A variety of models of irreversible investment under uncertainty are considered. The analysis of irreversible investment is generalized to jump-diffusions. The bankruptcy process, consisting of a jump-diffusion, whose sole jump is to zero, is introduced. The value of the project and the option to invest in it are obtained under several models of taxation. In addition, the government may confiscate the project. The hazard rate of confiscation may be constant or a function of time, price, or project value. Linear taxation generally reduces project value in proportion to the tax rate. The critical price for investment is obtained as a function of the tax rate. The government's revenue-maximizing choice of tax and confiscation hazard rates when the confiscation hazard rate is constant are obtained. Immediate confiscation is optimal when the number of firms is fixed ex ante. When the number of firms decreases in the tax and confiscation hazards rates, the government never confiscates and a simple tax rule is found. When the confiscation hazard rate is proportionate to a power of price, the homogeneous portions of the solutions for project and investment option value become Bessel functions.
An endogenous model of tax reform is solved when price is deterministic. Firms purchase tax cuts from the government. The hazard rate of tax reform increases with present value of the tax cut to the firm. The government's optimal tax break size and pricing rules are found.
Several models of stochastic taxation are considered. A stochastic tax rate which is revealed upon investment has no effect relative to the certainty-equivalent rate. One-time tax changes have ambiguous effects due to the different discounting of the pre- and post-tax change processes. Simulations are used to value the project when the tax reform hazard rate is proportionate to a power of price. Uncertainty may increase the value of the project in the low tax state. Finally, a system of integrodifferential equations is obtained when the tax rate is a function of a marked Poisson process.
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