To determine how many workers the firm will employ when the cost per good is $6 and the wage rate is $25, we need to consider the Marginal Revenue Product of Labor (MRP) in relation to the wage rate.
The MRP is calculated as follows:
\[ \text{MRP} = \text{Marginal Product of Labor} \times \text{Price per Good} \]
Given that the price per good is $6, we can calculate the MRP for each level of labor input:
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For 1 worker:
- Marginal Product of Labor = 7
- MRP = 7 × $6 = $42
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For 2 workers:
- Marginal Product of Labor = 9
- MRP = 9 × $6 = $54
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For 3 workers:
- Marginal Product of Labor = 8
- MRP = 8 × $6 = $48
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For 4 workers:
- Marginal Product of Labor = 4
- MRP = 4 × $6 = $24
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For 5 workers:
- Marginal Product of Labor = 2
- MRP = 2 × $6 = $12
Now, we compare the MRP of each labor level with the wage rate of $25:
- 1 worker: MRP = $42 (greater than wage, so the firm will hire)
- 2 workers: MRP = $54 (greater than wage, so the firm will hire)
- 3 workers: MRP = $48 (greater than wage, so the firm will hire)
- 4 workers: MRP = $24 (less than wage, so the firm will not hire)
- 5 workers: MRP = $12 (less than wage, so the firm will not hire)
The firm will continue to hire workers until the MRP is equal to or less than the wage rate. Thus, the firm will employ 3 workers because this is the last level of labor where MRP exceeds the wage rate.
Final Answer: three workers
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