[inventory_dynamics] Update code to JAX and latest style guide

[kp992]

This PR:

• Removes numba and numpy support.
• Updates all the code to use JAX.
• fixes minor typos and title errors.

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-623--sunny-cactus-210e3e.netlify.app (2b7c4fe)

📚 Changed Lecture Pages: inventory_dynamics

[Copilot]

Pull Request Overview

This PR updates the inventory dynamics lecture to use JAX instead of numba and numpy, modernizing the codebase and improving performance. The changes align with the latest style guide and fix minor formatting issues.

Key changes:

• Replaces numba-based Firm class with JAX-based functions using NamedTuple
• Converts simulation functions to use JAX's functional programming paradigm with jax.lax.scan and jax.vmap
• Updates all numpy operations to JAX numpy equivalents

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-623--sunny-cactus-210e3e.netlify.app (54d1cac)

📚 Changed Lecture Pages: inventory_dynamics

[HumphreyYang]

Many thanks @kp992! These are really nice! Just two very minor observations.

I think we should remove the grid in the figures to maintain consistency in the style:

for ax in axes:
    ax.grid(alpha=0.4)

[HumphreyYang]

I think it might look better if we add some spaces in between:

Suggested change

	# Generate independent random keys for each firm
	firm_keys = random.split(key, (num_firms, sim_length))
	# Run simulation for all firms
	restock_indicators = vectorized_simulate(firm_keys)
	# Compute frequency (fraction of firms that restocked > 1 times)
	frequency = jnp.mean(restock_indicators)
	return frequency
	# Generate independent random keys for each firm
	firm_keys = random.split(key, (num_firms, sim_length))
	# Run simulation for all firms
	restock_indicators = vectorized_simulate(firm_keys)
	# Compute frequency (fraction of firms that restocked > 1 times)
	frequency = jnp.mean(restock_indicators)
	return frequency