Deriving the Long Run Marginal Cost Curve

Summary

This video explains the derivation of the long-run marginal cost (LRMC) curve, starting with a review of the long-run average cost (LRAC) curve. The LRAC is the lower envelope of a firm's short-run average cost curves, where capital is fixed in the short run but flexible in the long run. The LRMC is derived by tracing marginal costs at different quantities, showing how it is flatter than short-run marginal cost curves due to the firm’s ability to adjust inputs. The LRMC also intersects the LRAC at its minimum, with key insights into their relationship.

Takeaways

• 📉 The long-run marginal cost curve is derived from understanding the long-run average cost curve.
• 📊 The long-run average cost curve is the lower envelope of the firm’s short-run average cost curves.
• 🔄 In the short run, the firm faces a fixed input, typically capital, which leads to different short-run average cost curves depending on the level of capital.
• 🏗️ In the long run, the firm can choose any level of capital, selecting the one that minimizes production costs for each output level.
• 📐 The long-run marginal cost for each quantity is derived from the corresponding short-run marginal cost curve.
• 🔗 The long-run marginal cost curve is created by connecting points from short-run marginal cost curves that correspond to the firm’s chosen level of capital for each output quantity.
• 📍 The marginal cost always intersects the minimum point of the average cost curves, both in the short run and the long run.
• 🔄 The long-run marginal cost curve is flatter than the short-run marginal cost curves because the firm has more flexibility in adjusting inputs over time.
• 📉 The long-run marginal cost curve passes through the minimum point of the long-run average cost curve, following a logic similar to short-run curves.
• 🔗 The relationship between long-run curves and total cost curves can be better understood with additional diagrams, as mentioned in the video.

Q & A

What is the first step in understanding the derivation of the long-run marginal cost (LRMC) curve?

The first step is to understand the derivation of the long-run average cost (LRAC) curve, which is shown as the lower envelope of the firm's short-run average cost (SRAC) curves.

How is the long-run average cost curve derived?

The long-run average cost curve is derived by tracing the lower envelope of all the firm's short-run average cost curves, which correspond to different levels of capital. In the long run, the firm can choose the level of capital that minimizes production costs for each quantity.

What does each short-run average cost curve represent?

Each short-run average cost curve represents the firm’s average costs when a particular input, such as capital, is fixed at a certain level. These curves differ depending on the level of fixed capital.

Why does the long-run average cost curve appear smoother than the short-run average cost curves?

The long-run average cost curve is smoother because it is the lower envelope of many short-run average cost curves, each representing different levels of capital. Since the firm can adjust its capital in the long run, this creates a smoother curve.

How is the long-run marginal cost (LRMC) curve constructed?

The LRMC curve is constructed by tracing the long-run marginal cost for each quantity produced. For each level of output, the corresponding short-run marginal cost (SRMC) curve is used, and the long-run marginal cost is read off from this curve.

At what point are the long-run marginal cost and long-run average cost equal?

The long-run marginal cost and long-run average cost are equal at the minimum point of the long-run average cost curve. This occurs because marginal cost always intersects the average cost at its minimum.

Why is the long-run marginal cost curve flatter than the short-run marginal cost curve?

The LRMC curve is flatter than the SRMC curves because, in the long run, the firm has the flexibility to adjust all inputs, such as labor and capital. This allows the firm to choose the most cost-efficient combination of inputs, leading to slower increases in marginal cost compared to the short-run, where some inputs are fixed.

What happens to the relationship between marginal cost and average cost when average costs are decreasing?

When average costs are decreasing, marginal cost must be lower than average costs. This relationship holds for both short-run and long-run cost curves.

What is the significance of the tangency point between the long-run average cost curve and short-run average cost curve?

The tangency point indicates the optimal level of capital for a given level of output. At this point, both the short-run and long-run average cost curves are at their minimums, and the marginal cost equals the average cost.

Why is the relationship between long-run cost curves and total cost curves important to understand?

Understanding the relationship between long-run cost curves and total cost curves helps to see how costs behave as output expands. This can offer insights into cost structures, economies of scale, and production efficiency in the long run.