Show that marginal revenue (MR) must equal marginal cost (MC) at the profit-maximizing level of output. By

Show that marginal revenue (MR) must equal marginal cost (MC) at the profit-maximizing level of output.

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By definition, = TR - TC. Taking the derivative and setting it equal to zero, since d/dQ must equal zero for to be at a maximum, dTR dTC == 0 dQ dQ dQ Solving algebraically, recalling that dTR/dQ = MR, dTC/dQ = MC, dTR dTC = dQ dQ MR = MC Q.E.D.