Suppose that a household lives for two periods and has a utility,r function and intertemporal budget constraint as follows: (rs-5 + ass-Era U(L'1.2) = 1 _l' lrsc;cl+=}rl+ r 1+r a} Derive step by step the Euler equation faced by this consumer [dene the Lagrangian and then obtain first order conditions as we did it in the lecture]. Explain the intuition of the Euler equation. h} Find a solution for optimal consumption in both period I and 2 as a function ofthe parameter l3 as well as the variables r, F1 and y2. c} What is the ceteris parihus effect on consumption today.r {Cl} and tomorrow {(72} of the following shocks: {i} An increase in ,8. {ii} A decrease in lifetime income. [iii] An increase in \"y. d} Is there a condition where 1= (:2? If so, what value must [3 assume? Consider an economy existing for four periods following the government budget constraint as follows: But1 = (1+i)B: + Gt - Tt a) Define each of the variables above and explain, in words, why the equality holds. Re-write this budget constraint during each of the four periods that the economy exists. b) The Australian government is trying to decrease the country's stock of debt. Using the equation above, discuss two possible ways this could be achieved using fiscal policy, only. What challenges do you anticipate? (Hint: think of how tax collections change given changes to government spending). c) Using the elements in the equation above, discuss the likely effects on the future stock of debt (Br+1) of an expansionary monetary policy. Explain. d) What will the equation look like in the fourth period and what does this imply for the economy as a whole? e) Using backwards iteration from the fourth period, form and interpret (in at least two sentences) the intertemporal government budget constraint for this economy