Working Paper（23-002E）Necessity of Rational Asset Price Bubbles in Two Sector Growth Economies

One possibility is that the economy converges to the steady state, where the output from the tech sector and the dividend from the land sector are of the same order of magnitude. [...] However, a positive interest rate is necessary for a finite asset value, yet in this case the fundamental value of the asset is bounded and the asset price may be insufficient to absorb the savings of the young. [...] The fact that the Pareto exponent is lower (wealth inequality is higher) in the bubbly regime than in the fundamental regime corresponding to the same equilibrium interest rate is that the “growth shock” g(z) in (4.12) is multiplied by 1− β in the bubbly regime (see (4.13)), whereas it is multiplied by 1− βR in the fundamental regime (see (4.11), and we have 1− β > 1− βR because R > 1. [...] As discussed in the introduction, Santos and Woodford (1997) proved the impossibility of bubbles under borrowing constraints if the asset is in positive net supply and the present value of the aggregate endowment is finite. [...] The growth rate of the economy is endogenously determined through the leverage constraint and the balance of the two sectors.