The following research shows there isn't really a gap between wages and productivity:
The Growing Gap between Real Wages and Labor Productivity by Robert Z. Lawrence (PIIE)
Summary
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First, production and nonsupervisory workers do not constitute the full US labor force.
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Second, workers are paid more than their take-home hourly wages.
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A third issue is that different price measures are used to estimate real output and real hourly compensation. It's missing one graph that really helps understand this: Price indexes, nonfarm business sector, first quarter 1947–third quarter 2010. Basically prices that consumers and businesses have to pay are not rising as fast as they used to but due to computers business prices have risen much slower than consumer prices.
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Fourth, the measure of output that is generally used to depict productivity is gross output and thus includes the consumption of capital. [Even though the price of computers goes down they need to be replaced more often making gross output higher. When net output is used the gap goes away.
jd@hoot.goldandblack.xyz 3 years ago
On top of all that, it's sometimes worth pointing out that, simply, value is subjective and that applies to both wages and productivity. How much is the productivity of a particular worker worth? At least the amount they're getting paid from the perspective of the employer. At least as much as they're getting paid, from the perspective of the worker.