Question

Does profit maximization imply cost minimization? Does cost minimization imply profit maximization?

Answer 1

No, there is no direct relationship between profit maximization and cost minimization. When a firm tries to maximize it's profit, it tries to produce the output in the cheapest way possible. Profit maximization leads to economic efficiency but not cost minimisation.

Cost minimization doesn't necessarily mean profit maximisation. Profit maximization is a combination of revenue maximization and cost minimization. Profit is derived from the difference between revenue and cost. Cost minimization alone cannot lead to profit maximization.