3. The Solow model with technological progress. In the lecture, we talked about the Solow model with technological progress and population growth. Now consider a simpler model with only technological progress. Denote the technology level at time t by At, and the growth rate of technology by g A. The number of worker is constant, N. The production mction is given by Yt = K?\" (AtN)1a1 where Ot is a constant. (a) Dene xt = X t /AtN , where X t stands for all relevant aggregate variables in the model. Write down the production function, investment equation, and the law of motion of capital in terms of per effective worker variables, xt. (b) Solve the steady-state capital, output, consumption, and investment per effective worker. (c) What are the growth rates of capital and output per effective worker, capital and output per worker, capital and output in the steady state