Sure! Let's go through the detailed steps to calculate the value added by firm [tex]\( X \)[/tex] based on the given data.
### Step 1: Understand the given data
Here is the data provided:
- Sales: 600
- Purchases of raw material: 200
- Import of raw material: 100
- Import of machines: 200
- Closing stock: 40
- Opening stock: 10
### Step 2: Calculate total input costs
The total input costs include the purchases of raw material, import of raw material, and import of machines. Hence, we calculate total input costs as follows:
[tex]\[
\text{Total input costs} = \text{Purchases of raw material} + \text{Import of raw material} + \text{Import of machines}
\][/tex]
Substituting the given values:
[tex]\[
\text{Total input costs} = 200 + 100 + 200 = 500
\][/tex]
### Step 3: Calculate the change in stock
The change in stock is the difference between the closing stock and the opening stock. Hence, we calculate the change in stock as follows:
[tex]\[
\text{Change in stock} = \text{Closing stock} - \text{Opening stock}
\][/tex]
Substituting the given values:
[tex]\[
\text{Change in stock} = 40 - 10 = 30
\][/tex]
### Step 4: Calculate the value added by the firm
The value added by the firm is calculated by subtracting the total input costs from the sales and then adding the change in stock. Hence, we calculate the value added as follows:
[tex]\[
\text{Value added} = \text{Sales} - \text{Total input costs} + \text{Change in stock}
\][/tex]
Substituting the calculated values:
[tex]\[
\text{Value added} = 600 - 500 + 30 = 130
\][/tex]
### Conclusion
Thus, the value added by the firm is:
- Total input costs: 500
- Change in stock: 30
- Value added: 130
The firm’s value-added calculation yields a final value-added amount of 130.
