I’m imagining something that is Cobb-Douglas between capital and land. Growth should be exponential (not super exponential) when A_auto is growing at a constant rate, same as a regular Cobb-Douglas production function between capital and labor. Specifically, I was thinking something like this:
X_old^beta(A_old K_old^alpha L^{1-alpha})^(1-beta) + X_auto^beta(A_auto K_auto)^(1-beta)
st X_old + X_auto = X_total (allocating land between the two production technologies)
As to your second point, yes, you are correct, as long as A_old is constant wages would not increase.
Thanks for this Phil,
A couple of questions regarding SWE:
So does this mean that in the research production function, the exponent on the stock of ‘ideas’ is one, and the exponent on the number of researchers is significantly less than one? It might be nice to see the equation.
Relatedly, isn’t endogenous growth a knife-edge case? Intuitively, it seems unlikely to be true, and SWE doesn’t seem to address this issue.