Short-run and long-run cost curves

💰 Short-Run Cost Curves: Understanding Firm Behaviour 💰

Hey Economists! This chapter is absolutely critical for understanding how firms make decisions about how much to produce. When you know a firm's costs, you know its limitations, its potential profits, and its competitive edge. Think of costs as the backbone of supply! We are focusing specifically on the Short Run, where things are a little restrictive for the firm.

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1. The Time Horizon: Short Run vs. Long Run

To understand short-run costs, we first need to define the time period we are looking at. Economists classify time into two periods based on a firm's ability to change its factors of production (FOPs).

What is the Short Run?

• The Short Run is a period where at least one factor of production is Fixed (cannot be changed).
• Typically, capital (like factory size, machinery, or building leases) is the fixed factor.
• To increase output in the short run, a firm can only increase its Variable Factors (like labour or raw materials).
• Analogy: A baker rents a tiny shop (fixed). If he wants to make more bread today, he can hire more staff and buy more flour (variable), but he cannot immediately build a bigger shop.

What is the Long Run?

The Long Run is a period where all factors of production are Variable. The firm can expand its factory, buy new machinery, or build a new office. (We save the long-run cost curves for a later topic!)

2. The Three Pillars of Cost: Total, Average, and Marginal

Firms need to measure their costs in three different ways to decide on their profit-maximising output. You must be able to calculate and interpret these three types of costs.

2.1. Total Costs (TC)

This is the simplest concept. It is the sum of all costs incurred by the firm.

\(TC = TFC + TVC\)

• Total Fixed Cost (TFC): The total cost of fixed factors (e.g., $1000 rent). This line on a graph is horizontal.
• Total Variable Cost (TVC): The total cost of variable factors (e.g., cost of flour increases as the baker makes more bread). This curve starts at the origin and rises.
• Total Cost (TC): Starts at the level of TFC (because when output is zero, variable costs are zero, but fixed costs still exist) and runs parallel to the TVC curve.

2.2. Average Costs (AC)

Average costs tell the firm the cost of producing a single unit of output. This is vital because if the average cost is higher than the price they charge, the firm is losing money!

• Average Fixed Cost (AFC): Fixed cost per unit of output.

\(AFC = \frac{TFC}{Q}\) (where Q is output)

Memory Aid: AFC always falls as output increases because you are spreading the fixed cost over more units. This is known as the "Spreading the Overhead" effect.



• Average Variable Cost (AVC): Variable cost per unit of output.

\(AVC = \frac{TVC}{Q}\)



• Average Total Cost (ATC) (often just called AC): Total cost per unit of output.

\(ATC = \frac{TC}{Q}\) OR \(ATC = AFC + AVC\)

2.3. Marginal Cost (MC)

Marginal cost is arguably the most important cost concept for decision-making. It tells the firm the extra cost of producing just one more unit of output.

\(MC = \frac{\Delta TC}{\Delta Q}\) OR \(MC = \frac{\Delta TVC}{\Delta Q}\)

Note: Since TFC is constant, the change in Total Cost is equal to the change in Total Variable Cost. Marginal Cost ignores Fixed Costs.

Why is MC important? A rational firm will only produce an extra unit of output if the revenue earned from that unit (Marginal Revenue) is greater than the cost of producing it (Marginal Cost).

3. The Reason for the Shapes: Law of Diminishing Returns

Don't worry if this seems tricky at first—the reason all the short-run curves (except AFC) are U-shaped comes down to one fundamental principle:

What is the Law of Diminishing Returns?

The law of diminishing returns states that in the short run, if a firm increases a variable factor of production (like labour) while keeping at least one factor fixed (like capital), eventually the extra output generated by each additional unit of the variable factor will start to fall.

Think of it like this: You have a single check-out counter (fixed capital). When you hire the first cashier, productivity is high. When you hire the second and third, they help speed things up even more. But if you try to squeeze ten cashiers behind that one counter, they start bumping into each other, arguing over the cash register, and waiting for space. The 10th cashier adds very little, if any, extra output.

• Initial Stage (Increasing Returns): Adding variable inputs boosts productivity, leading to falling Average and Marginal Costs.
• Later Stage (Diminishing Returns): Overcrowding the fixed factor causes productivity to slow down and eventually fall, leading to rising Average and Marginal Costs.

This rise and fall in productivity is what creates the characteristic U-Shape of the short-run average and marginal cost curves.

4. Drawing and Interpreting Short-Run Cost Curves

You must be able to draw and interpret these curves. They are usually plotted with Cost (\(\$\)) on the Y-axis and Quantity (Q) on the X-axis.

The typical Short-Run Average Total Cost (SRATC or SAC) and Marginal Cost (SMC or MC) graph shows four crucial relationships:

1. The AFC curve continuously slopes downwards (spreading the fixed cost).
2. The AVC curve is U-shaped, initially falling due to efficiency gains, then rising due to diminishing returns.
3. The ATC curve is also U-shaped. It is always above the AVC curve (because ATC = AVC + AFC). The gap between ATC and AVC shrinks as output rises (due to the falling AFC).
4. The MC curve is U-shaped and falls faster than the AC curves, but then rises faster.

The Critical Relationship: MC and AC

The Marginal Cost curve always intersects both the Average Variable Cost (AVC) curve and the Average Total Cost (ATC) curve at their lowest points.

• When MC is below AC: AC must be falling (the last unit was cheaper than the average, pulling the average down).
• When MC is above AC: AC must be rising (the last unit was more expensive than the average, pulling the average up).
• When MC = AC: AC is at its minimum point. This point of minimum ATC represents the productively efficient level of output in the short run.

Memory Aid: Think of your exam grades (AC) and your latest test score (MC). If your latest score (MC) is lower than your average (AC), your average drops. If your latest score (MC) is higher, your average increases.

5. Factors Affecting Short-Run Costs (Shifting the Curves)

The shape of the cost curves is determined by the fixed plant size and diminishing returns. However, the curves themselves can shift up or down due to changes in factor prices and productivity.

A. Changes in Factor Prices

• Increase in Variable Factor Prices: If the cost of raw materials (a variable factor) increases, the TVC, AVC, and MC curves will shift upwards. TFC and AFC remain unchanged. Example: Global oil prices rise, making shipping costs more expensive for a manufacturer.
• Increase in Fixed Factor Prices: If rent or insurance (a fixed factor) increases, the TFC, TC, AFC, and ATC curves will shift upwards. The TVC, AVC, and MC curves remain unchanged (because MC only measures the cost of the variable factor). Example: The annual property tax on the factory building increases.

B. Changes in Productivity

Productivity is key to cost reduction. If a factor becomes more productive, the cost per unit falls.

• Increase in Labour Productivity: If workers (a variable factor) become more efficient (e.g., through training or new management techniques), the firm requires less labour time per unit of output. This leads to a decrease in TVC, AVC, and MC. The curves shift downwards.
• Decrease in Factor Productivity: If machinery breaks down frequently, delaying production, costs per unit rise, and the curves shift upwards.

Did you know? Many economists argue that in the real world, firms rarely experience the steep initial fall in costs predicted by the textbook U-shape. Instead, due to modern manufacturing flexibility, some firms see more of a ‘saucer’ shape or a very flat U-shape in their average costs over a large range of output!

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📚 Study Notes: Long-Run Cost Curves (Economics 9640)

Hello everyone! This chapter is where we move from thinking about day-to-day decisions to long-term business strategy. Understanding long-run costs is crucial because it helps explain why large companies can often produce goods cheaper than small ones. It's all about efficiency, expansion, and finding the sweet spot for production!

Don't worry if this seems tricky at first. The concept of the long-run average cost curve is simply a way for a business to plan the most efficient size (or "scale") of its operations.

1. The Long Run vs. The Short Run: A Quick Refresher

Before tackling the long run, let's quickly remind ourselves of the difference between the two timeframes in economics (Section 3.1.3.3):

• The Short Run: A time period where at least one factor of production (usually capital, like factory size or machinery) is fixed. Firms can only change output by adjusting variable factors (like labour or raw materials).
• The Long Run: A time period long enough for a firm to vary all of its factors of production. In the long run, there are no fixed costs; everything is variable. The firm can choose to build a bigger factory or buy more machinery.

Analogy: If you own a small coffee shop (short run), you can only increase output by hiring more staff or using more coffee beans. In the long run, you could knock down the walls and build a much larger café or open a chain of new branches.

Key Takeaway: The long run is about changing the scale of production, which is the overall size of the firm's operations.

2. The Concept of Returns to Scale (RTS)

The shape of the long-run cost curves is entirely determined by what happens to output when a firm increases all its inputs proportionally. This is called Returns to Scale (Section 3.3.2.1).

2.1 Increasing Returns to Scale (IRS)

If a firm doubles all inputs (e.g., labour, capital, land), and output more than doubles.

• What this means for cost: Output grows faster than costs. Therefore, the average cost per unit falls. This is the stage of Economies of Scale.

2.2 Constant Returns to Scale (CRS)

If a firm doubles all inputs, and output exactly doubles.

• What this means for cost: Average cost remains the same.

2.3 Decreasing Returns to Scale (DRS)

If a firm doubles all inputs, and output less than doubles.

• What this means for cost: Output grows slower than costs. Therefore, the average cost per unit rises. This is the stage of Diseconomies of Scale.

3. The Long-Run Average Cost (LRAC) Curve

The Long-Run Average Cost (LRAC) Curve shows the lowest possible average cost for a firm to produce any given level of output, assuming all factors of production are variable (i.e., the firm has chosen the most efficient plant size for that output level).

3.1 The Traditional U-Shape of the LRAC Curve

Historically, the LRAC curve is often drawn as a shallow 'U' shape. This shape reflects the journey of a firm as it grows:

1. Falling Costs (Downsloping section): The firm experiences Economies of Scale (EoS) (or Increasing Returns to Scale). The LRAC falls.
2. Constant Costs (Flat section): The firm experiences Constant Returns to Scale. The LRAC is stable at its minimum point.
3. Rising Costs (Upsloping section): The firm experiences Diseconomies of Scale (DeS) (or Decreasing Returns to Scale). The LRAC rises.

Think of the LRAC as an "envelope" curve: It is the curve that just touches the bottom (lowest average cost) of a series of different short-run average cost (SRAC) curves, each representing a different size of factory or plant.

4. Economies of Scale: The Benefits of Getting Bigger

Economies of Scale (EoS) occur when the average cost of production falls as the firm increases the scale of its operation (i.e., when the firm is experiencing Increasing Returns to Scale).

4.1 Internal Economies of Scale

These are cost savings that arise from the growth of the firm itself. They depend on the scale of output of the individual firm.

• Technical Economies:
  • Specialisation: Large firms can use highly specialised machinery (e.g., a huge automated bottling plant) or specialised labour (e.g., hiring specific software engineers instead of general technicians).
  • Indivisibility: Some large capital items (like a giant crane or a major marketing campaign) only make sense if production is massive. They are "indivisible" and can't be scaled down for small firms.
  • The container principle: Doubling the capacity of a storage container (like an oil tank or a ship) doesn't double the amount of material needed to build it. Volume increases faster than surface area, leading to lower average costs.
• Financial Economies: Large firms can borrow money more easily and at lower interest rates than small firms, as they are seen as less risky.
• Managerial Economies: Large firms can afford to hire highly skilled, specialist managers (e.g., a full-time HR director or a Chief Financial Officer). Although their total salary bill is high, the average cost per unit of output is low because output is massive.
• Marketing (or Commercial) Economies:
  • Bulk Buying: Large firms receive substantial discounts when buying huge quantities of raw materials (e.g., a global airline buying jet fuel).
  • Advertising: The cost of a national TV campaign is spread over millions of units sold, making the average marketing cost per product very low.
• Risk-Bearing Economies: Large firms can diversify their product lines or their geographical markets, spreading the risk of failure across different areas.

4.2 External Economies of Scale

These are cost savings that benefit all firms in a particular industry (or geographical area) as the whole industry grows in size. They are external to the individual firm's growth.

• Improved Infrastructure: As an industry concentrates in one area (e.g., the automotive industry in certain regions), governments or private firms invest in better transport links, roads, and utilities, benefitting all local firms.
• Specialised Labour and Skills: When an industry grows, local colleges or training centres start offering specialised courses, ensuring a steady supply of skilled workers (e.g., IT professionals near Silicon Valley).
• Growth of Ancillary Industries: Supporting firms (e.g., repair services, component suppliers, packaging companies) spring up nearby, reducing transport and search costs for the core firms.

Key Takeaway: EoS drive the LRAC curve downwards. Internal EoS come from the firm's growth; External EoS come from the industry's growth.

5. Diseconomies of Scale: The Drawbacks of Excessive Growth

Diseconomies of Scale (DeS) occur when the average cost of production starts to rise as the firm increases its scale of operation (i.e., when the firm is experiencing Decreasing Returns to Scale).

These problems usually stem from the difficulty of managing extremely large, complex organisations.

5.1 Reasons for Diseconomies of Scale (Syllabus Requirement 3.1.3.4)

• Managerial Diseconomies (Coordination Issues): As a firm grows, management structures become more complex and bureaucratic.
  • Example: Decision-making slows down because information must pass through many layers of management. This can lead to inefficiency and missed opportunities.
• Communication Problems: As the workforce increases and is spread across different locations or departments, communication becomes more difficult and prone to error (the "corporate telephone game" analogy). Workers may also feel alienated and unmotivated.
• Control and Monitoring Difficulties: It becomes harder for senior managers to monitor the performance and efficiency of every employee or department, potentially leading to waste and slack (X-inefficiency).
• Labour Relations: Larger workplaces often lead to depersonalisation, potentially resulting in poor labour relations, industrial disputes, and reduced productivity.

Did You Know? The traditional "U-shape" LRAC curve implies that eventually, these managerial diseconomies will always outweigh technical economies. However, some economists suggest modern technology and management techniques have made the upsloping section much less steep or even eliminated it entirely (leading to the L-shaped curve, see Section 6.2).

Key Takeaway: DeS drive the LRAC curve upwards, usually due to the complexities of managing and coordinating a vast enterprise.

6. Minimum Efficient Scale (MES)

The Minimum Efficient Scale (MES) is the lowest level of output at which a firm’s Long-Run Average Cost is minimised. It is the output level at the start of the Constant Returns to Scale section of the LRAC curve.

At this point, the firm has achieved all possible internal economies of scale.

6.1 Significance of MES for Market Structure

The size of the MES relative to the size of the total market is incredibly important for determining the structure of an industry (Syllabus 3.3.2.3):

• Small MES relative to market size: If the MES is achieved at a very low output level (e.g., a local bakery), many small firms can operate efficiently in the market. This tends to lead to highly competitive markets (e.g., local retail, restaurants).
• Large MES relative to market size: If the MES is only achieved at a very high output level (e.g., aircraft manufacturing or car production), the market can only support a small number of large firms, as they need to be massive just to be cost-competitive. This leads to concentrated markets like Oligopoly or, in extreme cases, Natural Monopoly.

MES and Barriers to Entry: If the MES is large, it acts as a significant barrier to entry. Any new firm entering the market would have to start producing on a small scale, meaning they would face much higher average costs than the established, large firms, making it difficult for them to survive.

6.2 The L-Shaped Long-Run Average Cost Curve

The syllabus specifically mentions the L-shaped long-run average cost curve (3.3.2.3).

• Traditional View: LRAC is U-shaped, implying DeS eventually set in.
• Modern View (L-Shape): Many economists argue that modern manufacturing and communication technologies (like global ERP software and flexible production methods) have mitigated or postponed significant managerial diseconomies.
• The L-Shape Explained: Costs fall steeply (EoS) until MES is reached, but then costs remain largely constant (CRS) for a vast range of output, rather than rising sharply (DeS). The curve is flat after the MES is reached, forming an 'L' shape rather than a 'U'.

Key Takeaway: MES dictates the minimum size a firm needs to be to compete effectively. The modern L-shape suggests firms can grow huge without necessarily suffering the negative cost impact of traditional diseconomies.