1. Consider the basic Solow growth model with a production technology in which aggregate output (income) Y}, is given by: n = KfLi'\" where Kt represents the physical capital stock and Lt represents labor (the population of adults), and or E (0, 1). Suppose in this model1 we now introduce an unproductive government which taxes income at the rate 'r i.e. government income is Gt = TY}. It consumes this amount entirely without any benet for the country. As in the stande model, a fraction 3K of disposable income gets invested to enhance the capital stock, which depreciates at the rate 6. Lt grows at the exogenously given rate of n. (i) Write this model in terms of output per labor i.e. in terms of yt = Y; [Lt1 and derive the dierential equation characterizing the dynamic path for the evolution of kt. Obtain the steady state values of k and y. How are these affected by the level of the tax rate 7'? (ii) Suppose the government was instead productive i.e. uses its income Ct to provide infrastructure, law and order etc. Now the aggregate output {incorne} Y}, is given by: n = ems-H with a + ,8