For most buildings it's more effective to build the first "Double the output" then to build new buildings when you have 15 of them already. For Time machines it's 14. (ignoring the cookies you can bake with the new building while you save for the upgrade. That's too difficult to calculate and seems to have way to many variables)

For example:

Once you have 14 grandma's a new grandma costs 704 C and gives you one grandma in extra production. Steel-plated rolling pins costs 10,000 C and gives you 14 grandma's of production. This means that Steel-plated rolling pins is 14 times as valuable as a single grandma. Thus it can cost 14 times as much. That is 9,856 C. Not worth it.

However, once you have bought the 15^{th} grandma the new grandma would cost 814 C. The Steel-plated rolling pins still cost 10,000 C and they now give 15 grandma's of production. That's worth 12,210 C (ignoring time-based effects)

The 14^{th} Time machine costs 759,603,403 C. The Time paradox resolver costs 9,876,543,210 C. 14 * 759,603,403 = 10,634,447,642. More than the 9 GC the Time Paradox resolver costs. That's one machine sooner.

If I have the time I'll calculate the other upgrades to. The first upgrade will be the last to be calculated because it's more difficult.