold. If investors anticipate price inflation, then gold prices will move up disproportionately to prices of other assets.
The claim that the rate of interest is an opportunity cost of holding an asset applies only to cash itself. Buying and holding goods is done to earn the rate of interest. And the rate of interest on all investments (loans, production, assets, commodities, etc.) will be brought into conformity through arbitrage.