Economics 320 Fall 1998

Macroeconomic Theory II Marc-André Letendre

Answer all questions. Notice the number of points assigned to each question.

Part 1 - Short Questions

For questions 1 to 5 answer (a), (b), (c) or (d), no justification is necessary.

Consider an overlapping generations model where agents live for two periods only. Let c^h_t(s) denote the consumption of the time s good by member h of generation t. Let N(t) denote the number of people born in period t (generation size) and Y(t) total endowment of the time t good. In part 1, the generation sizes are N(0) = N(1) = ... = 2. Consider a consumption allocation where members of generation 0 have consumption c¹₀(1) = 0.75 and c²₀(1) = 0.75 of the time 1 good; members of generation t, for t ³ 1, consume c¹_t(t) = 1.00 and c²_t(t) = 0.95 of the time t good and consume c¹_t(t+1) = 0.80 and c²_t(t+1) = 0.85 of the time t+1 good.

Question 1 (6 %)

What is the total consumption of the time 1 good by members of generation 0?

answeranswer

answeranswer a

answeranswer b

answeranswer c

answeranswer d

(a)    0.75

(b)    1.50

(c)    1.65

(d)    3.45

Question 2 (6 %)

What is the total consumption of the time 1 good?

(a)    2.85

(b)    3.15

(c)    3.45

(d)    3.60

Question 3 (6 %)

Suppose that Y(1) = Y(2) = ... = y. What is the lowest value of y for which the consumption allocation is feasible?

(a)    1.50

(b)    3.15

(c)    3.45

(d)    3.60

Question 4 (6 %)

Suppose that Y(1) = Y(2) = ... = 4. Is the allocation efficient?

(a)    Yes

(b)    No

Question 5 (6 %)

Member 2 of generation 3 has utility function u²₃ = c²₃(3)×c²₃(4). What is the utility level of member 2 of generation 3?

(a)    0.5625

(b)    0.646

(c)    0.8

(d)    0.8075

Question 6 (10 %)

Explain why, in any given period, there is no trade between young and old people.

Part 2 - Computational Questions

In this part we use a different OLG model with a government to study the effects of a natural disaster on the economy. In period 2, a terrible disaster (e.g. an ice storm, a hurricane) hits the economy forcing the government to engage in massive spending. Member h of generation t has utility function u^h_t = ln(c^h_t(t))+bln(c^h_t(t+1)) with b = 0.7.

Question 7 (10 %)

Maximize the utility of member h of generation t subject to her lifetime budget constraint

Let the generation sizes be N(0) = N(1) = N(2) = ... = 100. Members of generation 0 have endowments

Question 8 (15 %)

In this question, the government imposes taxes in period 2 to balance its budget. Therefore, all young people in period 2 have to pay a tax of 1 unit of the time 2 good. Solve for the competitive equilibrium.

Question 9 (25 %)

In this question, the government borrows to reduce the tax burden in period 2. In period 2, all young people have to pay a tax of 0.6 unit of the time 2 good and the government issues 1-period real bonds to borrow the remaining 40 units of the time 2 good. In period 3, all young people have to pay a tax of 0.6 unit of the time 3 good and the government issues 1-period real bonds to borrow what it needs to satisfy its budget constraint. In period 4, the government taxes all young people equally to totally pay off the bonds issued in period 3.

Let B(t) denote the number of bonds the government issues in period t. Each of these bonds sells at a price p(t). Solve for the competitive equilibrium.

Question 10 (10 %)

As a government advisor, what policy would you recommend to the government?

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