https://file.aiquickdraw.com/mathbot/file/1726861007586cjvz8zem.jpg

No work, just answers, Please be aware that multiple-choice questions are designed for multiple answers, meaning that there may be more than one correct option.

Based on the image, let's break down the key information required to provide the correct answers:

### Key Details:
- **Technology A**: Uses 1 worker and 4 tonnes of coal.
- **Technology B**: Uses 4 workers and 2 tonnes of coal.
- **Wage and Price of Coal in Period 1**: $ w = 10 $, $ p = 20 $.
- **Wage and Price of Coal in Period 2**: $ w = 20 $, $ p = 10 $.

### Cost Function Calculation:
1. **For Technology A**: 
   - In **period 1**, the cost = $ w \times 1 + p \times 4 = 10 \times 1 + 20 \times 4 = 10 + 80 = 90 $.
   - In **period 2**, the cost = $ w \times 1 + p \times 4 = 20 \times 1 + 10 \times 4 = 20 + 40 = 60 $.

2. **For Technology B**: 
   - In **period 1**, the cost = $ w \times 4 + p \times 2 = 10 \times 4 + 20 \times 2 = 40 + 40 = 80 $.
   - In **period 2**, the cost = $ w \times 4 + p \times 2 = 20 \times 4 + 10 \times 2 = 80 + 20 = 100 $.

### Comparison of Costs:
- In **Period 1**:
  - Technology A costs 90, and Technology B costs 80.
  - Therefore, **Technology B** is **cheaper in Period 1**.
  
- In **Period 2**:
  - Technology A costs 60, and Technology B costs 100.
  - Therefore, **Technology A** is **cheaper in Period 2**.

### Correct Answers:
- **Technology B is cheaper in Period 1 and Technology A is cheaper in Period 2.**

This matches the fourth option in the multiple-choice question.

Would you like more details on any step? Here are some related questions to explore:

1. How do isocost lines help in choosing the optimal technology?
2. What happens to the cost function if wages increase more than coal prices?
3. Can we optimize costs using a combination of technologies?
4. How does changing input prices influence cost minimization strategies?
5. What assumptions do we make when using the cost function in this context?

**Tip:** Always check the slopes of isocost curves to analyze cost efficiency when input prices change.

In the following diagram, you are given two technologies, A and B, which can produce 100 meters of cloth. Technology A uses 1 worker and 4 tonnes of coal, while Technology B uses 4 workers and 2 tonnes of coal. The diagram also depicts three examples of isocost curves: NM, GF, and JH. The wage cost and the price of coal are denoted by w and p, respectively. In period 1, the wage cost and the price of coal are (w, p) = ($10, $20), and in period 2, the wage cost and price of coal change to (w, p) = ($20, $10). Which of the following statements is correct?

Analyze the cost comparison between two production technologies (A and B) under changing wage and coal prices across two periods. Learn how to calculate the cost functions and determine which technology is cheaper depending on the input price variations.

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