https://file.aiquickdraw.com/mathbot/file/1730168025593hbg0ilrp.jpg

Let's go through each calculation step by step.

### Step 1: Calculate Physical Capital per Worker
Physical Capital per Worker is calculated as:
\[
\text{Physical Capital per Worker} = \frac{\text{Physical Capital}}{\text{Labor Force}}
\]

1. **For 2032:**
   \[
   \frac{120 \text{ servers}}{60 \text{ workers}} = 2 \text{ servers per worker}
   \]

2. **For 2033:**
   \[
   \frac{400 \text{ servers}}{100 \text{ workers}} = 4 \text{ servers per worker}
   \]

### Step 2: Calculate Labor Productivity
Labor Productivity is defined as:
\[
\text{Labor Productivity} = \frac{\text{Output}}{\text{Labor Hours}}
\]

1. **For 2032:**
   \[
   \frac{21,000 \text{ TB of data storage}}{3,000 \text{ hours}} = 7 \text{ TB per hour}
   \]

2. **For 2033:**
   \[
   \frac{49,000 \text{ TB of data storage}}{3,500 \text{ hours}} = 14 \text{ TB per hour}
   \]

### Summary of Calculations

| Year | Physical Capital per Worker (Servers) | Labor Productivity (TB per hour) |
|------|---------------------------------------|----------------------------------|
| 2032 | 2                                     | 7                                |
| 2033 | 4                                     | 14                               |

### Answer to the Fill-in-the-Blank
- The increase in physical capital per worker from 2032 to 2033 is associated with an **increase** in labor productivity.

### Policy Recommendations
For greater productivity in the cloud computing industry, the following policies would likely be effective:
- **Subsidizing research and development into new cloud computing technologies**: This could lead to innovation and efficiency improvements.
- **Encouraging saving by allowing workers to set aside a portion of their earnings in tax-free retirement accounts**: This indirectly encourages investment and economic stability, which can support productivity growth.

Let me know if you'd like further details or have any questions. Here are five related questions to expand on this topic:

1. What factors other than physical capital can affect labor productivity?
2. How would changes in labor hours impact productivity measures?
3. Why is research and development crucial for industries like cloud computing?
4. How does foreign ownership of domestic capital affect productivity and policy decisions?
5. What role does education play in increasing labor productivity in high-tech industries?

**Tip:** When evaluating productivity, always consider both input resources and output efficiency to get a complete picture.

Consider a hypothetical small island nation in which the only industry is cloud computing. The following table displays information about the economy over a two-year period. Complete the table by calculating physical capital per worker as well as labor productivity.

Learn how to calculate physical capital per worker and labor productivity in a cloud computing industry context with this detailed example. This problem covers key economic and productivity concepts, suitable for college-level economics or business studies.

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