Consider the following information about baseball production at Bobby’s Baseball Factory:
WorkerMarginal Product
- 13
- 25
- 38
- 410
- 57
- 64
- 72
Bobby pays all his workers the same wage, and labor is his only variable cost. From this information we can conclude that Bobby’s average variable cost decreases
a. as output rises from 0 to 10, but rises after that.
b. as output rises from 0 to 26, but rises after that.
c. as output rises from 0 to 33, but increases after that.
d. continually as output rises.
The correct answer and explanation is :
The correct answer is (c) as output rises from 0 to 33, but increases after that.
Explanation:
To determine when Bobby’s average variable cost (AVC) decreases or increases, we need to examine marginal product (MP) and its relationship with cost.
Step 1: Understanding AVC and Its Relationship with MP
- AVC = Total Variable Cost (TVC) / Quantity of Output (Q)
- Since labor is the only variable cost, TVC = Wage × Number of Workers.
- AVC is inversely related to average product (AP) (total output per worker). When MP is greater than AP, AP rises, leading to a decrease in AVC. However, when MP falls below AP, AP starts to decrease, which makes AVC increase.
Step 2: Calculating Total Output
We sum the marginal product (MP) values to find total output at each worker level:
| Workers | MP | Total Output |
|---|---|---|
| 1 | 13 | 13 |
| 2 | 25 | 13 + 25 = 38 |
| 3 | 38 | 38 + 38 = 76 |
| 4 | 10 | 76 + 10 = 86 |
| 5 | 7 | 86 + 7 = 93 |
| 6 | 4 | 93 + 4 = 97 |
| 7 | 2 | 97 + 2 = 99 |
Step 3: Identifying the Point Where AVC Starts to Rise
- AP increases when MP > AP and decreases when MP < AP.
- MP is highest at Worker 3 (38).
- After Worker 3, MP drops significantly (10, then 7, then 4), meaning AP starts declining.
- Since AVC moves opposite to AP, it decreases until Worker 3, then starts rising after that.
Conclusion
Since output at Worker 3 is 33 (from summing MP for the first three workers: 13 + 25 + 38 = 33), the AVC decreases until 33 units of output and then starts increasing after that.
Thus, the correct choice is (c) as output rises from 0 to 33, but increases after that.