证明marginal cost >average cost,average cost increase
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证明marginal cost >average cost,average cost increase
最容易的办法就是看那张图,就是短期AC curve &MC curve cross那张图,你所指的情况就是相交以后.当边际量大于平均量时,才能带动平均量的上升,也就是交点是AC的最低点.不过用数学推比较严密.
不妨设总成本函数TC=F(Q) MC=F'(Q) AC=F(Q)/Q
当MC>AC 有 F'(Q)-F(Q)/Q>0
此时,AC'=[F'(Q)Q-F(Q)]/Q²=[F'(Q)-F(Q)/Q]/Q>0 即average cost increase
不妨设总成本函数TC=F(Q) MC=F'(Q) AC=F(Q)/Q
当MC>AC 有 F'(Q)-F(Q)/Q>0
此时,AC'=[F'(Q)Q-F(Q)]/Q²=[F'(Q)-F(Q)/Q]/Q>0 即average cost increase
证明marginal cost >average cost,average cost increase
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