Econ Homework

Econ303 Homework 9B 1

Zoe lives for two periods and has life-time utility √ c1 + 0.8

√ c2. Zoe’s income are as follows:

y1 = 60, 000 and y2 = 25, 000. The real interest rate r = 7%.

1. (3 points) How much will Zoe consume in each period? How much does she save?

2. (3 points) Now suppose that Zoe cares about her future more; the subjective discount factor increases to 0.9. The increase of the subjective discount factor could due to technology advances in medicine; Zoe could stay healthy and live longer. How much will Zoe consume in each period? How much does she save? Compared with part (1), what do you find?

3. (4 points) Now suppose that the subjective discount factor has’t changed. Suppose that government levies flat rate tax on capital income, with tax rate τk = 40%. Zoe’s budget constraint becomes

c1 + c2

1 + (1 − τk)r = y1 +

y2 1 + (1 − τk)r

How much will Zoe consume in each period? How much does she save? Compared with part (1), what do you find? How much revenue can government collect?

4. (4 points) Now suppose that government levies flat rate consumption tax instead of capital income tax. The tax rate on consumption is τc = 2%. Zoe’s budget constraint becomes

(1 + τc) · c1 + (1 + τc) · c2

1 + r = y1 +

y2 1 + r

How much will Zoe consume in each period? How much does she save? Compared with part (1), what do you find? How much revenue can government collect in this case? Compare the result in part (4) with the result in part (3), what do you find?

5. (3 points) Now suppose that government does not collect consumption tax and capital income tax, but decides to implement social security. Zoe’s income when young(first period) is subject to 15% social security tax. The benefits when old (second period) is Zoe’s contribution when young plus interest. (Fully funded social security system). Zoe’s budget constraint becomes

c1 + c2

1 + r = (1 − 0.15) ·y1 +

y2 + (1 + r) · 0.15 ·y1 1 + r

How much will Zoe consume in each period? How much does she save? (s = (1 − 15%)y1 − c1) Compared with part (1), what do you find?

6. (3 points) Suppose that the return on social security contribution differs from interest rate. The benefits of the old is determined by the amount contributed by current

Econ303 Homework 9B 2

working population. (Pay-as-you-go social security system) Suppose that the return is 4% currently. Zoe’s budget constraint becomes

c1 + c2

1 + r = (1 − 0.15) ·y1 +

y2 + (1 + 0.04) · 0.15 ·y1 1 + r

How much will Zoe consume in each period? How much does she save? Compared with part (1) and (5), what do you find?