Two-identical-sector model with CRS - collinearity issue


I tried a model with two identical (!) sectors (i.e., not consumption and investment), just two production functions for two identical goods (same price). The file is attached (CRS_NoLand.mod). I get the message that a set of equations is collinear.

I suspect this is because in such model it is not determined how big sector 1 and sector 2 is (it can be anything), but I am not sure if this line of thinking is correct. To look into this further, I made a version of the model with land and hence decreasing returns to scale for capital-and-labour-part of the production function (attached, DRS_WithLand.mod). Now the collinearity message is gone, and I think this is because sectors now have to be of equal size in order for the equilibrium to be symmetric.

CRS_NoLand.mod (1.5 KB)
DRS_WithLand.mod (1.6 KB)

Does this make sense? Many thanks in advance!

Hard to tell, but it sounds reasonable.

Thank you very much! Well, then it is two of us who believe this is reasonable. I hope it does not mean we have converged to the same fallacy :slight_smile: If I find out more about this, I’ll post it here.