g For this question, ignore inflation. Suppose Jenny earns $60,000 per year working as a tax analyst. After ten years, she quits her job and pursues a PhD in Art History. For the 5 years she is in school, she gets a teaching stipend of $12,000 per year. For the next 35 years, she is an art director and earns $95,000. If she expects to live for 20 years in retirement. If Jenny doesn’t earn any interest on her savings and wants to perfectly smooth consumption across her life, how much will she consume every year? What might prevent her from perfectly smoothing consumption?

If Jenny doesn’t earn any interest on her savings and wants to perfectly smooth consumption across her life, how much will she consume every year?

Jenny's total income during her life = income as tax analyst ($60,000 x 10) + income as PhD student ($12,000 x 5) + income as Art Director (35 x $95,000) = $3,985,000

she generated income during 50 years and expects to live 20 more, so in order to perfectly smooth consumption across her life, she must divide her total life income by 70 years = $3,985,000 / 70 years = $56,928.57 per year

What might prevent her from perfectly smoothing consumption?

First of all, besides inflation, you also earn interest on your savings. That is why 401k and other retirement accounts work so well (the magic of compound interest). Even if inflation and interests didn't exist, you cannot know exactly what you are going to earn in the future and for how many years. In this case, she earned $60,000 for 10 years, but then earned only $12,000 during 5 years. If she really wanted to smooth her consumption, she would have needed to get a loan because her savings during the first 10 years wouldn't be enough.

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30