2. (20 points) A simple decentralized economy with portfolio choice A typical household aims to maximize its expected discounted lifetime utility function given by: Vi = _ BU(c) where the period utility is U(c) = _ and the discount factor B = . 0 denotes the rate of time preference and o is the coefficient of relative risk aversion discussed in class. The household receives exogenous income r, in each Lou period which can be either consumed (@) or invested in physical capital , or invested in one-period bonds b, issued by the government. Let ry - o denote the net rate of return to physical capital, where o represents the depreciation rate, and R, denotes the gross interest rate on one-period bonds. The household pays taxes only on earnings from physical capital assets at the proportional rate TK, where 0