Queen's University Economics Department
Economics 320A - Macroeconomic Theory II
Fall 1998
Assignment 2

Instructor: Marc-André Letendre

Deadline: October 15, 1998 (in class)

Question 1

Consider an economy with population growth. In each period t, a generation of N(t) young people is born. The generation sizes are: N(0) = 100, N(1) = 110, N(2) = 121 and N(3) = N(4) = ... = 133. Government consumption is G(1) = 10, G(2) = 5 and G(3) = G(4) = ... = 0. Endowments are: w^h₀(1) = 1 and [w^h_t(t), w^h_t(t+1)] = [2,1] for t ³ 1. The government taxes the young of each generation to finance: (1) its consumption, (2) a transfer of 0.2 units to each old person.

(a) How many young people and how many old people are there in periods 1, 2, 3 , 4 and 5?

(b) What are the total transfer payments the government makes in periods 1, 2, 3, 4 and 5?

Consider the following tax/transfer scheme:

In this economy, all people are identical within a generation (no trade) and the government balances its budget. We will see how to easily solve for a competitive equilibrium in such a case.

(c) Given there is no trade in this economy, what is the consumption of members of generations 0, 1, 2, 3, 4 and 5?

(d) We can easily find the equilibrium interest rate in each period using the condition r(t) = MRS(t). In this exercise, we have

(e) Give a complete description of the competitive equilibrium. Note that periods t ³ 4 are all identical.

Question 2

Consider an economy where the government imposes taxes and issues one-period real bonds. Only the young agents can purchase the government bonds.

(a) Write down the budget constraint member h of generation t faces when young, the budget constraint he faces when old and derive his lifetime budget constraint. Clearly explain each step in your derivation.

(b) Derive the competitive equilibrium condition S_t(r(t)) = p(t) B(t) by explicitly imposing the following conditions: market clearing on the goods market, market clearing on the private borrowing/lending market, market clearing on the government bonds market, utility maximization and the government budget constraint.

In this economy, generation sizes are N(t) = 100 for all t ³ 0. Endowments are: w^h₀(1) = 1 and [w_t^h(t), w_t^h(t+1)] = [2,1] for t ³ 1. Member h of generation t has the utility function u_t^h = ln(c_t^h(t))+bln(c_t^h(t+1)) where b = 0.95. The government consumes G(1) = 5, G(2) = 5 and G(3) = ... = 0. The savings function and the consumption function of member h of generation t are

(c) In order to balance its budget, the government imposes the following taxes: t^h₀(1) = 0, [t^h₁(1), t^h₁(2)] = [0.05, 0], [t^h₂(2), t^h₂(3)] = [0.05, 0] and [t^h_t(t), t^h_t(t+1)] = [0,0] for t ³ 3. Solve for the competitive equilibrium.

(d) In this part the government runs a deficit in periods 1 and 2. It issues bonds and does not levy any taxes in periods 1 and 2. It then levies taxes on period 3 young to pay off the bonds. Therefore, the government issues bonds to collect G(1) units in period 1 and issues bonds to collect G(2)+B(1) units in period 2. Solve for the competitive equilibrium and explain the movements in the interest rate.

(e) Explain why the Ricardian equivalence of debt and taxes do not hold in this case.

Back to main page