Cost Analysis and Long Run Average Total Cost
Short Run vs. Long Run
Short Run:
At least two graphs indicate fixed costs.
The gap between the lines represents fixed costs.
Long Run:
No fixed costs or fixed inputs.
All costs are variable.
No average fixed cost.
Deriving the Long Run Average Total Cost (LRATC)
Businesses choose their size from the start, influencing the short-run average total cost (SRATC) curve.
SRATC curves correspond to different business sizes.
In the long run, firms aim to produce as cheaply as possible, at the lowest point on the SRATC curves.
If producing above the lowest point on SRATC1, it's not as cheap as possible, but short-run constraints may prevent optimization.
Example: High rent or insurance contracts can't be immediately changed.
In the long run, these constraints are flexible, allowing for production at the bottom of each SRATC curve.
The LRATC curve is formed by connecting the lowest points of each SRATC curve, resembling a scalloped graph.
Understanding Average Total Cost (ATC)
ATC represents the per-unit cost of production.
The goal is to minimize ATC.
Long Run Average Total Cost Curve Shape
The LRATC curve typically has a specific shape: a downward sloping side (economies of scale), a flat side (constant returns to scale), and an upward-sloping side (diseconomies of scale).
Y-axis: Costs, X-axis: Output.
The shape reflects the idea that costs initially fall with increased production but eventually rise.
Economies of Scale
Also known as scale economies or increasing returns to scale.
Characterized by falling per-unit costs of production as output increases.
Desirable for businesses.
Formally, if you double your inputs, you more than double your output.
Example:
Initial production: 500 units at $1000 total cost.
ATC_1 = \frac{1000}{500} = $2
Double inputs: $2000 total cost.
More than double output: 2000 units.
ATC_2 = \frac{2000}{2000} = $1
The average total cost decreases.
Constant Returns to Scale
A desirable state.
If you double your inputs, you exactly double your output.
Example:
Initial production: 6000 units at $3000 total cost.
ATC_3 = \frac{3000}{6000} = $0.50
Double inputs: $6000 total cost.
Exactly double output: 12000 units.
ATC_4 = \frac{6000}{12000} = $0.50
The average total cost remains costant.
Benefits from economies of scale have been exhausted.
Diseconomies of Scale
An undesirable state.
Unit costs are rising.
Often due to growing too fast, leading to management, communication, or supply problems.
If you double your inputs, you less than double your output.
Example:
Initial production: 20,000 units at $20,000 total cost.
ATC_5 = \frac{20000}{20000} = $1
Double inputs: $40,000 total cost.
Less than double output: 30,000 units.
ATC_6 = \frac{40000}{30000} = $1.33
The average total cost increases.
Reasons for Economies and Diseconomies of Scale
Economies of scale:
Specialization: Hiring specialists for specific tasks increases production efficiency.
Mass production.
Diseconomies of scale:
Growing too fast.
Perspectives on the LRATC Curve
From the Business Owner/CEO Perspective:
The goal is to minimize costs.
It doesn't matter where on the Constant Returns to Scale (CRS) portion the firm operates as long as it's on that line.
From Society's Perspective:
Firms should be efficient and not squander resources.
Firms should produce just enough to be efficient.
Minimum Efficient Scale (MES)
The lowest level of output where CRS is attained.
It is the socially optimal level of output.
Businesses may not prioritize MES if it doesn't align with their profitability goals.
MES as a Percentage of Total Industry Sales
MES is often reported as a percentage of total industry sales to standardize the measure across industries.
Example: MES at 5% means firms reach the socially optimal level when they capture 5% of total industry sales.
Determining the Optimal Number of Firms
If all firms produce at the MES level, the optimal number of firms can be calculated.
Calculation:
(where MES is a percentage)
Example: If MES is 5%, then the optimal number of firms is 20 (
Alternatively: