Externality Cost of Capital Investment in Limited Commitment

We study externality costs of capital investment under limited commitment. We solve for the constrained efficient allocation with a limited commitment environment and find positive externality costs of capital investment provided that full-risk-sharing is not feasible. In a decentralized version of limited commitment environment, a one unit increase of capital investment by an agent increases all individuals' autarky values in the economy and generates externality costs in the economy. This externality cost provides a rationale for positive capital taxation even in the absence of government expenditure. In order to internalize this costs, the government use a positive rate of linear capital tax in the decentralized economy