In 2014, Thomas Piketty came out with a popular book, “Capital in the Twenty-First Century.” In it was a model not unlike the Solow growth model, discussing the long-run implications for the capital-to-income ratio, k/y. His model differs slightly from ours, and it’s nice to know how. In our typical model, we have: ct + it = yt k(t+1) = (1 − δ)kt + it
1) The traditional Solow growth model assumes: it (Gross Investment) = s (Gross output)
Piketty assumes: it − δkt (Net Investment) = ˜s(yt − δkt) (Net output)
2) Using the law of motion of capital: k(t+1) = (1 − δ)kt + it
Assuming that yt and kt are growing at a constant rate g (i.e. y(t+1) = (1 + g)yt and k(t+1) = (1 + g)kt), use the Solow assumption and the law of motion of capital to derive a relationship between kt/yt and s, g and δ.