The graph above illustrates the Solow growth model for the given production function, investment rates, and depreciation. Key features:

1. Production Function (Blue Curve): This represents $y = k^{1/2}$, showing how output per worker increases with capital per worker.
2. Investment Curves (Green and Orange):
   • The green dashed line represents investment when $\gamma = 0.20$, relevant when $y < 10$.
   • The orange dashed line represents investment when $\gamma = 0.40$, applicable when $y > 10$.
3. Depreciation Line (Red): This is the linear function $\delta k$, showing the constant depreciation rate of 2%.

The two steady states are marked:

• First steady state at $k = 100$, where output per worker $y = 10$, and investment with $\gamma = 0.20$ intersects depreciation. This point is unstable.
• Second steady state at $k = 400$, where output per worker $y = 20$, and investment with $\gamma = 0.40$ intersects depreciation. This point is stable.

Summary of Behavior:

• Below $k = 100$, capital accumulates, pushing the economy toward the unstable steady state.
• Between $k = 100$ and $k = 400$, capital accumulates due to the higher investment rate, moving the economy to the stable steady state.
• Above $k = 400$, capital depreciates, bringing the economy back to the stable point.

Would you like any further details or explanations?

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5 Related Questions:

1. How does a change in the depreciation rate affect the steady states?
2. What happens if the investment rate does not increase after $y = 10$?
3. How would population growth impact the steady-state values?
4. Can we derive a long-term growth rate in this model?
5. What happens to output when technological progress is added?

Tip: In the Solow model, a higher investment rate leads to a higher steady-state capital level, but diminishing returns to capital still hold.