Supplemental Notes to “Demographic Transition and Industrial Revolution: A Macroeconomic Investigation.”

2 Characterization of the competitive equilibrium 3 2.1 Dynastic Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Existence and uniqueness of the solution to (DP) . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Sufficiency of first order and transversality conditions . . . . . . . . . . . . . . . . . . 3 2.1.3 Derivation of first order and transversality conditions . . . . . . . . . . . . . . . . . . 4 2.2 Firms maximization and optimal resource allocation . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 The Malthusian technology is always employed . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Necessary condition for operating the Solow technology . . . . . . . . . . . . . . . . . 5 2.3 Summary of conditions that characterize the competitive equilibrium . . . . . . . . . . . . . . 6