2. Embodied Technological Change (from Romer) One view of technological progress is that the productivity of capital goods built at time I depends on the state of technology at r and is unaffected by subsequent technological progress. This is known as embodied technological progress (technological progress must be embodied in new capital before it can raise output). This problem asks you to investigate its effects. (a) First, let us modify the basic Solow model to make technological progress capital augmenting rather than labor augmenting. So that a balanced growth path exists, assume that the production function is Cobb-Douglas of the form: Y0) = [A(t)K( t)]\"L(t)\"\" Assume that population grows at a constant rate It , A grows at rate it [i.e. A(t) = yAU) ], and capital accumulates as usual: Km = sY(t)-5K(t) (i) Show that the economy converges to a balanced growth path. [Hint Show that we can write Y/AL as a function of K IAl'L , where q: =u/(lu). Then analyze the dynamics of K/A'L ]. (ii) Find the growth rateS of Y and K on the balanced growth path