A frictionless economy

3. A Frictionless Economy Consider an economy where a representative consumer receives Y in income each period and max2mizes her expected discounted utility E: i Emmi) (1) t=0 subject to the following budget constraint PtCt + B: = Pry + (1 + it1)Bt1- (2) The price of consumption goods is denoted as Pt, B: represents one-period nominal bonds, and it is the nominal interest rate. (a) Solve for the first order conditions of the consumer's problem. Write out the consumer's Euler equation. Note that since this is an endowment economy Ct = CH1 2 Y in all periods and this is known with certainty. (4 points) (b) Take logs of the Euler Equation (assume Log(1/)9) : 'F) to find a Fisher relationship between 2?, Etrrt+1, and it. (Note: Just take logs of both sides of the equation and use what you know about logs to find the Fisher relationship.) (4 points) (0) Monetary policy in this economy is assumed to follow a Taylor rule with an inflation target of zero it = i" + 935114715 + \"is (3) where v: is a mean zero AR(1) monetary policy shock (of = va + at). Using your Fisher equation and the monetary policy rule find a linear function that relates inflation today to expected inflation. (2 points) (d) Under what condition does the inflation process found in (c) have a unique Rational Expectations Equilibrium (REE)? (3 points) (e) Using the method of undetermined coefficients, solve for the minimum state variable REE inflation process. (2 points)