Progressive Income Taxes and Option Values: The Case of a Farmer Who Owns a Forest Available to Purchase

Consider an individual having two sources of taxable income. First, a stochastic, e.g. farm income. Secondly, a controllable arising when a stock of capital is converted into taxable income, e.g. the harvesting of a stock of timber. The harvest decision is an optimal stopping problem when the individual i) maximises expected post-tax income, ⁽ⁱⁱ⁾ has the option to observe a period's farm income before deciding on the harvest policy, and ⁽ⁱⁱⁱ⁾ income taxes are progressive. Two cases are considered. The case where farm income is generated by random draws from a stationary distribution, and the case where farm income is generated by a stationary, autoregressive process. In the first case, the solution is a single value of farm income for each period. In the second case, the optimal stopping rule is a set of two values of farm income.