Economia V; Instructor: Marco Del Negro

Problem set 5

1) Assume logarithmic utility: $max_{\{C1,C2\}} ln(C1) +\beta ln(C2)$, Cobb-Douglas production function ( $Y=AK2^{\alpha}N^{1-\alpha}$), complete depreciation ($\delta =1$), 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, $\delta =1$, 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.