1. [50 points] Consider that capital accumulation with constant population growth and no technological change is given by k(t)=sf(k(t))(n+)k(t) where f(k) is the production function in intensive form. Let k(t) be the solution to this equation with the initial condition k(0)=k0>0. (a) Let k be the steady state capital-labor ratio. Intuitively show that k is asymptotically stable, (that is, k(t)k). (b) Let w(t) and R(t) be the corresponding equilibrium factor prices at date t. Recall that the firm is taking as given the rental prices of labor and capital and thus they are equal to their marginal products. i. Find w(t) and R(t). ii. Intuitively show that w(t) and R(t) are monotone functions of time. (c) Sketch k(t),y(t),c(t),w(t) and R(t) for a given k00. (a) Let k be the steady state capital-labor ratio. Intuitively show that k is asymptotically stable, (that is, k(t)k). (b) Let w(t) and R(t) be the corresponding equilibrium factor prices at date t. Recall that the firm is taking as given the rental prices of labor and capital and thus they are equal to their marginal products. i. Find w(t) and R(t). ii. Intuitively show that w(t) and R(t) are monotone functions of time. (c) Sketch k(t),y(t),c(t),w(t) and R(t) for a given k0