Ah I didn’t realize that a balanced growth path is important for analytical tractability, thanks for that insight. And yes I’m reading your paper (haven’t gone thoroughly through the model yet though), really interesting!
That’s a great idea to add land to the production function to bring back diminishing returns to capital. I am hoping to extend the model to include capital accumulation, and I’ll think about including land when I do that. I suppose this will lead to a balanced growth path if A_auto is constant, but if A_auto is growing then growth could still be super exponential. (Regarding whether wages will eventually rise, I actually think wages would remain at zero in this model with capital accumulation and without land, because the marginal product of labor with the old tech will remain below the reservation wage).
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:
Ah I didn’t realize that a balanced growth path is important for analytical tractability, thanks for that insight. And yes I’m reading your paper (haven’t gone thoroughly through the model yet though), really interesting!
That’s a great idea to add land to the production function to bring back diminishing returns to capital. I am hoping to extend the model to include capital accumulation, and I’ll think about including land when I do that. I suppose this will lead to a balanced growth path if A_auto is constant, but if A_auto is growing then growth could still be super exponential. (Regarding whether wages will eventually rise, I actually think wages would remain at zero in this model with capital accumulation and without land, because the marginal product of labor with the old tech will remain below the reservation wage).
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!