Cost minimization requires only that the ratios of marginal product to price be equal for all inputs. Alternatively, cost minimization dictates that inputs be combined in optimal proportions for a given or target level of output.
Profit maximization requires that a firm employ optimal input proportions and produce an optimal quantity of output. Cost minimization and optimal input proportions are necessary but not sufficient conditions for profit maximization.
Profit maximization dictates that the firm employ all inputs up to the point where MCq = MRq. Profit maximization requires for each and every input that
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