3) Consider the following variant of the basic growth model: include a government that consumes output (G) and pays for it by imposing (7). Assume that the government balances its budget in every period. With these modifications the model becomes: Y = Ka Ni-a N. =1 Y, = C, +I, +G, I, = S( Y, - T,) T = G K,H = K,(1-S) +1, Suppose that the government revenue is obtained by taxing capital at every period. As the country grows, the government collects more taxes and spends more and more. Specifically suppose that government tax revenue is T, = TK, where r is between 0 and 1. a) Plug the relevant equations into the capital accumulation equation to derive an expression for Ki+1 involving only Ki (and some parameters)