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15 changes: 7 additions & 8 deletions rst_files/opt_tax_recur.rst
Original file line number Diff line number Diff line change
Expand Up @@ -194,26 +194,25 @@ from the allocation

The primal approach uses four steps:

1. Obtain first-order conditions of the household's problem and solve them for :math:`\{q^0_t(s^t), \tau_t(s^t)\}_{t=0}^\infty` as functions of
1. Obtain first-order conditions of the household's problem and solve them for :math:`\{q^0_t(s^t), \tau_t(s^t)\}_{t=0}^\infty` as functions of
the allocation :math:`\{c_t(s^t), n_t(s^t)\}_{t=0}^\infty`

2. Substitute these expressions for taxes and prices in terms of the allocation
2. Substitute these expressions for taxes and prices in terms of the allocation
into the household's present-value budget constraint

* This intertemporal constraint involves only the allocation and is regarded
as an *implementability constraint*
* This intertemporal constraint involves only the allocation and is regarded
as an *implementability constraint*

3. Find the allocation that maximizes the utility of the representative household
3. Find the allocation that maximizes the utility of the representative household
:eq:`TS_prefr_opt_tax` subject to the feasibility constraints :eq:`feas1_opt_tax`
and :eq:`TSs_techr_opt_tax` and the implementability condition derived in step 2

* This optimal allocation is called the **Ramsey allocation**
* This optimal allocation is called the **Ramsey allocation**

4. Use the Ramsey allocation together with the formulas from step 1 to find
4. Use the Ramsey allocation together with the formulas from step 1 to find
taxes and prices



The Implementability Constraint
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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