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

2.5 Equilibrium conditions

1. Aggregate and individual behavior are consistent, i.e. the sum of the individual
consumption, effective labor supply, wealth, and money is equal to the aggregate
level of consumption, effective labor supply, wealth, and money, respectively:

ne T+T^R=^XX

j=1 s=1

s,j ^μ (^j )

с ^,∙^j -----------------

^t T + T^R

ne T

Nt = XX n e ( s^,j ) ::■
j=1 s=1

ne T+T^R

Kt = XX ks^j TTR
j=1 s=1

ne T+T^R

Σ∖ ʌ s,j ^μ (^j )

m ^m^mt τ+TR

j=1 s=1

(23a)

(23b)

(23c)

(23d)

2. Households maximize life-time utility (1).

3. Firms maximize profits.

4. The goods market clears:

ztKt^αNt¹^-^α =Ct+Kt+1+(1-δ)Kt.

5. The government budget (21) balances.

6. Monetary growth (18) is stochastic and seignorage is transferred to the govern-

ment.

7. Technology is subject to a shock (14).

The non-stochastic steady state and the log-linearization of the model at the non-
stochastic steady state are described in more detail in the appendix. In addition, we
will compare our OLG model with the corresponding representative-agent model which
we briefly describe in the following.

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