Exercise on consumption with different generations An economy is composed of identical individuals. Each individual lives for 2 periods (you may imagine them as adulthood and old age]. individuals may work during the rst period of their life for a proportion L of the day, for an income equal to ME. In the second period they retire and consume their remaining lifetime savings. Their lifetime utility is given by U = log(t'1) + logfz) -l- log(1 L) where CE is consumption in period t and L is the fraction of time the individual spends working in period 1. i) If the rate of interest on savings is R. write down the individual's budget constraints for both periods, and then combine them in a lifetime (intertemporal) budget constraint. ii] Solve for optimal consumption each period and the optimal work effort. Comment on what you nd. iii) The government introduces a fixed pension paid to individuals in the second period of their lives. funded by a 'lurnp sum' tax paid by those who work.2 Re-write the intertemporal budget constraint. What will be the impact of the pension on consumption and labour supply decisions of the young? What about the old when the pension is introduced? Give intuition for your answers. iv] The pension is now funded by an income tax, Le. a tax equal to twL where t is the tax rate. Will the behaviour of the young change in the case where R = D? Interpret this result