Intertemporal equilibrium with production: bubbles and efficiency

We consider a general equilibrium model with heterogeneous agents, borrowing constraints, and exogenous labor supply. First, the existence of intertemporal equilibrium is proved even if the aggregate capitals are not uniformly bounded above and the production functions are not time invariant. Second, (i) we call by physical capital bubble a situation in which the fundamental value of physical capital is lower than its price, (ii) we say that the interest rates are low if the sum of interest rates is finite. We show that physical capital bubble is equivalent to a situation with low interest rates. Last, we prove that with linear technologies, every intertemporal equilibrium is efficient. Moreover, there is a room for both efficiency and bubble.