Question

The long-run average cost curve is called the envelope curve as it envelops the SAC's. Comment.

Short answer

Q: Comment on the long-run average cost (LRAC) curve, also known as the envelope curve, and its relationship with the short-run average cost (SAC) curves. A: The LRAC curve, or envelope curve, shows the lowest possible average cost for a firm in the long run for every production level. It envelops the SAC curves by marking the lowest point of each SAC curve, considering all possible production facility sizes and input combinations. This optimality can be reached by firms adjusting both labor and capital in the long run, as opposed to only adjusting labor in the short run. The distinctive shape of the envelope curve reflects the firm's ability to choose the optimal production level and input combination in the long run.

Step-by-step solution

Define Short-run Average Cost

Short-run Average Cost (SAC) refers to the average cost of production when at least one input, typically capital, is fixed. This means that the company can only adjust certain inputs, like labor, to change output levels. So the SAC curve represents the average cost of producing varying output levels with a fixed amount of capital.

Define Long-run Average Cost

Long-run Average Cost (LRAC) refers to the average cost of production when all inputs, including capital, can be adjusted. In the long run, companies can enter or exit a market and adjust the size of their production facilities, which allows them to invest in more or less capital. As a result, the LRAC represents the lowest average cost achievable when the firm has the freedom to choose the optimal combination of inputs for any level of output.

Relationship between SAC and LRAC

There are multiple short-run average cost curves, each of which corresponds to a specific level of fixed capital. The long-run average cost curve is formed by plotting the lowest point of each short-run average cost curve. In other words, the LRAC curve represents the minimum average cost that can be achieved for each level of output by adjusting both labor and capital optimally as opposed to only adjusting labor in the short run.

Explain the Envelope Curve

The Long-run average cost curve "envelops" the Short-run average cost curves because it marks the boundary for the lowest possible average cost for each level of output, considering all possible sizes of production facilities and input combinations. The LRAC acts as an envelope because it "hugs" the lowest points of each of the individual SAC curves, and as such, it represents the optimal production level for the firm in the long run.

Comment on the Envelope Curve

In conclusion, the long-run average cost curve, also known as the envelope curve, envelops the short-run average cost curves, because it represents the lowest possible average cost for the firm in the long run for every level of output. Firms can achieve this optimality by adjusting both labor and capital in the long run, as opposed to only adjusting labor in the short run. The envelope curve's distinctive shape is the result of the firm's ability to choose the optimal production level and input combination.

Key concepts

Long-run Average Cost

In economics, the Long-run Average Cost (LRAC) is crucial to understanding how companies can optimize production costs over time. Unlike in the short run, where some inputs like capital are fixed, the long run allows firms to alter all inputs. This includes both labor and capital. The LRAC curve represents the lowest possible cost per unit of output when firms have the flexibility to choose the most efficient combination of all inputs for any given level of production. In practical terms, this means businesses can change the size of their production facilities or enter or exit an industry or market entirely.
This flexibility helps companies to achieve economies of scale, which in turn reduces costs. Economies of scale occur when increasing production leads to a lower cost per unit.

• When inputs are perfectly scalable, firms can reach an optimum point where marginal costs decrease as production expands.
• This point is where firms are achieving the most efficient scale of production.

As a consequence, the LRAC curve typically has a U-shape, reflecting decreased costs with increased production up to a certain point. Beyond this point, costs start to rise due to diseconomies of scale.

Short-run Average Cost

Short-run Average Cost (SAC) takes a different angle by focusing on production costs when at least one input remains unchanged. Generally, this fixed input is capital, like machinery or factories, which cannot be adjusted instantly. In the short-run scenario, firms can adjust other variables such as labor, but they must work within the constraints of their existing capacity.
This means that the SAC curve displays the cost dynamics of producing different output levels, given a fixed quantity of capital. For example, if a factory has a set number of machines, the company can only hire more or fewer workers without altering the number of machines.

• The curve is usually U-shaped, reflecting first the declining costs as production increases, thanks to labor specialization and efficiency improvements.
• However, as production increases beyond a certain point, costs begin to rise due to inefficiencies and factors like worker crowding.

In essence, the SAC curve provides insights into the short-term operational efficiency of a firm, based on its current resources. As such, it is an essential tool for analyzing short-term managerial decisions.

Envelope Curve

The concept known as the Envelope Curve is a fundamental idea connecting both the LRAC and SAC curves. The Long-run Average Cost curve is often referred to as the Envelope Curve because it wraps around multiple Short-run Average Cost curves, capturing the essence of their interaction. Imagine multiple SAC curves, each representing different levels of fixed capital.
The LRAC curve traces the lowest points of these SAC curves, portraying the minimum average cost attainable for each production level.

• It essentially 'hugs' these lowest points because it exemplifies the ideal scenario where a firm can modify both labor and capital to reach the ultimate cost efficiency for each output quantity.
• The LRAC acts as a boundary that outlines the most cost-effective strategy for output generation over the long term.

This envelope phenomenon results from a firm's ability to be dynamic in choosing the optimal scale and combination of inputs (both labor and capital) in the long run, thereby achieving the best possible productivity level. The Envelope Curve's critical role is to guide firms in making strategic decisions about production scale and resource allocation, blending short-term constraints with long-term potential.