\(A\): total factor productivity, which describes how productive capital and labor are.
As you can see here, given the same amount of capital and labor, a larger total factor productivity leads to a larger economic output.
The variable we are interested here is \(A\), total factor productivity. It describes how productive the economy is, and can be increased by many factors, such as the advancement of technology. For example, since the end of the 19th century, the use of electricity spread out and changed the way people used to work and live, which increased total factor productivity.
However, one may argue that if no proprietary software is allowed, who would invent these new technologies in the first place? Well, I have two arguments against this.
First, "open source" does not necessarily lead to "non-profit". Many companies do make money over their open source products, such as Android, RedHat Enterprise Linux, Docker. What they really need to do is to build an open source business model that makes their open source software generate revenue.
Secondly, even if no open source business model is available for a specific type of software, we can do something similar to the medical world—patents are granted when new medicine is first developed for some years and then the technology becomes accessible to the rest of the world. This mechanism makes a great compromise: on one hand, it promises the profit to the developers; on the other hand, it contributes to the productivity of the whole economy after some years. The software industry can do something similar, which I would call "lagged open source".