Complete the following table by calculating the marginal physical product of labor (MPPL
) of each worker.
Labor
Output
Marginal Physical
(Number of workers)
(Shovels)
Product of Labor
(Shovels)
0	0
1	95
2	185
3	260
4	320
5	355

Plot the MPPL
curve on the following graph using the blue points (circle symbol).
MPP
L
0
1
2
3
4
5
100
90
80
70
60
50
40
30
20
10
0
MPPL (Shovels per worker)
LABOR (Number of workers)
Step 2: Demand for Labor
Consider again Gopher Excavators's total physical product and its marginal physical product of labor.
Labor
Output
Marginal Physical
(Number of workers)
(Shovels)
Product of Labor
(Shovels)
0	0
95
1	95
90
2	185
75
3	260
60
4	320
35
5	355

The following graph shows the demand for labor for three different prices per shovel:
0
1
2
3
4
5
300
270
240
210
180
150
120
90
60
30
0
WAGE (Dollars per worker)
LABOR (Number of workers)
O
N
M
Given the company’s marginal physical product of labor, line    on the previous graph shows Gopher's demand for labor when the price of a shovel is $1.00, and line    shows Gopher's demand for labor when the price of a shovel is $2.00.

To calculate the Marginal Physical Product of Labor (MPPL) for each worker, we find the change in output as each additional worker is hired. The MPPL can be calculated using the formula:

\[
\text{MPPL} = \text{Output}_{n} - \text{Output}_{n-1}
\]

where $ n $ is the number of workers.

### Step 1: Calculate MPPL

| Labor (Number of workers) | Output (Shovels) | MPPL (Shovels) |
|---------------------------|------------------|-----------------|
| 0                         | 0                | -               |
| 1                         | 95               | 95              |
| 2                         | 185              | 90              |
| 3                         | 260              | 75              |
| 4                         | 320              | 60              |
| 5                         | 355              | 35              |

### Step 2: MPPL Values

The MPPL values calculated are as follows:
- 1 worker: MPPL = 95
- 2 workers: MPPL = 90
- 3 workers: MPPL = 75
- 4 workers: MPPL = 60
- 5 workers: MPPL = 35

### Step 3: Plotting MPPL Curve

To plot the MPPL curve using blue points (circle symbols), place the points on a graph where the x-axis represents the number of workers and the y-axis represents the MPPL in shovels per worker:

1. (1, 95)
2. (2, 90)
3. (3, 75)
4. (4, 60)
5. (5, 35)

### Step 4: Demand for Labor

Given the additional MPPL values for the labor demand when the price of a shovel is $1.00 and $2.00:

| Labor (Number of workers) | Output (Shovels) | MPPL (Shovels) | Price = $1.00 | Price = $2.00 |
|---------------------------|------------------|-----------------|----------------|----------------|
| 0                         | 0                | -               | 0              | 0              |
| 1                         | 95               | 95              | 95             | 190            |
| 2                         | 185              | 90              | 90             | 180            |
| 3                         | 260              | 75              | 75             | 150            |
| 4                         | 320              | 60              | 60             | 120            |
| 5                         | 355              | 35              | 35             | 70             |

### Demand Lines on Graph

- The demand line at $1.00 will intersect the MPPL values at the respective quantities.
- The demand line at $2.00 will be double the MPPL values.

### Summary

This calculation allows Gopher Excavators to determine the optimal number of workers based on the price of shovels and their corresponding MPPL.

Do you want more details or have any questions? Here are some related questions to consider:

1. How does the MPPL influence hiring decisions?
2. What factors could affect the MPPL in real-world scenarios?
3. How does the price of a shovel impact the demand for labor?
4. What are the implications of decreasing MPPL with increasing labor?
5. How can Gopher Excavators optimize their labor force based on this analysis?

**Tip:** Always consider how external factors (like market demand and costs) can influence your labor decisions.

Complete the following table by calculating the marginal physical product of labor (MPPL) of each worker.

Explore how to calculate the marginal physical product of labor (MPPL) for Gopher Excavators with a detailed table and analysis. This problem demonstrates the calculation of MPPL values for up to five workers, with corresponding output data.

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