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Long run equilibrium for a purely competitive firm

In long-run equilibrium for a purely competitive firm: (w) MC = P = MR = min.(LRAC). (x) MC = TR = PQ = AVC. (y) LRAC = PQ = TVC + TFC = MR. (z) P = Q = wL + rK = Y.

Can anybody suggest me the proper explanation for given problem regarding Economics generally?

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