320A Final Exam

QUEEN'S UNIVERSITY

FACULTY OF ARTS AND SCIENCE

DEPARTMENT OF ECONOMICS

ECONOMICS 320A

FINAL EXAMINATION

DECEMBER 11, 1998, 9:00AM

INSTRUCTOR: MARC-ANDRÉ LETENDRE

INSTRUCTIONS:

Follow the instructions provided for each part.

Notice the number of points assigned to each question and budget your time accordingly.

Only calculators are allowed.

Do not hand in the question sheet.

Part I - 21 points

Answer 3 of the 5 questions in part I. Each question is worth 7 points.

Question 1.1

Explain the following statement: Perfect foresight is the limit of rational expectations when the information set (of the agent making the forecast) grows to include all information.

Question 1.2

Explain the difference between a feasible consumption allocation and an efficient consumption allocation.

Question 1.3

Explain why Ricardian equivalence generally fails in OLG models.

Question 1.4

Without reference to any specific model, give a general description of a competitive equilibrium.

Question 1.5

What are the differences between the facts growth theory seeks to explain and the facts real business cycle theory seeks to explain?

Part II - Compulsory Question - 39 points

Answer the following question

Question 2

In this question, we want to identify the effects of a government policy that reduces the work time.

Member h of generation t has the utility function

u^h_t = ln(c^h_t(t))+bln(c^h_t(t+1)) b = 1,

and receives lifetime labor endowment

[D^h_t(t), D^h_t(t+1)] = [2, 2].

The competitive firms are represented by the aggregate production function

Y(t) = K(t)^0.3 (g(t) L(t))^0.7,

where g(t) = (1+g)g(t-1) and g(0) = 1.

The number of (identical) people born in period t is N(t), where N(t) = hN(t-1) and N(0) = 100.

Suppose there is no growth in the economy so that g = 0 and h = 1.

In this economy, member h of generation t has the consumption function

c^h_t(t) =

wage(t) D^h_t(t)

1+b

wage(t+1)D^h_t(t+1)

(1+b) r(t)

Part (a) 3 points

What are the 4 competitive equilibrium conditions for this economy?

Part (b) - Periods 1 to 100 13 points

Calculate the capital stock in the steady-state equilibrium. Also calculate the utility of an agent who lives when the economy has reached its steady state. Suppose the economy has reached its steady state in period 100.

Part (c) - Periods 101 and following 12 points

In period 101, the government introduces a legislation reducing the number of hours people can work. From period 101 on, no one is allowed to supply more that 1 unit of labor when young and 1 unit of labor when young old. Therefore, lifetime labor endowment is now [1,1]. Calculate the capital stock in this new steady-state equilibrium. Also calculate the utility of an agent who lives when the economy has reached its new steady state.

Part (d) 7 points

Suppose that the initial capital stock is K(1) = 1. Use a phase diagram to explain the evolution of the capital stock from period 1 to the new steady state reached in part (c).

Part (e) 4 points

Is the government policy welfare enhancing in the long-run?

Part III - 40 points

Answer 1 of the 2 questions in part III.

Question 3.1

Consider an endowment economy where the generation size is constant: N(t) = 100 "t. Member h of generation t has utility function u^h_t = ln(c^h_t(t))+0.7 ln(c^h_t(t+1)), lifetime endowment [w_t^h(t), w_t^h(t+1)] = [4, 3], and consumption function

c^h_t(t) =

w^h_t(t)-t^h_t(t)

1.7

w^h_t(t+1)-t^h_t(t+1)

1.7 r(t)

In period 1, government consumption is G(1) = 7.851.

Part (a) 14 points

In this part, the government issues 1-period bonds in periods 1 and 2 to finance G(1) and taxes equally the young in period 3 to totally pay off its debt. Solve for the competitive equilibrium interest rates and utility levels in periods 1, 2, and 3.

Part (b) 14 points

In this part, the government issues 10 2-period bonds in period 1 (B₂(1) = 10) and taxes equally the young in period 3 to totally pay off its debt. Solve for the competitive equilibrium interest rates and utility levels in periods 1, 2, and 3.

Part (c) 4 points

If the government cares only about people's utility, what policy should it implement?

Part (d) 8 points

Does Ricardian equivalence hold in this problem?

Question 3.2

Consider a two-country endowment economy. The generation size in the domestic country is constant: N(t) = 100 "t. The generation size in the foreign country is also constant: N^*(t) = 100 "t.

Member h of generation t in the domestic country has utility function u^h_t = ln(c^h_t(t))+0.7 ln(c^h_t(t+1)), lifetime endowment [w_t^h(t), w_t^h(t+1)] = [4, 3], and consumption function

c^h_t(t) =

w^h_t(t)-t^h_t(t)

1.7

w^h_t(t+1)-t^h_t(t+1)

1.7 r(t)

Member h of generation t in the foreign country has utility function u^*h_t = ln(c^*h_t(t))+0.5 ln(c^*h_t(t+1)), lifetime endowment [w_t^*h(t), w_t^*h(t+1)] = [4, 3], and consumption function

c^*h_t(t) =

w^*h_t(t)-t^*h_t(t)

1.5

w^*h_t(t+1)-t^*h_t(t+1)

1.5 r^*(t)

Part (a) 12 points

Solve for the free-trade equilibrium interest rate and explain the pattern of international borrowing and lending among domestic and foreign young people.

Part (b) 14 points

Suppose the foreign government consumes G^*(t) = 10 "t and levies taxes t^*h_t(t) = 0.1 "t on all young people alive in its country. Solve for the free-trade equilibrium interest rate and explain the pattern of international borrowing and lending among domestic and foreign young people.

Part (c) 4 points

Comparing part (a) and part (b), explain the change in savings of member h of generation t in the domestic country.

Part (d) 10 points

Comparing part (a) and part (b), explain the change in savings of member h of generation t in the foreign country.

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