Show that in the simplied version of the Romer model, there is a balanced growth path. Follow the steps:
a) Using the production function show that if the growth rates of K, and A are constant, then the growth rate of Y will also be constant.
b) In the previous exercise you have already shown that A grows at a constant rate in the long-run. So, all that is left is to show that K will grow at a constant rate in the long-run. Use the capital accumulation equation to show that ˜k = K/ALY is constant in the long-run. Then, argue that it follows that K must be growing at a constant rate.(Hint: Look at how the steady state capital accumulation is derived in the Solow model in Chapter 2.)
c) Show that in such a balanced growth path gy = gk = gA (where gx denotes the growth rate of any variable x in the balanced growth path).