Supposed That Firms' Only Variable Input Is Labor When 50 Wo

Supposed That Firms Only Variable Input Is Labor When 50 Workers Are U

Supposed that firms only variable input is labor when 50 workers are used, the average product of labor is 50, and marginal product of the 50th worker is 75. The wage rate is $80, the total number of workers hired is 75, and the total cost of the fixed input is $500. Based on this information, we are asked to determine the average variable cost, marginal cost, and average total cost, and to evaluate statements regarding the behavior of costs.

Paper For Above instruction

Calculating the different costs in the context of labor as the only variable input involves understanding the relationships between productivity, input costs, and total costs. Here, the analysis hinges primarily on the marginal and average product of labor and their influence on cost calculations.

A. What is the average variable cost? Show your calculation.

Average Variable Cost (AVC) is calculated as the total variable cost divided by the quantity of output produced. The total variable cost (TVC) is obtained by multiplying the wage rate (W) by the total number of workers hired (L). In this case:

• Wage rate (W) = $80
• Total workers hired (L) = 75

Therefore, the total variable cost (TVC) is:

TVC = W × L = $80 × 75 = $6,000

Next, the total output (Q) can be inferred from the average product of labor (APL):

APL = Q / L

Given that when 50 workers are employed, the average product is 50 units per worker, so the total output at that point is:

Q = APL × L = 50 × 50 = 2,500 units

This indicates the total output corresponding to the 50 workers. Since the marginal product of the 50th worker is 75 units, it suggests that the production process yields increasing marginal returns at that point. Assuming that the additional output produced by the 75th worker is consistent with the marginal product, the total output with 75 workers is:

Q = 50 workers × 50 units/worker + (additional output from the 75th worker)

• The total output contributed by the extra 25 workers (from 50 to 75) can be approximated assuming the marginal product for these workers is similar to the marginal product of the 50th worker, which is 75 units (though actual marginal products for these workers are not explicitly provided). For simplicity, assume a consistent marginal product per worker at this stage, which suggests total output increases proportional to marginal product.

Alternatively, given the average product at 50 workers is 50 units per worker, total output at 50 workers is 2,500 units. The increase in output with additional workers depends on the marginal product, which is 75 for the 50th worker, indicating that each additional worker produces 75 units of output. Therefore, the total output with 75 workers is approximately:

Q = 2,500 units + (additional 25 workers × 75 units/worker) = 2,500 + 1,875 = 4,375 units

Now, the average variable cost is:

AVC = Total Variable Cost / Total Output = $6,000 / 4,375 ≈ $1.37 per unit

B. What is marginal cost? Show your calculations.

Marginal Cost (MC) is the increase in total cost resulting from producing one additional unit of output. It can be calculated as:

MC = Change in Total Cost / Change in Quantity

The change in total variable cost (ΔTVC) when moving from the production level with 50 workers to 75 workers involves the additional cost of hiring 25 workers:

• ΔTVC = W × (Number of additional workers) = $80 × 25 = $2,000

The change in output (ΔQ) is from 2,500 units to approximately 4,375 units, which is:

ΔQ = 4,375 – 2,500 = 1,875 units

Thus, the marginal cost is:

MC = ΔTVC / ΔQ = $2,000 / 1,875 ≈ $1.07 per unit

C. What is average total cost? Show your calculations.

Average Total Cost (ATC) is the sum of average fixed cost (AFC) and average variable cost (AVC). It can also be directly computed as total cost divided by total output:

• Total fixed cost (TFC) = $500
• Total variable cost (TVC) = $6,000
• Total cost (TC) = TFC + TVC = $500 + $6,000 = $6,500

Total output is approximately 4,375 units, so:

ATC = TC / Q = $6,500 / 4,375 ≈ $1.49 per unit

D. Is each of the following statements true or false? Explain your answer.

1. Marginal Cost is increasing

Based on the calculations, the marginal cost is approximately $1.07 per unit, which is lower than the average variable cost of about $1.37. Typically, when marginal cost is below average total cost or average variable cost, and is increasing as output increases, it indicates diminishing marginal returns have set in. Since the marginal cost is relatively stable but could increase with further production, it is plausible that marginal cost is increasing in this scenario, especially beyond the current production level. Therefore, it is likely true that marginal cost is increasing as output expands further, reflecting the law of diminishing marginal returns which causes marginal costs to rise after a certain point.

2. Average variable cost is increasing

Given that AVC is approximately $1.37 at the current production level, and marginal cost ($1.07) is less than AVC, AVC is decreasing at this point. However, if marginal cost eventually exceeds AVC as output increases, AVC will start to rise. Since the current marginal cost is lower than AVC, and marginal cost tends to increase with rising marginal returns diminishing, it suggests at present, AVC may be decreasing, and thus, the statement that AVC is increasing may be false in the immediate context. Nonetheless, the overall trend at higher output levels could differ.

3. Average total cost is decreasing

With an ATC of approximately $1.49 per unit, the trend depends on the relationship between marginal cost and average total cost. Because marginal cost ($1.07) is less than ATC, and the fixed costs are spreading over a larger output, ATC tends to decrease as production increases, especially at current output levels. Therefore, this statement is likely true, but only if production continues to increase within ranges where marginal cost remains below ATC. If marginal cost surpasses ATC at higher outputs, the ATC could begin to rise. Given the current data, the decreasing trend is plausible.

Conclusion

In summary, the calculations indicate that the average variable cost is approximately $1.37 per unit, marginal cost about $1.07 per unit, and average total cost roughly $1.49 per unit. Judging from these figures, marginal cost is increasing, average variable cost is decreasing at this stage, and average total cost is decreasing as well. These observations align with typical cost behaviors in production, assuming diminishing marginal returns eventually set in, causing marginal cost to rise beyond certain output levels. Understanding these cost dynamics is crucial for firms when making decisions about scaling production to optimize profitability and efficiency.

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