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Economia V; Instructor: Marco Del Negro
Problem set 5
1) Assume logarithmic utility:
,
Cobb-Douglas production function (
),
complete depreciation (), and an available amount of resources Y1 inherited from the previous period (as
in class):
1a) write the problem of the consumer (objective function and constraints)
in the decentralized economy.
1b) write the problem of the firm (objective function and constraints)
in the decentralized economy.
1c) solve for the equilibrium in the decentralized economy, and show
that it is the same as the social planner equilibrium found in class.
1d) explain briefly why the two equilibria are the same.
1f) find the equilibrium real interest rate.
2) Using the same identical framework (logarithmic utility, Cobb-Douglas
production function, ,
and an available amount of resources Y1
inherited from the previous period) introduce a government which borrows
in period 1 in order to finance an amount G1 of public spending, and taxes
(T2) in period 2 only (no public spending in the second period).
2a) write the problem of the consumer (objective function and constraints)
in the decentralized economy.
2b) write the problem of the firm in the decentralized
economy.
2c) write the budget constraints of the government in period 1 and 2.
2d) solve for the equilibrium in the decentralized economy, and show
that it is the same as the social planner equilibrium found in class.
2e) show that if the government decides to tax only in the first period
(T1=G1) the equilibrium is the same.
2f) discuss briefly whether Ricardian Equivalence holds or not in this
model, and why.
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Marco Del Negro
2000-02-09