Question 2 Impact of Government Debt in a RA Framework (total 18 marks) Consider an economy that is populated with a representative household who is infinitely lived. The household has an endowment of y, in each period t and has to pay a lump-sum tax T in period t to the government. The household can save through holding capital k, or one period government bonds, both assets paying the same rate of return 1+r. The government has an expenditure ge in each period t which can be financed either by tax revenues or issuing government bonds, be. The household maximizes her life time utility given by 00 [Bru(cc) t=0 (a) Write down household budget constrain in period t. Write down the government budget constraint in period t. Clearly define your notations. (4 marks) (b) Suppose in periods, there is tax cut of 100 goods, i.e t = Ts - 100. Government expenditure does not change in any period. How b, changes following this tax cut? Suppose the government will retire the newly issued debt in some period afterwards say period j > s. Then, how much Tj should increase? (4 marks) (c) Write household's lifetime budget constraint (5 marks) (d) How the consumptions, savings, capital holdings of the household would change following the tax cut in period s. (5 marks)