Taking the investment tax rate, the wage rate, and the rental rate of capital as given, formulate the householdís dynamic optimization problem and calculate the Örst-order conditions with respect to Ct;Kt+1; and Nt: DeÖne t as the Lagrange multiplier on the householdís budget con- straint (2) in the optimization problem and substitute (3) in (2) for It. What is the marginal utility of consumption and how is it related to the interest rate rt; the investment tax It ; and the investment shock t? Ex- plain the Euler equation with respect to the physical capital stock and show how it is a§ected by rt; It; and t. Hints: follow the householdís problem solution strategy presented in Parts I and II of the lecture notes and read Greenwood, Hercowitz, and Hu§man (1988); Chari, Kehoe, and McGrattan (2007); Brinca et al. (2016) to develop further intuition.