Fisher and OLG Models

Solve it Step by Step Please

6. Consider the problem of optimal consumption in the presence of sales taxes. There are two periods. There is a representative household with CRRA utility with a coefficient of relative risk aversion >0. Denote household expenditure on consumption in period t by et. Denote the sales tax in each period t by t. Assume that collected tax is completely wasted. Household starts and ends life with zero assets. It earns w in the first period and then in subsequent periods wage grows at rate gw. Discount rate are given by r and which are constant all throughout, and r=>0. a) First suppose that 1=2=. Compute the level of optimal consumption and expenditure in each period. 2 b) Again suppose that 1=2=, but then consider a small decrease in 1. For what values of will e1 increase in response to this tax decline? c) Suppose that 1=2=, and then consider a small decrease in 1. For what values of will tax revenue in period 1 increase in response to this tax decline? 6. Consider the problem of optimal consumption in the presence of sales taxes. There are two periods. There is a representative household with CRRA utility with a coefficient of relative risk aversion >0. Denote household expenditure on consumption in period t by et. Denote the sales tax in each period t by t. Assume that collected tax is completely wasted. Household starts and ends life with zero assets. It earns w in the first period and then in subsequent periods wage grows at rate gw. Discount rate are given by r and which are constant all throughout, and r=>0. a) First suppose that 1=2=. Compute the level of optimal consumption and expenditure in each period. 2 b) Again suppose that 1=2=, but then consider a small decrease in 1. For what values of will e1 increase in response to this tax decline? c) Suppose that 1=2=, and then consider a small decrease in 1. For what values of will tax revenue in period 1 increase in response to this tax decline