Example #2 – optimal tax policy

Another example is the optimal taxation level in an LQ economy. Here, LQ stands for Linear Quadratic (model). This example is borrowed from Thomas J. Sargent and John Stachurski. Their webpage is at https://lectures.quantecon.org/py/lqramsey.html. They modify a well-known model of Robert Lucas and Nancy Stokey so that convenient formulas for solving linear-quadratic models can be applied to simplify the calculations. There are two types of player in the economy: the household and a benevolent government. The government finances an exogenous stream of government purchases with state-contingent loans and a linear tax on labor income. The household maximizes its utility function by choosing paths for consumption and labor, taking prices and the government's tax rate and borrowing plans as given. Note that to maximize attainable utility...