Assume that consumers are free to decide how many hours to work. Consumers have the following utility: U = U(c1, l1, c2, l2) where c1, c2, l1, and l2 are consumption and leisure in the first and second period respectively. Consumers earn a wage w1, profits 1 and pay lump sum taxes T1 in the first period and w2, 2 and T2 respectively in the second period. They have a total h hours at their disposal for work and, and can buy or sell any amount of bonds at the same interest rate r.

(i) Derive the optimality conditions for consumption c1, c2 and leisure l2, l2. Explain the intuition behind these conditions.

(ii) Due to a financial crisis that created a lot of uncertainty, bonds have a risk premium x. How does this affect the borrowing and lending interest rate? Show in a graph how does this affect labor supply. Explain the intuition.