The marginal product of labor for a firm is given by: MPL = 176 - 4H, where H is the number of hours they hire workers to work. For example, the marginal product of the first hour of labor would be 176-4*1, and the marginal product of the second hour of labor would be 176-4*2. If the market wage is $14 per hour, how many hours of labor will this firm hire? Round your final answer to two decimal places.
The marginal product of labor for a firm is given by: MPL = 176 - 4H, where H is the number of hours they hire workers to work. For example, the marginal product of the first hour of labor would be 176-4*1, and the marginal product of the second hour of labor would be 176-4*2. If the market wage is $14 per hour, how many hours of labor will this firm hire? Round your final answer to two decimal places.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![**Understanding Marginal Product of Labor for a Firm**
The marginal product of labor (MPL) for a firm is given by the formula:
\[ \text{MPL} = 176 - 4H \]
Here, \( H \) represents the number of hours the firm hires workers to work.
#### Example Calculations:
- For the first hour of labor:
\[ \text{MPL} = 176 - 4 \times 1 = 176 - 4 = 172 \]
- For the second hour of labor:
\[ \text{MPL} = 176 - 4 \times 2 = 176 - 8 = 168 \]
If the market wage is $14 per hour, the firm will hire labor up to the point where the marginal product of labor equals the market wage.
#### Question:
**How many hours of labor will this firm hire?**
**Solution:**
To find how many hours the firm will hire, set the marginal product of labor equal to the market wage:
\[ 176 - 4H = 14 \]
Solve for \( H \):
1. Subtract 14 from both sides:
\[ 176 - 14 = 4H \]
2. Simplify:
\[ 162 = 4H \]
3. Divide by 4:
\[ H = \frac{162}{4} = 40.50 \]
Thus, the firm will hire **40.50 hours of labor**.
**Note:** Always round your final answer to two decimal places, where applicable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6387f1fe-f7de-460c-a439-51c8967659dd%2Fa6715a72-5ceb-48cc-a615-66b086f52adf%2Fk6g8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Marginal Product of Labor for a Firm**
The marginal product of labor (MPL) for a firm is given by the formula:
\[ \text{MPL} = 176 - 4H \]
Here, \( H \) represents the number of hours the firm hires workers to work.
#### Example Calculations:
- For the first hour of labor:
\[ \text{MPL} = 176 - 4 \times 1 = 176 - 4 = 172 \]
- For the second hour of labor:
\[ \text{MPL} = 176 - 4 \times 2 = 176 - 8 = 168 \]
If the market wage is $14 per hour, the firm will hire labor up to the point where the marginal product of labor equals the market wage.
#### Question:
**How many hours of labor will this firm hire?**
**Solution:**
To find how many hours the firm will hire, set the marginal product of labor equal to the market wage:
\[ 176 - 4H = 14 \]
Solve for \( H \):
1. Subtract 14 from both sides:
\[ 176 - 14 = 4H \]
2. Simplify:
\[ 162 = 4H \]
3. Divide by 4:
\[ H = \frac{162}{4} = 40.50 \]
Thus, the firm will hire **40.50 hours of labor**.
**Note:** Always round your final answer to two decimal places, where applicable.
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