ECON6002 Tutorial 3 (OLG Models)
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ECON6002
Tutorial 3 (OLG Models)
1. Consider a Diamond OLG economy where g is zero, A(0) = 1, 1/(1 + ρ) = β, population growth is n > 0, production is Cobb-Douglas, δ = 0, and utility is logarithmic.
(a) Pay-as-you-go social security: Suppose the government taxes each individual an
amount T and uses the proceeds to pay benefits to old individuals such that each old person receives (1 + n)T. Assume that tax is small enough that Cl,t s Wt - T.
i. Write the Lagrangian for the households consumption/saving problem.
ii. Solve the household maximization problem and deriver the law of motion for kt+l .
iii. How does this policy affect the balance growth path value k, the capital stock per worker? (Hint: there is no closed form solution for the k* . You don’t need to solve for it to answer the question.)
iv. If the balance growth path is dynamically inefficient, how does a marginal increase in the tax rate affect current and future welfare? Explain.
(b) Fully funded social security: Suppose the government taxes each your individual
an amount T and use the proceeds to purchase capital. Individuals born at t therefore receive (1 + rt+l)T when they are old.
i. Write the Lagrangian for the households consumption/saving problem.
ii. Solve the household maximization problem and deriver the law of motion for kt+l .
iii. How does this policy affect the balance growth path value k, the capital stock per worker?
2022-11-09