University of Toronto Mississauga
Department of Economics
ECO 325S: Advanced Economic Theory − Macro
Prof. Zhao
Assignment 4
Deadline: 11:59pm, Thursday, April 6, 2023
Note: Please show clear derivations (if applicable) for all questions. Results
without a proper derivation will receive a grade of zero.
Question 1: Social Security in an OLG Model. (40 points) Consider an OLG
economy where Y = Kα(AN)1−α and the growth rate of A and N are zero and n,
respectively. Households’ instantaneous utility function is given by U = ln(C).
Pay-as-you-go social security. Suppose the government taxes the young individuals’
labor income at rate τ and redistribute the benefits to old individuals.
1. (10 points) How, if at all, does this change affect kt+1 as a function of kt? Please
explain.
2. (10 points) How, if at all, does this change affect the balanced-growth-path value of
k? Please explain.
3. (10 points) Suppose that the economy is dynamically inefficient. Prove that the
proposed tax policy is a Pareto improvement.
Fully funded social security. Suppose the government taxes each young person an
amount T and uses the proceeds to purchase capital. Individuals born at t therefore
receive (1 + rt+1)T when they are old.
4. (10 points) How, if at all, does this change affect kt+1 as a function of kt? Please
explain.
Question 2: Taxation in a Ramsey model. (30 points) Consider a Ramsey-Cass-
Koopmans economy that is on its balanced growth path. Suppose that at time 0, the
government announces that at some later time, time t1, investment income will begin to
be taxed at rate τ . Namely, households anticipate the change in the tax regime. The real
interest rate from t = t1 will be r(t) = (1 − τ)f
′(k(t)) . Assume that the government
returns the revenue it collects from this tax through lump-sum transfers.
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1. (10 points) How, if at all, does the tax affect the c˙ = 0 and the k˙ = 0 loci at time
t = 0? What about after time t1? Please explain.
2. (10 points) Draw the phase diagram to show the dynamics of c and k from t = 0
until the economy arrives at the new BGP.
3. (10 points) Does consumption change discontinuously at time t = 0? What about
at t = t1? Please explain.
Question 3: Essay (30 points) Please write a short report on one of the following
pension plans in Canada.
Old age security program and Canada Pension Plan
Requirements:
1. The report should be less than two pages (including reference, excluding graphs).
2. Include in your report a brief introduction of the pension plan.
3. Focus mainly on discussing whether the plan is fully-funded, or pay-as-you-go,
or a hybrid of the two. A discussion about the rationale for the pension design
is desirable.
4. A brief discussion about the implications or challenges of the current demo-
graphic changes (e.g., aging, a change in the population growth due to immi-
gration policies, etc.) on the pension plan.
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