At the beginning of year 1, Julie Ripe has D dollars (this includes year 1 income). During each year, Julie earns i dollars and must determine how much money she should consume and how much she should...

At the beginning of year 1, Julie Ripe has D dollars (this includes year 1 income). During each year, Julie earns i dollars and must determine how much money she should consume and how much she should invest in Treasury bills. During a year in which Julie consumes d dollars, she earns a utility of ln d. Each dollar invested in Treasury bills yields $1.10 in cash at the beginning of the next year. Julie’s goal is to maximize the total utility she earns during the next 10 years.

a Why might ln d be a better indicator of Julie’s utility than a function such as d²?

b Formulate a dynamic programming recursion that will enable Julie to maximize the total utility she receives during the next 10 years. Assume that year t revenue is received at the beginning of year t.