Progressive taxation, tax exemption, and irreversible investment under uncertainty

We analyze the impact of progressive taxation on irreversible investment under uncertainty. We show that if tax exemption is lower than sunk cost, higher tax rate will decelerate optimal investment by increasing the optimal investment threshold, while if tax exemption exceeds sunk cost, three different regimes arise. For "small" volatilities the optimal investment threshold is a positive function of volatility, but independent of tax rate. For "medium" volatilities it is independent of both tax rate and volatility. Finally, for "high" volatilities the optimal investment threshold depends positively on volatility, but negatively on tax rate so that we have "tax paradox".