1. Continuos time Ramsey: Let the utility and production functions of the representative household and rm, in the continuous time Ramsey model, are given by, respectively, u (t) c (t) 1 1 1 (1) Y (t) = K (t) L(t) 1 (2) where c (t) represents the consumption of a household member; Y (t), K (t) and L(t) denote output, capital and labor, respectively. Each household member owns a unit of labor that supplies to rms and earn a wage w (t). The household also owns an asset A (t) at time t, and receives interest income for exchange of its service. The size of the household grows at n rate. (a) Dene the household problem, derive the optimal conditions and the Euler equation and interp