Question

The marginal cost curve intersects the average variable cost curve at the _____. a) shut-down point b) break-even point c) maximum profit point

Short answer

The marginal cost curve intersects the average variable cost curve at the \(a)\) shut-down point. This is because when the two cost curves intersect, marginal cost equals the average variable cost, meaning producing another unit will have no impact on the average variable cost. The shut-down point represents the critical point at which the firm will choose to halt production if prices fall below the average variable cost and continue production if prices are above it.

Step-by-step solution

Understanding Marginal Cost

Marginal cost refers to the cost of producing one additional unit of output. It is defined as the change in total cost when producing an additional unit of a product.

Understanding Average Variable Cost

Average variable cost is the variable cost per unit of output. It's calculated as the total variable cost divided by the quantity of output produced.

Relation between Marginal Cost and Average Variable Cost

When marginal cost is below the average variable cost, it means that producing an extra unit will bring down the average variable cost. Conversely, if marginal cost is above the average variable cost, it implies that producing an additional unit will increase the average variable cost. Thus, when the two cost curves intersect, marginal cost equals the average variable cost. This means that producing another unit will have no impact on the average variable cost.

Analyzing the options

a) Shut-down point: This is the point at which the firm will choose to temporarily halt production rather than continue to operate at a loss. In this case, the intersection point refers to the instance when the price is equal to or lower than the average variable cost. b) Break-even point: At this point, the firm's total revenue equals its total cost, resulting in zero economic profit. The break-even point is not necessarily the intersection point of marginal cost and average variable cost curves. c) Maximum profit point: This occurs at the output level where the difference between total revenue and total cost is greatest.

Conclusion

From the analysis, we can deduce that the correct answer is a) shut-down point. This is because when the marginal cost curve intersects the average variable cost curve, it represents the point at which the firm's operating costs are minimized and producing an additional unit will not impact the average variable cost. This is the critical point at which the firm will choose to shut down if prices fall below the average variable cost and continue production if prices are above it.

Key concepts

Average Variable Cost

The Average Variable Cost (AVC) is a crucial concept in understanding how firms decide on production levels. AVC is simply the total variable cost divided by the quantity of output produced. It gives insights into how much it costs, on average, to produce one unit of output when only considering variable costs. Variable costs change with the level of production, such as costs for raw materials and labor. Here's how to calculate it:

• If your total variable cost is $300 for 50 units, the average variable cost would be AVC = \( \frac{300}{50} = 6 \) dollars per unit.

The AVC provides a benchmark depicting how efficiently a firm utilizes its variable resources. If AVC decreases as production increases, it implies the firm is benefiting from economies of scale. However, if AVC starts rising with an increase in production, it’s an indication of potential inefficiencies, possibly due to overutilization of resources.

Shut-down Point

The Shut-down Point refers to the specific level of operations where a firm will cease production, even in the short run. This occurs when the market price falls to the level of the Average Variable Cost. Why is this important? If a firm's total revenue falls below its total variable costs, it implies each unit produced increases the firm's overall loss. Therefore, if the price received for a product is less than the AVC, continuing production would result in losses greater than the fixed costs that will still need to be paid irrespective of production decisions. Instead of operating at a loss, the firm is better off temporarily ceasing production. In practical terms:

• At the shut-down point, price = AVC. If a firm finds itself in this scenario, it would stop production if the situation persists in the short-run as producing any further would simply add more to their loss.

Cost Curves Intersection

The intersection of cost curves, particularly the Marginal Cost (MC) and Average Variable Cost (AVC) curves, plays a pivotal role in determining production decisions. At this intersection point, the marginal cost matches the average variable cost. Why does this matter?

• If the Marginal Cost is less than the AVC, producing an extra unit will decrease the AVC, indicating efficient production.
• If the Marginal Cost is more than the AVC, the reverse happens — each additional unit produced raises the AVC.
• When both intersect, it means producing an extra unit will not affect the AVC.

This point is crucial in the context of operational economics because it indicates the minimum AVC the firm should target to cover its variable costs effectively. If prices drop below this level, the company risks operating at a loss and might consider shutting down.