3. War and the Current Account [10 points] The country of lmperia likes to light wars (sometimes) and smooth consumption. It has a GDP of $1 trillion [$1000 billion] every year. [t is year 0 and lmperla has zero external wealth W=0 initially (inherited from year -1). The world real interest rate is 5%. If there is no war (Le... peace] lmperia consumes all GDP. and never invests. with C=GNE=GDP in all future years, and l=G=0. However. lmperia starts a war in year 0. Fighting a war costs G=$84 billion per year. The Long Run Budget Contsralnt {LRBC} must hold. Assume there are no capital gains or capital transfers, KG=lA =0, so the change in Weach period is exactly equal to CA. a. Let us assume that, at rst, lmperians think the war will last only 1 year. Under that assumption. how much will they borrow in year 0 to nance the war? How much do they cut their consumption? [2] Borrow __L__ Cut _1___ [use 5 billions) HINT Check your answer by uniting down the country's planned path from Year 0: Year 0: C TB NFlA _ CA_ W Year 1 & later: C l 6 TB Ensure planned C is smooth and LRBC holds: is future TB equal to interest on debt? Ifnot, go back and correct your answer. Write units in S billions. b. Treat the events in year 0 as given above in part 3. Now in year 1, the lmperians nd they can't exit the war, and they now update their beliefs and think the war will lat 1 more year. How much extra should they borrow at this point? How much more do they cut consumption? [2] Borrow 3" Cut ' [use 3 billions] HINT Check again by writing down the country's planned path from Year 1: Yearl: C_ _ TB NFM _ CA_ W Year2&later: C_ l_ 6 TB_ NFM _ CA W Ensure planned C is smooth and LRBC holds: is future TB equal to interest on debt? if not, go back and correct your answer. Write units in I billions. c. The same thing happens in years 2, 3, and 4? How much more do they borrow and how do they cut their consumption each time? [2] Borrow_ 80 Cut (use $ billions) HINT If in doubt, for each year, check your answer again by verifying C smoothing and the LRBC as in parts a and b d. Now suppose Imperians had known the war would last 5 years (year 0 to 4) from the very beginning in year 0. Would they have chosen this consumption path? Why or why not? [2] They would have chosen a different smooth consumption path from the start if they had known the war would keep going. Instead of consuming (996, 992, 988, 984, 980, . .. .), they would have cut more in year 0 to a smooth level of C such that PC (C+G)=PV(Q) taking into account the now expected 5-year war. correction: e. It turns out that the rest of the world will not lend unlimited amounts to $800 bn Imperia. In fact Imperia's debt limit is 80% of Imperian GDP or $8 trillion. How long a war can Imperia afford to fight using external finance to smooth consumption when it proceeds as above [in parts a/b/c], extending the war one year at a time? [2] If Imperia needs to borrow 80 each year (1, . . . , N) then its net debt at the end of year N is 80*N. It will reach the debt limit of 800 in the year N where 80*N = 800. That is, N=10. Imperia can fight at most a 10 year war using the above approach to consumption smoothing. 7
