为什么利润最大化原则MR=MC?在完全竞争市场条件下可表达为P等于MC?

为什么利润最大化原则MR=MC?在完全竞争市场条件下可表达为P等于MC?
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为什么利润最大化原则是MR=MC?

Total Profit (TP) = Total Revenue (TR) - Total Cost (TC)
If a company wants to maximize it's total profit, it means to find the maxima of the above TP function of Q (Quantity), which is dTP/dQ = 0
dTP/dQ = dTR/dQ - dTC/dQ and dTP/dQ = 0
0 = dTR/dQ - dTC/dQ
dTR/dQ = dTC/dQ (where dTR/dQ = MR and dTC/dQ = MC)
MR = MC

在完全竞争市场条件下可表达为P等于MC?

P = Price and Q = Quantity
TR(Q) = P(Q)*Q
TR'(Q) = MR = P'(Q)*Q + P(Q)
For profit maximization under perfect competition
MR = MC
P'(Q)*Q + P(Q) = MC
Under perfect competition, the market price is a constant (P(Q) = P), which is beyond the control of the firm, so P'(Q) = 0
0*Q + P = MC
P = MC
With Quantity, Q = optimum production volume S, P = MC = TC'(S) and this curve is the supply curve under perfect competition

in general MR = dTR/ dQ = d(Q*P(Q)) / dQ = P(Q) + Q * dP(Q)/dQ
under PC, P(Q) is contant.  dP(Q)/dQ = 0

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Thank you LZ