Is the definition for productivity given in the question below correct?

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This statement is not true.  The ratio of input to output would give us a number that could be used in a way that is similar to how we use productivity statistics, but it would not be the same thing.

When we say that something is the ratio of input to output, we mean that we would derive that measure by dividing input by output.  So, we would be dividing hours worked by units of output produced.  This would give us a measure of how many hours were worked for each unit of output.  This would be a useful thing to know, but it is not the same thing as productivity.

Productivity is typically measured in units produced per hour worked.  That means that it is the opposite of what is described in this question.  Productivity is not the ratio of inputs to outputs.  Instead, it is the ratio of outputs to inputs.  It is generally measured in units produced per hour worked.

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