For the U.S. economy, productivity is defined as (output measured in $)/(input measured in $). Typically, new technologies (computers, internet, AI) reduce input costs, and due to competition in the market, companies are required to reduce their prices, thereby having an overall deflationary effect on the economy. It's entirely possible that AI will have a small or no effect on productivity as measured above, but society will benefit by getting access to inexpensive products and services powered by inexpensive AI. Individual companies won't use AI to improve their productivity but will need to use AI just to stay competitive.