Endogenous mortality Consider the model of fertility choice in section 9.2.2. Suppose that the mortality rate, d, can be influenced by family or public expenditures on health.
a. Assume that d depends on the household's current flow of expenditures on health. Determine the optimal path of these expenditures. How does d evolve as the economy develops? What are the implications for the behavior of the fertility rate, n, and the capital intensity, k?
b. Assume now that d depends on public health expenditures per capita. Suppose that the ratio of this spending to total output is the constant g and that this spending is financed by a lump-sum tax. How do the paths of the fertility rate, n, and the capital intensity, k, depend on the choice of g? What is the government's optimal choice of g? Would it be preferable to allow g to vary over time?