Suppose the both Arthur and his son Adam have preferences over consumption today (c) and consumption tomorrow (c') given by w: + 0.95%?r so that their marginal rate of substitution is Arthur's income today (3;) and tomorrow (y') are y : 500,y' : 210. Adam's income today and tomorrow are 3; = 200 and y' = 525. Suppose there are no lump-sum taxes. A) Suppose that the interest rate is 5% (r = 0.05). What are the present values of Arthur and Adam's income? B) How much would each of them optimally consume in each period? C) How much would each of them optimally save or borrow in the rst period? D) Suppose now that the interest rate 8%. What are the present values of their income? E) How much would each of them consume in each period in this case? How much do they save or borrow in the rst period now? Do they consume more or less in the rst period versus when the interest rate was 5%? How is their savings or borrowings affected? F) Who is better off after the interest rate increase? Explain why a change of interest rate affects Arthur and Adam differently using graphs which illustrate the income and substitution effects for both Arthur and Adam. For each result, do NOT simply provide an answer be sure to show your work