Hi, please list out the formulas where necessary , graphs where necessary , if the question doesnt require it, its fine not have it but please do put it down if it helps you to explain . If the answer is provided, its because I struggled to understand the answer, please dont just reproduce it, but rather explain it and list out the formulas used with explanations OF FORMULAS USED IN THE QUESTION , the procedure etc.Thank you!

Q10. Assume that the real interest rate and the subjective rate of discount are both zero. A person is 20 years old and expects to live to 00 - working for an after-tax salary of 50,000 per year until the age of 60, then retired with a state pension of 5,000 per year from age 60 until death [and no pension from work - only whatever savings they have]. To simplify. we assume that the person acts as if future incomes and the length of life were known with certainty. What is his optimal level of consumption and how much do they save? Li! C ] 1+r . . i ' = we see that if r = ,9, real consumption must be \"'{Ch 1] \"1'I 50kx4o+5kx20 2100k constant over time, so we have C = T = T = 35k (note: if there is ination, it may be that nominal consumption is rising, but we are concerned with real values]. Optimal consumption is thus 35,000 per year in all years the person will save 15,000 per year while they work, and dissave 30,000 per year while retired. From the rst order condition