Derivation Of Long Run Marginal Cost Curve (LRMC) | Ecoholics

Summary

The video provides a detailed explanation of how to derive the long-run marginal cost (LRMC) curve, a topic frequently seen in competitive exams. It begins by defining the LRMC, describing how it shows the additional cost incurred when one more unit of output is produced in the long run. The video explains the relationship between short-run and long-run cost curves, highlighting their U-shaped nature and the impact of economies of scale. Finally, the derivation of the LRMC curve is illustrated graphically, emphasizing its flatter shape compared to short-term marginal cost curves.

Takeaways

• 📉 The long-run marginal cost (LRMC) curve shows the additional cost incurred when one more unit of output is produced in the long run.
• 🧮 Mathematically, LRMC is the change in total cost divided by the change in quantity, or the first derivative of total cost with respect to quantity.
• 📊 The LRMC curve is derived from short-run marginal cost (SRMC) curves, but it tends to be flatter.
• ⬇️ Short-run average cost (SAC) curves are U-shaped due to initially decreasing costs (increasing returns) and later increasing costs.
• 🏭 In the long run, firms can choose between operating on one plant’s increasing cost portion or adding more plants, providing flexibility with inputs.
• 📈 The long-run average cost (LRAC) curve is derived by connecting the minimum points of SAC curves from different plants.
• 🔄 The LRAC curve is often referred to as the 'planning curve' as it accounts for optimal plant size based on economies and diseconomies of scale.
• ⚠️ The SRMC curve intersects the SAC curve at the SAC's minimum point.
• ✏️ The long-run marginal cost curve is derived by connecting the points of tangency between SRMC and LRMC curves at different output levels.
• 🛠️ The LRMC curve also follows a U-shape but is generally flatter than the short-run cost curves.

Q & A

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

The long-run marginal cost curve shows the additional cost incurred when producing one more unit of output in the long run. It is mathematically defined as the change in total cost divided by the change in quantity produced.

How is the long-run marginal cost curve mathematically represented?

It is represented as the first derivative of total cost with respect to quantity produced, i.e., ΔTotal Cost / ΔQuantity.

What is the relationship between short-run and long-run marginal cost curves?

The long-run marginal cost curve is derived from the short-run marginal cost curves. It tends to be flatter because firms have more flexibility with input factors in the long run.

What is the shape of the long-run marginal cost curve?

The long-run marginal cost curve is typically U-shaped, reflecting economies and diseconomies of scale.

How do short-run average cost curves influence the long-run average cost curve?

The long-run average cost curve is derived from the points of tangency between different short-run average cost curves, representing different plant sizes or production scales.

What is the importance of the tangency points between the short-run average cost and long-run average cost curves?

The tangency points determine the optimal production levels where the firm minimizes costs for each output level. These points are used to construct the long-run average cost curve.

Why does the long-run marginal cost curve tend to be flatter than short-run marginal cost curves?

In the long run, firms have more flexibility in adjusting their inputs, such as deciding whether to produce with one or multiple plants. This flexibility leads to a flatter cost curve as the firm can minimize costs more efficiently.

How is the U-shape of the short-run average cost curve explained?

The U-shape of the short-run average cost curve is due to increasing returns to scale at low production levels, followed by decreasing returns as production increases, which eventually raises costs.

What role do economies of scale play in the long-run cost curves?

Economies of scale reduce the average cost of production as output increases, leading to a downward-sloping portion of the long-run average cost curve. Diseconomies of scale eventually increase the cost, resulting in the U-shape.

How are short-run marginal cost curves related to short-run average cost curves?

Short-run marginal cost curves intersect the short-run average cost curves at their minimum point. This relationship helps identify the optimal production levels in the short run.