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update captions for graphs in lectures
  • Loading branch information
HumphreyYang committed Mar 21, 2024
commit c2a58e14b2d2b93e29651fae7e4a036f1272b7e2
9 changes: 9 additions & 0 deletions lectures/laffer_adaptive.md
Original file line number Diff line number Diff line change
Expand Up @@ -445,6 +445,15 @@ def draw_iterations(π0s, model, line_params, π_bars, num_steps):
Let's simulate the result generated by varying the initial $\pi_{-1}$ and corresponding $p_{-1}$

```{code-cell} ipython3
---
mystnb:
figure:
caption: Starting from different initial values of $\pi_0$, paths of $m_t$ (top
panel, log scale for $m$), $p_t$ (second panel, log scale for $p$), $\pi_t$ (third panel), and $\mu_t$ (bottom
panel)
name: pi0_path
width: 500px
---
πs = np.linspace(π_l, π_u, 10)

line_params = {'lw': 1.5,
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12 changes: 11 additions & 1 deletion lectures/money_inflation_nonlinear.md
Original file line number Diff line number Diff line change
Expand Up @@ -402,6 +402,16 @@ def draw_iterations(p0s, model, line_params, p0_bars, num_steps):
```

```{code-cell} ipython3
---
mystnb:
figure:
caption: Starting from different initial values of $p_0$, paths of $m_t$ (top
panel, log scale for $m$), $p_t$ (second panel, log scale for $p$), $\pi_t$ (third panel), and $\mu_t$ (bottom
panel)
name: p0_path_nonlin
width: 500px
---

# Generate a sequence from p0_l to p0_u
p0s = np.arange(p0_l, p0_u, 0.1)

Expand All @@ -419,7 +429,7 @@ THE LECTURE MONEY_INFLATION.MD

IF WE ZOOM, I CAN EXPLAIN QUICKLY.

Staring at the paths of price levels in {numref}`p0_pathnonlin` show indicate that almost all paths converge to the **higher** inflation tax rate displayed in the stationary state Laffer curve. %displayed in figure {numref}`infl_tax`.
Staring at the paths of price levels in {numref}`p0_path_nonlin` show indicate that almost all paths converge to the **higher** inflation tax rate displayed in the stationary state Laffer curve. %displayed in figure {numref}`infl_tax`.

Thus, we have indeed discovered what we earlier called "perverse" dynamics under rational expectations in which the system converges to the higher of two possible stationary inflation tax rates.

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