Consider a competitive, closed economy. Time is continous. Production employs the standard neoclassical production function Y = F(K, AL) = ALf(k) where k = K/AL is capital in efficiency units of labor; time indices are sup- pressed in the interest of brievity. Technology and population grows at constant rates A i L = 9 = N And the production function exhibits the usual properties: f' > 0, f" < 0 and the Inada conditions. We shall assume the real wage is w and the real rate r are both taken as given. Capital depreciation is ignored (equal to zero). The price of output is normalized to one. Question 1. Solve the profit maximization problem for the representative firm which operates this technology and show the following first order conditions need to be fulfilled A [(k) ' (k)k] = - = W and |' (k) = = r. Now, assume that the economy is also charactarized by K = I S = I S=sr K,0 < s