Question

If both the marginal cost and the average variable cost curves are \(J\) -shaped, at the point of minimum average variable cost, the marginal cost must be a. greater than the average variable cost. b. less than the average variable cost. c. equal to the average variable cost. d. at its minimum.

Short answer

At the point of minimum average variable cost, the marginal cost is equal to the average variable cost (MC = AVC). This occurs since the MC curve intersects the AVC curve at the point of minimum AVC. Therefore, the correct answer is c. equal to the average variable cost.

Step-by-step solution

Understand the definition of Marginal Cost (MC) and Average Variable Cost (AVC)

Marginal Cost (MC) is the increase in total cost that occurs as production is increased by one unit, whereas the Average Variable Cost (AVC) is the total variable cost divided by the quantity of output produced. It's important to note that if both the marginal cost and the average variable cost curves are J-shaped, they are decreasing initially and then increasing.

Analyze the position of MC and AVC Curves

At the point of minimum AVC, the AVC curve is at its lowest point and begins to increase. When the AVC curve is decreasing, the MC is less than the AVC, since, if the MC were greater than the AVC, the AVC curve would increase. Conversely, when the AVC curve is increasing, the MC is greater than the AVC because an increase in the MC would push the AVC upward. So, at the point of minimum AVC, the MC must be equal to AVC, which is when the MC curve intersects the AVC curve.

Apply the analysis to the given options

Given the analysis above, we can now evaluate each of the given choices: a. MC > AVC: This would be true if the AVC curve is increasing. However, we are looking for the relationship at the point of minimum AVC, where the MC and AVC curves intersect. b. MC < AVC: This would be true if the AVC curve is decreasing. But, at the point of minimum AVC, this isn't the case. c. MC = AVC: This is the correct relationship as the MC curve intersects the AVC curve at the point of minimum AVC. d. MC at its minimum: This statement doesn't address the relationship between the MC and AVC; therefore, it's not valid for this exercise. So, the correct answer is: c. equal to the average variable cost.

Key concepts

Marginal Cost

The concept of Marginal Cost (MC) is fundamental in understanding how costs change with production. Simply put, marginal cost is the additional cost a firm incurs when producing one more unit of a product.
It's the cost of "the next unit up" in manufacturing.
To calculate marginal cost, focus on the change in total cost from producing additional units:

• Mathematically, it can be expressed as: \( MC = \frac{\Delta TC}{\Delta Q} \)
• Here, \( \Delta TC \) is the change in total cost, and \( \Delta Q \) is the change in quantity produced.

Marginal cost can change due to factors like additional material costs, labor, or cost efficiencies as production increases.
Understanding marginal cost is crucial for firms to decide optimal production levels and pricing strategies.

Average Variable Cost

Average Variable Cost (AVC) refers to the variable costs incurred per unit of output. These costs fluctuate based on the level of output.
To compute AVC, divide total variable cost (TVC) by the quantity of output (Q) produced:

• So, \( AVC = \frac{TVC}{Q} \)

Variable costs include expenses like materials and labor used directly in production.
Unlike fixed costs, these can vary with production volume.The average variable cost curve is typically J-shaped.
It initially decreases, given fixed overheads are spread across more units, and later rises due to factors like overtime and resource constraints.
Recognizing this pattern helps firms in understanding how efficiently they are operating as production scales.

Cost Analysis

Cost analysis is a critical tool for businesses to understand the dynamics of their cost structures and profitability.
It involves examining different types of costs, namely fixed, variable, and total costs, and how they interact with each other. One essential aspect is identifying the relationship between Marginal Cost (MC) and Average Variable Cost (AVC).
This relationship is crucial when determining the profit-maximizing level of production. At the minimum point of the AVC curve, marginal cost equals the AVC. This is significant because:

• Below the minimum AVC, MC is less than AVC indicating efficiency is improving with additional units.
• Above the minimum, MC surpasses AVC, suggesting producing extra units becomes less cost-effective.

Effective cost analysis allows firms to strategize better, optimize operations, and align production decisions with market conditions.