Why Do We Care About Productivity?

When a manager is trying to figure out how much to pay an employee, the upper bound has to be the employee’s marginal revenue product: how much extra revenue that one employee adds from their production. Basically, the employee's marginal costs can't exceed their marginal revenue product.
But an employee has a lower bound on what they’ll accept for their time. Sometimes this is zero, but typically it’s quite a bit higher than that (we call that a reservation wage). And sometimes a statutory minimum wage is part of the lower bound.
When you combine those two together, for people who are employed, the intersection is a narrow band of possible levels of compensation that both parties will agree to.
To this, we add several other considerations.
First off, employees have a lot more control over their marginal product (how much they produce) than they do over their marginal revenue product (how much what they produce is sold for). Both sides know this, and there’s a (tacit) implicit contract just about everywhere that you get compensated for the typical value of what you produce, and the owner’s handle any risk (upside and downside) involving the revenue.
Secondly, owner’s and employees generally arrange compensation so that you’re the total marginal compensation over a long period of time matches up with marginal revenue product over a long period of time. Then that’s paid out over shorter increments. For example, getting $10/hour doesn’t mean your production in each specific hour is worth $10; rather it means that if we add up your marginal production over many hours, and then divide by the number of hours, that the result is $10.
Tie all this together, and perhaps your marginal revenue product, averaged over many hours, is $20/hour. And perhaps your reservation wage is $15/hour. How much do you end up getting? To the extent that you think that employers can take advantage of employees, you think you’d end up near $15/hour. Alternatively, if you think that employees have a great deal of ability to leave jobs in which the division of gains is unfair (recall the ultimatum game), then you’d think you’d end up near $20/hour.
Assessing this relationship is a key to understanding how political opponents view the labor market.
But, there’s two problems. First, the theory says we need marginal product for individuals, but what we have is total factor productivity — a form of average product for a country. It’s easy to find an average wage for a country. But this brings up the second problem: both marginal and average product are real, while wages are nominal. So we have to filter those nominal wages with a price index to get to real wages. The first problem means that our comparison is less than perfect, and the second one means that it can be manipulated to satisfy non-economic ends.