There's no exponential growth, that's thermodynamically impossible. Heating the Earth with the microwaves would increase the Earth's radiation into space commensurately. It doesn't get stored forever. This would result in a new equilibrium almost immediately, with an unmeasurably greater temperature.
The Earth is always almost exactly in a radiative balance with space, except on pretty short timescales. If it weren't, we'd quickly cook. The radiation the Earth receives from the Sun fluctuates orders of magnitude more over solar cycles, but it's debated whether that even has a meaningful effect on global temperature.
(I'm not referring to exponential growth in temperature over time due to constant input power, but rather to exponential growth in input power over time because it's required for economic growth).
> exponential growth in input power over time because it's required for economic growth
It isn't. The amount of energy (and raw materials generally) required to produce a given amount of economic output is not constant. It gets smaller as technology advances. That offsets the effect of increased economic output. Indeed, as more and more economic output becomes information instead of physical objects, the average amount of energy required per unit of economic output will shrink even more.
Not only is this not guaranteed, it is not possible to be sustained in the long term, either physically or economically. Physically, there are bounds on the energy inputs required for any process, including information processing. Economically, if economic output increases exponentially while energy input is constant, this creates a contradiction, as it becomes exponentially easier over time for one individual to monopolize the entire energy supply.
The notion that economic growth can continue without growth of energy is a short-term illusion created by the transition to an information economy, outsourcing of manufacturing, and perhaps a lack of appreciation for the ongoing growth in energy consumption even within countries like the United States as the economy shifted away from physical goods, let alone the growth in energy consumption in countries like China that ramped up physical manufacturing to make this possible.
Per capita energy consumption has not been growing in developed countries like the US. It has been decreasing for at least a couple of decades. Total energy consumption has been increasing because of population increase, but that is expected to level off around the middle of this century.
> it becomes exponentially easier over time for one individual to monopolize the entire energy supply
No, it doesn't, because everyone else is also increasing their economic output. Assuming stable population, one individual's share of the energy supply remains constant.
And yet, the industrial manufacturing sector uses more! As does the computing sector.
This is because energy consumption reduction due to efficiency improvements goes -- to be very generous -- as 1/t, and exponential growth goes as e^t, and e^t/t is still exponential for large t.
That's a graph of CO2 concentration in the atmosphere, not human emissions. It won't look exponential until the magnitude of human emissions exceeds the magnitude of the natural carbon cycle by several times. Give it a decade or three.
