Question

Given the Long Run Average Cost curve, LAC, could the Short Run Average Cost curves \(\mathrm{SAC}_{1}, \mathrm{SAC}_{2}, \mathrm{SAC}_{3}\), and \(\mathrm{SAC}_{4}\) all correspond to the given LAC in Figure \(1 ?\)

Short answer

In order to determine if the given Short Run Average Cost (SAC) curves \(\mathrm{SAC}_{1}, \mathrm{SAC}_{2}, \mathrm{SAC}_{3}\), and \(\mathrm{SAC}_{4}\) could correspond to the Long Run Average Cost (LAC) curve in Figure 1, we need to ensure that the lowest points of each SAC curve touch the LAC curve, and SAC curves don't fall below the LAC curve. Upon reviewing the figure, we can see that at least some of the SAC curves fall below the LAC curve. Therefore, not all of the given SAC curves can correspond to the given LAC curve in Figure 1.

Step-by-step solution

Identify the relationship between LAC and SAC curves

The Long Run Average Cost (LAC) curve is also known as the 'planning curve' and is created by plotting the minimum average cost for producing different levels of output. The Short Run Average Cost (SAC) curves represent the cost structures in different short run scales of production. The LAC curve is the envelope curve of various SAC curves, meaning it is the curve that "hugs" the lower points of each SAC curve.

Analyze the SAC curves in relation to LAC curve

To determine if all of the given SAC curves (\(\mathrm{SAC}_{1}, \mathrm{SAC}_{2}, \mathrm{SAC}_{3}\), and \(\mathrm{SAC}_{4}\)) could correspond to the LAC curve in Figure 1, we need to check if the following conditions are met: 1. The lowest points of each SAC curve must touch the LAC curve. 2. The SAC curves must not fall below the LAC curve. If these conditions hold true for all the given SAC curves, then these curves can correspond to the given LAC curve.

Review the SAC curves and the LAC curve

By reviewing the given SAC curves and the LAC curve in Figure 1, we can make the following observations: 1. The lowest points of each SAC curve appear to touch the LAC curve. 2. At least some of the SAC curves do fall below the LAC curve. From these observations, we can conclude that not all of the given SAC curves can correspond to the given LAC curve in Figure 1.

Key concepts

Short Run Average Cost Curves

Understanding the short run average cost curves (SAC) is vital for students studying economics. Each SAC curve represents the average cost of production when at least one factor of production, such as equipment or factory space, is fixed. Imagine a local bakery that can only fit ten ovens—this limitation affects the bakery's costs in the short run. It can increase production only up to a point before costs per item start to rise, due to factors like overtime pay or increased energy usage.

As more units are produced, the average cost per unit initially decreases due to the spreading of fixed costs over more items. This is known as achieving economies of scale. However, once the bakery reaches a certain level of production, adding more work or hours doesn't equally translate to more goods produced, and the average cost starts to climb again—this illustrates the 'law of diminishing returns'.

Each SAC curve typically has a 'U-shape' due to this process of decreasing then increasing marginal outputs. The lowest point on any given SAC curve represents the most efficient level of production for that amount of fixed resources.

Envelope Curve

The long run average cost (LAC) curve acts as an envelope curve for all possible SAC curves. An envelope curve is a visual concept that combines all the efficient points of production for different scales of production capacity into one graph. In a graph, think of the LAC as a gentle curve that just barely 'kisses' the lowest points—the points of maximum efficiency—of each SAC curve. In our bakery analogy, it means plotting the least cost at which the bakery can provide its goods over time, transitioning to newer, larger or more technologically advanced ovens when it's cost-effective to do so.

The LAC is significant because it showcases the cost advantage of optimal scale adjustment in the long run when all inputs are variable. The business can adjust all factors, including the number of ovens and space size, as opposed to the short run, where something is always held fixed. If the SAC curves dip below the LAC, it indicates that there has been a miscalculation, as the LAC should represent the lowest possible cost of production for each level of output over time.

Production Cost Structure

Delving into the production cost structure allows students to understand how costs are allocated within a business operation. Essentially, this structure breaks down into fixed and variable costs. Fixed costs, such as rent or salaries, do not change with the level of output. On the other hand, variable costs, such as raw materials or utilities, fluctuate with the quantity of goods or services produced.

When we look at the SAC, we're analyzing the blend of fixed and variable costs at a given level of production in the short run. As production scales, this combination shifts on each SAC curve. In the long run, businesses aim for production cost structures that minimize costs—this often involves investing in technology or facilities that alter fixed and variable costs in beneficial ways.

For students visualizing this, imagine a chart with various SAC curves representing different technological states or production capacities. Each SAC shows a snapshot of costs at that point in time. The LAC, in concert with these SACs, tells us that the optimal cost structure evolves as the business grows and the scale of operation changes. By understanding this, businesses can make informed decisions about scaling up or down to maintain economic efficiency.