1.Formulate the relevant equations for a two period borrowing/savings utility maximizationproblem with log utility.There is a fund that provides you withZ₁endowment in the firstperiod, andZ₂endowment in the second period.ris the interest rate,is the discount factor,andbistheborrowing/savingschoice.

2.

Now there is an infinite number of periods. However, you can only can make a single bor-rowing/savingschoicebintheinitialperiod.Ifyouborrow,youwillhavetopaybackbrininterests ineverysingle future periodimagine you get a zero down-payment auto-loan withsomepositiveinterestrateandyouneverpaydowntheprincipal.Ifyousave,youwillearnbrinterestsineverysinglefutureperiodthinkofthisasinvestinginastockthatyouneversellandthatearnsyouthesameamountofdividendsinallfutureperiods.Yourendowmentinthefirstperiodise₁(1standsforthefirstperiod);youhaveidenticalendowmentsineveryfuture period,e_f(fstands for future).Suppose0< r <1, meaning the interest rate ispositiveandlessthan100percent.Formulatetherelevantequationsforthisinfinitehorizonutilitymaximizationproblem.Assumealsothat0<<1.