no. exchange presupposes a party giving something up to another party. this is paying a price. even autarkic exchange involves paying prices. (not monetary ones)
Price without money is barter. I exchange 2 apples for 4 oranges, or whatever the going price is. I would argue that money cannot exist without price, since money derives from the exchanges.
IIRC, in Hayek’s Prices and Production, Hayek argues that all one needs is price for exchange and allocation of resources. When he speaks of price, is he referring to monetary price or “price price”, or perhaps both?
Yes, it’s called the “opportunity cost.” But money prices cannot exist without money, and complicated capitalistic economies require money prices for economic calculation. It’s too vast and complex to rely on pure intuition (subjective measures of opportunity costs). Money prices turn subjective opportunity costs into objective information signals.
Exchange can exist without money, but money cannot exist without exchange.
Exchange exists because of subjective value. Without money, people still engage in valuation, that is, they measure the opportunity costs. We can technically call this opportunity cost a price, but it contradicts the more commonly understood notion of price.
Prices are ratios of valuations of goods in exchange. Any time an exchange occurs prices form. So the two go hand in hand. My first “no” needs qualification though. It’s “no, but you can exchange less desired present for more desired future states”. That wouldn’t be a price… but not sure if I am playing with words there.