Skip to content

Fix SymPy overflow error in solow lecture #27

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
mmcky merged 1 commit into from
Jan 15, 2026
Merged

Fix SymPy overflow error in solow lecture #27

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
13 changes: 9 additions & 4 deletions lectures/solow.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -510,21 +510,26 @@ plt.show()
One can also try to solve this mathematically by differentiating $c^*(s)$ and solve for $\frac{d}{ds}c^*(s)=0$ using [sympy](https://www.sympy.org/en/index.html).

```{code-cell} ipython3
from sympy import solve, Symbol
from sympy import solve, Symbol, Rational
```

```{code-cell} ipython3
# Use Rational for exact symbolic computation to avoid overflow
A_sym = Rational(2)
alpha_sym = Rational(3, 10)
delta_sym = Rational(1, 2)

s_symbol = Symbol('s', real=True)
k = ((s_symbol * A) / delta)**(1/(1 - alpha))
c = (1 - s_symbol) * A * k ** alpha
k = ((s_symbol * A_sym) / delta_sym)**(1/(1 - alpha_sym))
c = (1 - s_symbol) * A_sym * k ** alpha_sym
```

Let's differentiate $c$ and solve using [sympy.solve](https://docs.sympy.org/latest/modules/solvers/solvers.html#sympy.solvers.solvers.solve)

```{code-cell} ipython3
# Solve using sympy
s_star = solve(c.diff())[0]
print(f"s_star = {s_star}")
print(f"s_star = {float(s_star)}")
```

Incidentally, the rate of savings which maximizes steady state level of per capita consumption is called the [Golden Rule savings rate](https://en.wikipedia.org/wiki/Golden_Rule_savings_rate).
Expand Down
Loading