QUESTION 2: TIME DISCOUNTING

Viggo is thinking about retirement. He knows that he will live for only two more periods beyond today, or period 1. He will have only an income in period 1 of $10000 and needs to decide about retirement in period 2 and 3.

He has a discount rate of 5% and a utility function () = .. He is an expected utility maximizer and uses exponential discounting to discount consumption over time. Therefore, he makes intertemporal choices according to the following valuation function

= () + () + (), where = ( 1 / 1+ discount rate )

QUESTION - Viggo is considering buying an annuity pension product in period 1 that pays 3,000 DKK in each of the three periods. The interest rate is so low that it is basically equal to zero so the value of the annuity is equal to the sum of all annuity payouts (9,000 DKK) and an administrative cost of 1,000 DKK to be paid upfront in period 1. Is the annuity better or worse than consuming all his income in period 1?