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).
Hi Caleb, thanks for your comment! That’s a great point that workers’ desire for savings prior to their jobs being automated may drive people to work more (similarly, people may work more as wages drop in order to maintain a subsistence level of consumption). On the other hand, if wages drop so low that workers can’t subsist, then labor supplied will drop regardless.
When you say it would be tricky to model savings with my production function, is the reason that superexponential growth with exponential time discounting in the utility function will lead to diverging utilities? That’s an interesting point. Do you know if there has been work on more realistic utility functions to address this issue?
Ah yes that makes sense that growth will be exponential if A_auto has a fixed growth rate. Thanks!
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).
Hi Caleb, thanks for your comment! That’s a great point that workers’ desire for savings prior to their jobs being automated may drive people to work more (similarly, people may work more as wages drop in order to maintain a subsistence level of consumption). On the other hand, if wages drop so low that workers can’t subsist, then labor supplied will drop regardless.
When you say it would be tricky to model savings with my production function, is the reason that superexponential growth with exponential time discounting in the utility function will lead to diverging utilities? That’s an interesting point. Do you know if there has been work on more realistic utility functions to address this issue?