Macroeconomic formulas for global limited raw material economy exist?
I am not an expert on the domain. However, a popular extension in various domains of macroeconomics is to replace the standard Cobb-Douglas function 

$$Y=AK^{\alpha}L^{1-\alpha}$$

by a production function that take a third resources (typically called land and noted $T$) which is supposed to be in a constant quantity. The production function hence becomes

$$Y=AK^{\alpha}L^{\beta}T^{1-\alpha-\beta}$$

With 


$$\frac{\dot{A}}{A}=g $$
$$\frac{\dot{L}}{L}=n $$
$$ \dot{K}=sY-\delta K $$
$$\frac{\dot{T}}{T}=0 $$


It is -to my knowledge, typically used in growth theory, to account for malthusian theories, more here for instance, and some empirics Here, but i guess every textbook in growth has a note or more on it. 

I also recall seeing it  in international trade, but less frequently.