Question 2 Representative agent economy Consider the basic representative agent economy discussed in class. A single individual produces a good that can either be consumed or invested to increase future output and consumption. The objective of the agent is how best to allocate output between consumption today and investment (i.e., to accumulating capital) so that there is more output and consumption tomorrow. The model consists of three equations. The first equation is the national income identityy = cut it in which total output yt in period t consists of consumption C plus investment goods it. The national income identity also serves as the resource constraint for the whole economy. The second equation is: dkul = , - ok. This shows how ky, the capital stock at the begin- ning of period t, accumulates over time, ie the increase in the stock of capital (net investment) during period t equals new (gross) investment less depreciated capital. A constant proportion of the capital stock is assumed to depreciate each period (i.e., to have become obsolete). This equa- tion provides the intrinsic dynamics of the model. The third equation is the production function) yt = ka where 0