3. Consider a consumer who lives for two periods and has a utility function, = 01. The consumer works only in the first period and is retired in the second period. The income of $100 in the first period will be either spent on consumption or saved for the second period. When the interest rate is 10%, answer the following questions.

1) Find the optimal present consumption (0 ), future consumption (1 ), and saving ( ).

2) When the government levies a tax on interest income by 20%, find the optimal present consumption (0 ), future consumption (1 ), and saving ( ). Is the substitution effect greater than the income effect?