2. In the exercise, we consider the Solow economy with a constant population growth in continuous time. Remember that the growth rate of capital per unit of labor is given as k(t) _sf(k(t)) Yk(t) - (n + 8) = G(k(t)). k(t) k(t) For simplicity, we assume that the production function is Cobb-Douglas, that is, y = f(k) = Aka (a) Under these assumptions, show Yk(t) = -B(log k(t) log k*), where = (1 a)(n+8). The symbol z implies that the above equation is approximation (Hint: Notice G(k(t)) = G(elog k(t)) and calculate a first-order Taylor expansion of G(elog k(t)) around logk(t) = log k*). (b) Derive the following expression (t) Vy(t) = -B(logy(t) log y*). y(t) (c) What does the coefficient mean? 2. In the exercise, we consider the Solow economy with a constant population growth in continuous time. Remember that the growth rate of capital per unit of labor is given as k(t) _sf(k(t)) Yk(t) - (n + 8) = G(k(t)). k(t) k(t) For simplicity, we assume that the production function is Cobb-Douglas, that is, y = f(k) = Aka (a) Under these assumptions, show Yk(t) = -B(log k(t) log k*), where = (1 a)(n+8). The symbol z implies that the above equation is approximation (Hint: Notice G(k(t)) = G(elog k(t)) and calculate a first-order Taylor expansion of G(elog k(t)) around logk(t) = log k*). (b) Derive the following expression (t) Vy(t) = -B(logy(t) log y*). y(t) (c) What does the coefficient mean