19. Suppose that the saving rate, s, can vary as an economy develops. a) The equation for the growth rate of capital per worker, k, is given by Δk/k = s⋅(y/k) - sδ - n Is this equation still valid when s is not constant?
b) Suppose that s rises as an economy develops; that is, rich countries save at higher rate than poor countries. How does this behavior affect the results about convergence?
c) Suppose, instead, that s falls as an economy develops; that is, rich countries save at lower rate than poor countries. How does this behavior affect the results about convergence?
d) Which case seems more plausible - b) or c) above? Explain.        Now suppose that the population growth rate, n, can vary as an economy develops.
e) The equation for the growth rate of capital per worker, k, is still given by Δk/k = s⋅(y/k) - sδ - n Is this equation valid when n is not constant?
f) Suppose that n falls as an economy develops; that is, rich countries have lower population growth rate than poor countries. How does this behavior affect the results about convergence?
g) Suppose, instead, that n rises as an economy develops; that is, rich countries have higher population growth rate than poor countries. How does this behavior affect the results about convergence?
h) Which case seems more plausible - f) or g) above? Explain, giving particular attention to the views of Malthus about endogenous population growth.