1. Apply the discounted utility model and the hyperbolic discounting model to calculate the following example of a decision to save to retirement. (Note, for the exam, I would expect that you can explain the steps and write down what needs to be calculated but you do not need to solve such a problem, I use a software for that exercise as well (still its a good exercise to give it a try!). We assume that our agents live for three periods (think of early working life, late working life and retirement). Their income in period one is y1=500 is period 2 is y2=1000 and it is zero in period three. Whatever they save, the do earn 50% interest per period. Their per period utility function is given as u(x)=x0.5 and their discount rate is =0.8. a) If the agent applied the discounted utility model, how much will he save for retirement in period 1,2 respectively? b) Now assume that the agent is driven by hyperbolic discounting (=0.8) and has to decide in each period how much he wants to save for retirement. c) Closest to the save more tomorrow idea is that the agent decides in period one for both periods (one and two) how much to save for retirement (save more tomorrow allows an individual to commit about retirement savings at an early moment in time). What would be the outcome?