Eggertsson and Mehrota (2014) introduced capital in section 9 of their working paper.
The role of capital and investment in their model, however, is a bit different from my recent work:
First, the capital investment for the middle-aged is another way to smooth consumption just for the middle-aged, so more investment means less loan supply. While in my model, more investment means more borrowing and lending between the young and the middle-aged, hence also alleviating the borrowing constraint.
Second, Explaining the Keynesian paradox of thrift.Here’s the mechanism –> more desire to save –> less demand for today –> lower inflation –> higher real return –> leads to even lower demand. Really there’s no role for investment here in the story. The key is that the investment only respond passively to demand, a decreasing demand means we don’t need so much investment, and because of decreasing marginal returns, when Y is low, in the steady state we only need to replace a small amount of capital –> a low I/Y ratio.
In my model, however, I directly model this investment channel, which I think is not done in this paper.
Some other drafts that maybe useful for later use: (For my own reference)
Notice in their paper, Steady state investment to GDP ratio is low when real interest rate is high, that’s kind of natural, because when output is low, the return on capital would surely be high so r_K is high, but also we have I=\delta * K, so steady state investment is linear in capital, and output is a concave function in K, so when I/Y will be increasing in K. where as r_K is decreasing in K, so I/Y is decreasing in r_K