Suppose that we have an economy with many identical households. There is a government that exogenously consumes some output and pays for it with lump sum taxes. Lifetime utility for a household is: U...

Extracted text: Suppose that we have an economy with many identical households. There is a government that exogenously consumes some output and pays for it with lump sum taxes. Lifetime utility for a household is: U =InCt +ßlnCt+1 The household faces two within period budget constraints given by: Ct + St = Yt – Tt Ct+1 =Yt+1 -Tt+1 +(1+rt)St Use the Euler equation and intertemporal budget constraint to derive an expression for the consumption function. The government faces two within period budget constraints: (1) G_t + SG_t = T_t (2) G_(t+1) = T_(t+1) + (1 + r_t)SG_t In equilibrium, what must be true about S_t and SG_t?