Production function formula?

I think that you have identified a very interesting question. As I see it, you have realised that a country benefits not just from the production and consumption of products (and services) but also from the intellectual capital that it has produced during the year.

To take into account the intellectual capital (knowledge) that has accumulated in the year, you could combine various measures such as:

Number of patents registered;
Number of PhDs graduated;
Number of Research publications produced etc.

The country also benefits from the development and deployment of technology. To take this into account, you could combine measures such as:

Number of patents registered (again);
Number of Web sites registered etc.

The country also benefits from access to and the utilization of finance. To take this into account, you could combine measures such as:

Number of microloans granted;
Amount of deposits/reserves in insurance companies and banks etc.

The country obviously benefits from labour. To take this into account you have to find:

the total value of goods and services formally provided;
the same for the invisible trade on street corners and villages called the informal sector etc.

I must warn you of three things.

It is not possible for an individual to measure all the above. It has to be done by the Government. So you are constrained to work with available data and measures.

You have to avoid double counting. Many of the things I have itemised are already proxied or measured to some extent in GDP. For example, the value added by the financial sector is encapsulated in the Gross Sectorial Product GSP) for the Financial Industry; The value added to the GDP by the Gross Sectorial Product of the Government Sector encapsulates the value added by the Educational sector, etc.

The remaining problem is that you will want to add together measure that have different units: E.g. Number of graduates + Number of Web sites, and you cannot do this! The only solution is to reduce all measures to a common financial unit per year.

However, your study is not in vain. I suggest you look critically at the current practice of adding together all GSPs uniformly together to get the GDP. Surely some Sectors have greater FUTURE value that others. So you could investigate weightings to be applied to the GSPs to get a Future Production Function. Such a function could encourage growth in the knowledge economy which is already upon us.

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