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Question 2: Consider a two-period consumption-savings model, augmented with a government sector. Each consumer has preferences described by the utility function:
u(c1, c2)= lnc1 + lnc2
where c1 is consumption in period one, and c2 is consumption in period two.
Suppose that both households and the government start with zero initial assets (i.e., a =0 and b =0), and that the real interest rate is always 10 percent. Assume that government purchases in the first period are one (g1 = 9) and in the second period are 1 (g2 = 11). Finally, the real incomes of the consumer in the two periods are y1 = 20 and y2 =33.
1. In the first period, the government levies lump-sum taxes of 6 (t1 = 6). What are lump-sum taxes in period two (t2), given the above information? Compute the consumption and national savings in period one.
2. Consider in the first period the tax is reduced from 6 to 5 unit, with government purchases left unchanged. Will the consumption, national saving, and current account in period one change? Does this result satisfy the Ricardian equivalence or not?
3. Suppose that in period 1 the government increases spending from 9 to 10 units of goods. What is the effect of this policy change on the optimal consumption, fiscal balance, national saving, and current account in period 1?
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