2. A modified Solow model (or an AK model) in continuous time utility). The household's budget constraint is given by A~=W,L+rtAtCtL Assume the aggregate production function is given by Y(t)=AK(t). Suppose that the labor force L(t) grows at the constant rate n, that is, L(t)=L(0)ent. Define (1) Write down the equilibrium law of motion of k(t), i.e. write down for k(t). (2) Under what condition will the economy achieve sustained growth? 2. A modified Solow model (or an AK model) in continuous time utility). The household's budget constraint is given by A~=W,L+rtAtCtL Assume the aggregate production function is given by Y(t)=AK(t). Suppose that the labor force L(t) grows at the constant rate n, that is, L(t)=L(0)ent. Define (1) Write down the equilibrium law of motion of k(t), i.e. write down for k(t). (2) Under what condition will the economy achieve sustained growth