l. [60 marks in total] A general finding in macroeconomics is that households tend to smooth out their consumption over time. In other words, they prefer to have a stable consumption over years than very high consumption in some years and very low consumption in other years. Saving and borrowing are important ways to achieve this goal. In this question, we explore the effect of saving on consumption smoothing through a simple model. Bob currently has a job and earns $100K (after tax) per year. In this question, we consider his saving problem. For simplicity, we assume that there is no ination. Bob maximizes the expectation of the following utility index. 1 u(c1) + @1462), where C1 is his consumption in the current yeargg is his consumption in the next year, anddc) = C- \\/ Bob may deposit part of his current year income at a nominal interest of 3%. If he depositsl his income in the next year will be $100 + 1,03le if he keeps his job and $033K if he loses his job. For simplicity, we only consider five options: saving nothing, saving $10K, saving $20K, saving $30K, and saving $40K. For simplicity, we assume that Bob does not save the next year. Therefore, if he savesE this year,61 - (1005)K