Business Cycle Dynamics of a New Keynesian Overlapping Generations Model with Progressive Income Taxation

The ne[2(T + TR] + T] + 7 equations (27) through (34) define U_t for given x_t and λ_t.
The dynamics of the system is then determined from the ne[3(T+T^R- 1)] +2 equations
(35) through (41).

The log-linear system (26) is determined if ne[2(T + T^R - 1)] of its Eigenvalues are
within the unit circle and if ne(T + T^R - 1) + 2 Eigenvalues are outside the unit circle.
This condition holds in our calibration.

6.3 Non-stochastic steady state of the Ramsey model

The stationary solution of the representative agent model is characterized by the fol-
lowing set of equations. Since real money balances are constant, the inflation factor π
equals the money growth factor θ:

π = θ.

(42a)

Calvo price staggering implies

(42b)

The stationary version of the Euler equation for capital,

¹—^β(1—^δ) = n^{1 -α} k^α-1 τ 0 [ gn^{1 -α}k^α ]
αβg

can be solved for k given our predetermined value of n = 0.33. Given the solution for
k we can determine y. The stationary version of the economy’s resource constraint,

y = c + δk

(42c)

allows us, then, to compute c. Finally, the Euler equation (25c) implies the stationary
solution for the ratio between consumption and real money balances:

C = γ μ^

M/P 1 — γ[β

(42d)

We use this equation and (42c) to determine the value of γ. This is all we need to
compute the policy function of the log-linearized model.

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