2. (12 points) Savers and Borrowers All households in country Nocapital have the same life-time utility given below x/cT + awe2. 60% of households have $45,000 in the rst period and $0 the second period (Type A). 40% of households have $0 in the rst period and $50,000 the second period (Type B). (a) (4 points) Given real interest rate 'r, derive type A household's saving function. (b) (4 points) Derive type B household's saving function. (0) (4 points) As alluded earlier, there is no other demand for funds besides borrow- ing among households themselves. The net saving from all household should be zero at the equilibrium. What is the equilibrium real interest rate