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, we call by physical capital bubble a situation in which the fundamental value of physical capital is lower than its market price. We show that there is a physical capital bubble if and only if the sum (over time) of capital returns is finite. We also point out that there is no causal relationship between physical capital bubble and the fact that the present value of output is finite. Last, with linear technologies, every intertemporal equilibrium is efficient in sense of Malinvaud (1953). Moreover, there is a room for both efficiency and bubble.