Reference no: EM132422511

Problem: Consider the two-period consumption model with utility function: ln(c1)+βln(c2). Individuals have income y1 = 10,y2 = 20, and the discount rate β = 0.5. Individuals can borrow or lend at the interest rate r = 0.05.

Required:

Question 1: Find the optimal consumption in period 1 and period 2.

Question 2: Suppose interest increases to r = 0.06. Without solving the model, explain how consumption in period 1 and 2 will change. Discuss separately the income and substitution effects.

Question 3: Now suppose there is a government that imposes lump-sum taxes T1 in period 1 and provides a lump-sum transfer T2 in period 2. Carefully write down the individual's budget constraint. Explain how this affects individual consumption in period 1 and 2 (you need to consider several different cases).

Question 4: Now suppose individuals cannot borrow (but they can save and still earn the interest rate r). Carefully sketch the individual's budget constraint. Now suppose the government can borrow and lend at the same interest rate. Can you design a tax-transfer scheme, which is budget-balanced, that can improve individual welfare? (Graphical explanation suf?ces).