Question

ionSnfar gite te W(c,d)-In c + β Inc, Households have no initial wealth so that: e+s=y a) Derive the lifetime budget constraint and plot it on a diagram. Put con- sumption today on the horizontal axis and consumption in the future on the b) Suppose that the interest rate is initially-5% and goes up to 10%. Income c) How will the change in interest rate affect borrowers consumption? What d) Suppose that β(1 + r) 1. Solve for consu nition in period 1 and 2 at a real e) Solve for savings as a function of r in period 1. What is the derivative of vertical axis. What is the interpretation of the slope? is equal to S10 in each period. Draw the two budget constraints. about savers? Hint: for one of them the effect is ambiguous. interest rate of 10%.

Answer 1

IN YOUR QUESTION HOUSEHOLDS ARE NOT HAVING ANY INITIAL WEALTH So, C+S-Y HERE C= CONSUMPTION OF GOODS BY CONSUMER. S= SAVINGS OF CONSUMER Y= INCOME OF CONSUMER A)LIFE TIME BUDGET CONSTRAINT MEANS CURRENT AND THE FUTURE CONSUMPTION OF A CONSUMERTO BE MADE IN A PERIOD OF HIS LOW AND HIGHER INCOME LEVELS ALONG WITH CREDITS (DEBTS) BROUGHT FROM LENDINGS. DERIVE OF LIFE TIME BUDGET CONSTRAINTS: HERE CURRENT BUDGET CONSTRAINTS C+S=Y. FUTURE BUDGET CONSTRAINTS C Y1+R)S NOW SOLVING FUTURE BUDGET CONSTRAINT WE GET, FOR OBTAINING LIFE TIME BUDGET FIRST WE NEED TO SUBSTITUTE ea1 IN CURRENT BUDGET CONSTRAINTS HERE C+S=Y

C+C'll1+R)=YHYY1 +R WEALTH) (1+R IS ONLY FOR Y') (Y+Y'/1 +R= LIFETIME NOW LIFE TIME BUDGET CONSTRAINT CAN BE WRITTEN AS FOLLOWS:C+C'/(1 +R)=WE (LIFE TIME WEALTH) THAT IMPLIES C'=WE(1 +R) -C(1+R) べつ

B) CURRENT BUDGET CONSTRAINT ISG+s-Y HERE Y = $12. BUT RATE OF INTEREST IS NOT PRESENT ON INITIAL STAGES SO IT CANNOT BE VALUATED FUTURE BUDGET CONSTRAINT IS C-Y+(1+R)S Cz 10 1+10)s C'=10+1 1 S TO KNOW THE FUTURE CONSUMPTION OF CONSUMER WE CAN TAKE S AS INTEGER C) AS INA SOCIETY WE KNOW THAT MONEY IS THE PRIMARY THING AND HERE THE RATE OF INTEREST WOULD SHOW A GREAT AFFECT BECAUSE THE BORROWERS NEED MONEY BUT AS THE INTEREST RATES MAY TEND UPWARDS BUT THE LEVEL OF MONEY CIRCULATION FROM BORROWERS WOULD BE CONSTANT AND ON THE OTHER HAND THE SAVERS WOULD BE MUCH BENEFITED BECAUSE THEY SAVE THERE MONEY IN BANKS AS FIXED DEPOSITS AND EVENLEND DIRECTLY TO BORROWERS AT CHANGED RATE OF INTEREST WOULD INCREASE THERE SAVINGS INCOME

DIHERE β(1+r)=1 PERIOD1): CURRENT.BURGEİ CONSTRAINT C-S+Y C-Y-S 1) PERIOD 2 : FOR BUDGET CONSTRAINT C-Y+1+10)s C-Y+11S 12) SOUVONGM1) AND (2) C Y+115 (MULTIPLY BY 11) C Y+11s 11c =11%.us FINALLY C