Profit world compared to technology world

Most of the world economy is generated by companies operating to maximise their profits. How would its behaviour differ if the main economic agents were attempting to maximise their technological usage?

It might happen. Suppose global warming gets really bad or a serious pandemic without a known cure develops, and it becomes a social imperative to develop a response to which the economy is redirected. Or it might be that profits and technology become so identified in future that companies opt to follow technology maximisation as a simpler, albeit imperfect, criteria for maximising profit.

Profit maximising companies maximise a function like {Infinite stream of discounted future profits} subject to a budget constraint. Let us assume that profits are retained and equal a function A(t)*K(t)^a where A(t) is technology at time t, K(t) is capital at time t, and a is a constant. The budget constraint is A(t)+K(t)=A(t-1)*K(t-1)^a+A(t-1)+K(t-1). Then we can follow standard optimisation techniques in forming the Lagrangian and differentiating to get a solution a.A(t)=K(t).

A technology maximiser by contrast maximises a function like {Infinite stream of discounted future technology}. There is a question about what a sensible discount rate is in this equation. Technology at time t is A(t). The same budget equation is used. The solutions depend on the parameter values a and the discount rate.

It may be optimal to maximise the profit function as long as possible before changing all profits to technology if a is high and the discount rate is low. Equally it may be optimal to emphasise technology accumulation over profit accumulation if the discount rate is high.

The differential equations from the problem are not as neat as for profit maximisation, where an identical equation for A(t) and K(t) emerges independently of the number of discount periods. The solutions require the full set of equations for all time periods to be simultaneously specified, and unless there is a short cut (very possible) they have to be solved as a simultaneous system. I haven't done it yet.