Consider a two period economy in which the government collects taxes from the representative consumer. The lifetime utility function of the representative consumer is u(c_1, c₂) = ln c₁ + ln c₂;

who has a real LTBC of:

c₁ + c₂ /1 + r = (y₁ - t₁) + (y₂ - t₂)/ 1 + r ,

where Beta = 1/1.10, y₁ = 20 and y₂ = 25. The government's real budget constraints are:

g₁ + b₁ = (1 + r)b₀ + t_1,

g₂ + b₂ = (1 + r)b₁ + t_2,

Suppose that b₀ = b₂ = 0 and r = .10.

(a) Find the lifetime budget constraint of the government.

(b) Find the theoretical solutions for the optimal choice of c₁^* and c₂^* .

(c) Assume that government purchases are g₁ = 10 and g₂ = 10. In the first period government taxes t₁ = 8. What are taxes in period two and government asset purchases in period one for period two, b₁?

(d) Suppose that the government wants to cut taxes in the first period to t₁ = 7 but wants to keep spending in both periods the same. Show what happens to second period taxes and government asset purchases in period one for period two, b1?

(e) Does Ricardian equivalence hold in the above example? Prove your assertions with the information above.

(f) When would Ricardian equivalence not likely hold?