Question 4: Life-cycle model A household will live for 80 years (T = 80), work for 60 years and then retire (R = 60). It earns $100 per year while working (Y = 100), and earns nothing once retired. It currently has $400 of wealth (W = 400). It wants to perfectly smooth its consumption over life time. The interest rate is 0 (r = 0).

1. Solve for the optimal value of consumption per year.