Supply is thus a function and not a specific number: if price is 1, then supply 2 units, if price is 1.5 then supply 4 units, if price is 2, then supply 10 units etc. So, for every possible $P$, we solve $MC(Q)=P$ for $Q$ and call the solution $S(P)$. When calculating the equilibrium, we calculate the optimal quantity supplied and quantity demanded for every possible price and not just one price. Similarly, the consumers take the market price as given and choose the quantity to consume given the price. Thus, they take the price as given and choose the quantity to maximise their profit. In a perfectly competitive market, the sellers and the buyers are price takers, that is, they believe that no matter what they do, they cannot individually affect the price of the commodity (so $MR=P$ for firms always, and $MC=P$ for consumers always).
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