I got a practice question going through the 2-period model, trying to check if my theory is correct, so if you could go through it so I can check my answer that would be great.

3. (35 points) Consider the two-period model. The consumer's preferences over current and future consumption (c and c) is given by U(c) + BU(c) where U(c) = In(c). Households receive income only in the first period equal to y. Households can save s for the second period and receive interest rate r. (a) Set up the households optimization decision. What is the tangency condition? (b) Solve for the optimal levels of current consumption, future consump- tion, and saving. (c) The government decides people aren't saving as much as they should. A mandatory savings regime is implemented where the government takes T from households in the first period and gives back (1 +r)7 in the second period. Set up the households new optimization decision. What is the tangency condition? (d) Solve for the new optimal levels of current consumption, future con- sumption, and saving. (e) How have the optimal levels of current consumption, future consump- tion, and saving changed