Let’s take a scenario where the US taxpayers pay less for incarceration, thus making a sentence harsher.
Take an adult male with a ten-year prison sentence at a reduced $20,000 per year. The US taxpayer would spend $200,000 incarcerating that individual. He is not paying taxes on real income (prison income is criminally low, thus the taxes paid minor, if at all), he is not contributing to society in terms of purchasing goods and services, raising children, etc. And, once the ten years are up, he will go back into society without marketable skills or education, meaning that his likelihood of getting gainful employment is extremely low. More likely than not, this ex-con will recede into a life of crime. He has no other options to live. Thus, he will likely commit another crime and then cost taxpayers an additional $100-200,000 over another 5-10 year prison term, if not for life.
Now, let’s take that same individual, and instead of stripping him of all privileges, we keep them, even at the cost of $36,000 per year. Instead of being harsher, we ensure that he leaves prison with a useful associate’s degree, and with good behavior, moves from a medium-security prison to a halfway house with gainful employment after 3 years, where he works, pays rent and taxes, is involved in the local community, and is getting his life on track for success. Instead of the $200,000 and likely more that would cost the US, he is instead only costing $108,000 — significantly less and with a likely outcome of being a productive member of society.