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:
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.
Ah yes that makes sense that growth will be exponential if A_auto has a fixed growth rate. Thanks!