That they are set like any other price on the market, by adjusting supply and demand.
Inflation is on average given by the equation of exchange: the "price level" will on average increase with the "supply of money", diminish with the "supply of goods" and increase with the "number of times the money is used". On average, it will steadily and slowly diminish over time.
Interest rates will be set by the amount of savings available and by the amount of funds demanded by firms and those who consume on credit. It won't be set by the Central Bank anymore and it will be a free price like that of apples and oranges.
PS "" words refer to aggregate concepts that have no real objective existance in reality but may be of some use as a first order approximation.
What kind of gold standard do you mean ? If fractional reserves were allowed there would be the same problem with fiduciary media we have now. We need 100 percent gold standard to avoid credit expansion, inflation and business cycles. This is not the case how high interest rates would be. They would be market interest rates that allow the best possible coordination and avoiding of mislocation of capital (malinvestments).
Yaros: [...] If fractional reserves were allowed there would be the same problem with fiduciary media we have now. We need 100 percent gold standard to avoid credit expansion, inflation and business cycles.[...]
[...] If fractional reserves were allowed there would be the same problem with fiduciary media we have now. We need 100 percent gold standard to avoid credit expansion, inflation and business cycles.[...]
Fractional-reserve banking isn't really possible in truly free-market conditions. Normally, banks have to compete with each other for the trust of their depositors. Bank notes would (and in the past, did) trade at a discount from face value based on the inconvenience and risk associated with redeeming that note for specie
Fractional-reserve banking is only made possible when a specific bank is favored by government policy. For example, a bank would be granted a territorial monopoly on bank note issue, or the government would demand payment for taxes in the form of the politically-favored bank's notes, or the government would pass laws requiring that people accept these notes as payment. Usually the government would do all of these things. These actions create an artificial demand for those bank notes as money. The government would grant these political favors in exchange for financing government spending. The bank would be required to back their notes not with specie, but with government bonds. The bank wins, the government wins, and the rest of the economy pays for it with higher prices and boom/bust cycles.
As long as the government truly has no influence on what people are allowed to use as money, we don't really have to worry about fractional-reserve banking and its deleterious effects. But this is easier said than done.