Consider the Solow growth model with constant (positive) population growth (γN > 0) and technological change (γH > 0). Suppose that the aggregate production function is Yt = ztKt^a(HtNt)^1−α . (a) Derive the law of motion for capital per effective worker, ˜kt ≡ Kt/(HtNt). Describe your steps as you go along. (b) Using a diagram, show how to determine the steady state value of capital per effective worker (c) Absent shocks, why does capital per effective worker converge to its steady state value? (d) Assume that the economy starts in steady state. Suppose that at some time t0, a horrible plague wipes out half of the population. Miraculously, neither the aggregate capital stock nor total factor productivity, zt , nor human capital per worker, Ht , are affected by the plague. Sketch the time paths for the logs of: population, total factor productivity, aggregate consumption, aggregate capital and aggregate output.