Question

Consider the life-cycle model. The agent has income w only in the first period. The interest rate is r>0 and the utility function of the individual is quasi-linear U(C1,C2)=f(C1)+C2 where f is a function with f'>0 and f''<0. If we establish a tax on capital income, what is it going to happen with savings? Explain your answer

Answer 1

Life cycle model or life cycle hypothesis tells how the individual plan there consumption and saving in their life cycle which could be measured by number of period consumption.During the period when people earn they consume and save for the period when they won't be working or there will no earning.In this model there is an assumption that people tend consume equally in all the periods.Now, futher we will look at the images uploaded.

Hence as the taxes are imposed on capital income savings will reduce more than the amount of taxes considering the quasi linear utility function.Now assuming that interest rate remain same (as the mrs deepend on the interes shown on page 2) the consumer is willing to give up consumption from period 2(=to savings)in order to get more consumption in period.However if considering any linear function associted with this question the level of saving will reduce in manner that person consumption in both the periods reduces by equal amount.

Therefore saving will reduce as capital income tax is imposed.