Embodied technological progress. (This follows Solow, 1960, and Sato, 1966.) One view of technological progress is that the productivity of capital goods built at t depends on the state of technology at t and is unaffected by subsequent technological progress. This is known as embodied technological progress (technological 3 progress must be "embodied" in new capital before it can raise output). This problem asks you to investigate its effects. As a preliminary, 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: Y (t) = [A(t)K(t)]L(t) 1 . Assume that A grows at rate : A (t) = A(t). Show that the economy converges to a balanced growth path, and find the growth rates of Y and K on the balanced growth path. (Hint: Show that we can write Y/(AL) as a function of K/(AL), where = /(1). Then analyze the dynamics of K/(AL).)