6. Country X and Country Y have the same level of output per worker. They also have the same values for the rate of depreciation, 3, and the measure of productivity, A. In Country X output per worker is growing, whereas in Country Y, it is falling. What can you say about the two countries rates of investment?

Given that both Country X and Country Y have the same level of output per worker, the same depreciation rate, and the same measure of productivity, \( A \), the difference in the growth of output per worker between the two countries must stem from differences in their rates of investment.

To explain why, we can refer to the Solow-Swan model of economic growth. In this model, the key factors influencing the growth of output per worker are:

- **Investment rate (s)**: The portion of output that is invested in capital.
- **Depreciation rate (δ)**: The rate at which capital depreciates over time.
- **Productivity (A)**: A measure of technological progress or efficiency.
  
### Key Concept:
In the Solow model, growth in output per worker occurs when the economy is accumulating capital at a rate faster than it is losing capital due to depreciation. In this context:

- **Country X**: Since output per worker is growing, the investment rate in Country X must be high enough to more than compensate for the depreciation of capital.
- **Country Y**: Since output per worker is falling, the investment rate in Country Y must be insufficient to cover the depreciation of capital, meaning that capital per worker is declining over time.

### Conclusion:
The difference in the growth of output per worker between Country X and Country Y can be explained by the fact that **Country X has a higher rate of investment** than Country Y. This higher investment rate allows Country X to grow its capital stock, while Country Y's lower investment rate leads to a net decline in capital stock, resulting in falling output per worker.

Would you like more details or have any further questions?

Here are 5 relative questions to explore this concept further:
1. How does the Solow-Swan model explain long-term economic growth?
2. What is the role of technological progress in sustaining growth when investment alone cannot?
3. How does an increase in the depreciation rate affect an economy’s steady-state level of capital?
4. How would differing rates of population growth affect the two countries’ outcomes in this scenario?
5. How would introducing human capital into the model change the dynamics of investment and growth?

**Tip:** A higher investment rate leads to a higher steady-state level of capital per worker, but diminishing returns to capital mean that technological progress is necessary for sustained growth in the long run.

Country X and Country Y have the same level of output per worker. They also have the same values for the rate of depreciation, 3, and the measure of productivity, A. In Country X output per worker is growing, whereas in Country Y, it is falling. What can you say about the two countries rates of investment?

Explore how differences in investment rates impact economic growth in Country X and Country Y using the Solow-Swan growth model. Both countries have the same output per worker, depreciation rate, and productivity, but their differing investment rates lead to varying growth outcomes.

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