Types of cost, revenue and profit, short-run and long-run production

Understanding Costs, Revenue, and Production: The Firm's Engine Room

Welcome to one of the most fundamental areas of microeconomics! This chapter, part of the A-Level syllabus, is essential because it explains the decisions firms make about how much to produce and how much to charge. By mastering costs, revenue, and production theory, you unlock the secret to why companies behave the way they do—and how they determine their profit.

Don't worry if the formulas look complicated at first! We will break them down step-by-step and use real-life examples to show that these concepts simply reflect smart business logic.

1. The Importance of Time: Short Run vs. Long Run

In economics, the terms 'short run' and 'long run' do not refer to a specific amount of time (like six months or one year). They refer to how flexible a firm's factors of production are.

Factors of Production (Review)

• Fixed Factors of Production: Inputs that cannot be changed easily or quickly (e.g., factory size, heavy machinery, specialized land).
• Variable Factors of Production: Inputs that can be changed easily in line with output changes (e.g., raw materials, casual labour, electricity).

Defining the Time Periods (7.5.1, 7.5.3)

The Short Run (SR)

The short run is a period where at least one factor of production is fixed (usually capital, like the size of the factory). If a bakery wants to increase output quickly in the SR, it can hire more staff (variable factor) but cannot build a new oven (fixed factor).

The Long Run (LR)

The long run is a period long enough for the firm to vary all its factors of production. If the bakery decides the market is growing, in the LR it can expand its building, buy new ovens, and redesign its entire production line. There are no fixed factors in the long run.

2. Short-Run Production and the Law of Diminishing Returns

Production functions describe the maximum output achievable from a given set of inputs.

Key Production Concepts (7.5.1)

In the short run, we focus on what happens as we add more of the variable factor (usually labour) to a fixed factor (e.g., land/capital).

Total Product (TP): The total output produced by a given amount of inputs.
\(\text{TP} = Q\) (Quantity of Output)

Average Product (AP): Output per unit of the variable factor (e.g., output per worker).
\(\text{AP} = \frac{\text{Total Product}}{\text{Quantity of Variable Factor (L)}}\)

Marginal Product (MP): The extra output gained from adding one more unit of the variable factor (e.g., the output added by the last worker hired).
\(\text{MP} = \frac{\Delta \text{Total Product}}{\Delta \text{Quantity of Variable Factor (L)}}\)

The Law of Diminishing Returns (LDR) (7.5.1)

This is also called the Law of Variable Proportions. It is a fundamental concept for understanding the shape of short-run cost curves.

Definition: In the short run, as successive units of a variable factor are added to a fixed factor, the marginal product (MP) will eventually decline.

Analogy: Imagine a small coffee stand (fixed factor).

• Worker 1: Makes coffee, serves customers. MP is high.
• Worker 2: Can specialise—one makes coffee, one takes orders. Output more than doubles. MP is increasing (Increasing Returns).
• Worker 5: The staff start bumping into each other. They waste time waiting for the single coffee machine. MP is still positive, but the increase in output is smaller than the previous worker (Diminishing Returns Set In).
• Worker 10: Too crowded to work. Output might actually fall. MP is negative.

Key Takeaway for Production: Diminishing returns explain why production cannot increase forever just by hiring more staff; eventually, the fixed capacity constrains efficiency.

3. Costs in the Short Run (SR Cost Function)

A firm's costs are directly linked to its production efficiency. Since some factors are fixed in the short run, we split costs accordingly (7.5.2).

Total Costs (TC)

• Total Fixed Costs (TFC or FC): Costs that do not change with output (e.g., rent, insurance). These must be paid even if output is zero.
• Total Variable Costs (TVC or VC): Costs that change directly with output (e.g., raw materials, power, wages for production staff).
• Total Cost (TC): The sum of fixed and variable costs.
  \(\text{TC} = \text{FC} + \text{VC}\)

Average Costs (AC)

Average costs allow comparison with price (Average Revenue) to determine profit.

• Average Fixed Cost (AFC): Fixed cost per unit of output. This always falls as output increases ("spreading the overheads").
  \(\text{AFC} = \frac{\text{FC}}{Q}\)
• Average Variable Cost (AVC): Variable cost per unit of output.
  \(\text{AVC} = \frac{\text{VC}}{Q}\)
• Average Total Cost (ATC or AC): Total cost per unit of output.
  \(\text{AC} = \frac{\text{TC}}{Q} \text{ or } \text{AFC} + \text{AVC}\)

Marginal Cost (MC)

Marginal Cost (MC): The extra cost incurred by producing one additional unit of output. Since fixed costs don't change, MC is calculated solely by the change in variable costs.
\(\text{MC} = \frac{\Delta \text{Total Cost}}{\Delta Q}\)

Don't worry if this seems tricky at first—MC is the most important concept for a firm's day-to-day decisions. Firms always ask: "What does it cost me to make just one more unit?"

The Shape of SR Cost Curves (7.5.2)

The shapes of the AVC, AC, and MC curves are determined by the Law of Diminishing Returns:

1. When Marginal Product (MP) is rising, Marginal Cost (MC) is falling.
2. When MP is falling (LDR sets in), MC is rising.

Because of this relationship, the MC curve is U-shaped and intersects both the AVC and the AC curves at their minimum points.

The AC curve is U-shaped because of the balance between falling AFC (which pulls AC down) and rising AVC (due to diminishing returns, which pulls AC up).

4. Production and Costs in the Long Run (LR Cost Function)

In the long run, the firm can choose the scale of its operation (e.g., building a small, medium, or large factory). The goal is to find the most efficient scale.

Returns to Scale (7.5.3)

Returns to Scale describes what happens to output when a firm increases all inputs by a certain proportion (e.g., doubling the factory size, machinery, and labour).

• Increasing Returns to Scale (IRS): If inputs are doubled, output more than doubles. (This is generally due to Economies of Scale).
• Constant Returns to Scale (CRS): If inputs are doubled, output exactly doubles.
• Decreasing Returns to Scale (DRS): If inputs are doubled, output less than doubles. (This is generally due to Diseconomies of Scale).

The Long-Run Average Cost (LRAC) Curve (7.5.4)

The LRAC curve shows the lowest average cost of producing any given output when all inputs are variable. It is often called an envelope curve because it 'envelopes' (or touches) the minimum points of many possible Short-Run Average Cost (SRAC) curves.

• The downward-sloping part of the LRAC curve shows Increasing Returns to Scale (falling costs).
• The horizontal (or flat) part shows Constant Returns to Scale.
• The upward-sloping part shows Decreasing Returns to Scale (rising costs).

Minimum Efficient Scale (MES) (7.5.4)

The Minimum Efficient Scale (MES) is the lowest level of output at which the firm's LRAC reaches its minimum. Producing at MES means the firm has exploited all possible internal economies of scale.

Example: A car manufacturer reaches MES when its factory is large enough to use highly specialized robotic assembly lines. Making the factory even bigger might not reduce costs further.

5. Economies and Diseconomies of Scale (EoS/DoS)

These concepts explain why the LRAC curve first falls and then rises (7.5.5, 7.5.6, 7.5.7).

Internal Economies of Scale (7.5.6)

These are cost savings that occur inside the firm as a result of expanding its scale of production.

• Technical EoS: Achieved through large-scale machinery, specialization, and the principle of multiples (using inputs that only come in large, indivisible units). Example: A massive container ship is cheaper per tonne transported than 10 smaller ships.
• Managerial EoS: Large firms can afford specialist managers (e.g., HR, Marketing, Finance), leading to greater efficiency and lower average costs.
• Financial EoS: Large firms can borrow money more cheaply than small firms, as banks view them as less risky. They also have easier access to capital markets (selling shares).
• Marketing EoS: The fixed cost of a national advertising campaign is spread over millions of units, making the cost per unit very small.

Internal Diseconomies of Scale (DoS) (7.5.7)

These are cost disadvantages that occur inside the firm as it grows too large.

• Coordination and Communication Problems: As a firm gets huge (e.g., multinational), management becomes difficult. Bureaucracy slows down decision-making, leading to inefficiency and rising costs.
• Worker Alienation: Workers in very large firms may feel disconnected or insignificant, leading to lower morale, lower productivity, and higher wage demands.

External Economies and Diseconomies of Scale (7.5.6, 7.5.7)

These affect all firms in a particular industry or area, regardless of their individual size.

• External Economies (Cost Falling): When the industry grows in size, all firms benefit. Example: A cluster of high-tech firms attracts specialized suppliers and highly trained labour, lowering recruitment and supply chain costs for every firm in that cluster (e.g., Silicon Valley).
• External Diseconomies (Cost Rising): When the industry grows too large, it may cause problems for all firms. Example: Increased competition for land drives up rents, or traffic congestion makes transportation more expensive for everyone in the area.

6. Revenue Concepts

Revenue is the money a firm receives from selling its goods and services (7.5.8). Understanding revenue is crucial for calculating profit.

Total Revenue (TR): The total amount of money received from sales.
\(\text{TR} = \text{Price} \times \text{Quantity Sold} \quad (\text{TR} = P \times Q)\)

Average Revenue (AR): The revenue received per unit sold. In most cases, AR is simply equal to the price (P) of the good.
\(\text{AR} = \frac{\text{TR}}{Q}\)

Marginal Revenue (MR): The extra revenue gained from selling one additional unit of output.
\(\text{MR} = \frac{\Delta \text{Total Revenue}}{\Delta Q}\)

Did you know?

The relationship between AR and MR is determined by the market structure (a topic we cover later). If a firm can only sell more by lowering the price (a downward-sloping demand curve), then AR will always be greater than MR.

7. Types of Profit (7.5.9, 7.5.10)

Profit is the ultimate goal for most firms (in the traditional economic model). Economists distinguish between two components of cost: explicit (money paid out) and implicit (opportunity cost).

Total Profit Formula:
\(\text{Total Profit} = \text{Total Revenue} - \text{Total Cost}\)

When calculating costs for profit, we must include the opportunity cost of the factors owned by the entrepreneur (like the owner's time or capital).

Normal Profit

Definition: The minimum level of profit needed to keep the factors of production (including the entrepreneur) in their current use in the long run. It is considered an implicit cost.

• Normal profit is achieved when Total Revenue = Total Cost (TR = TC) or Average Revenue = Average Cost (AR = AC).
• If a firm only makes normal profit, it means the entrepreneur is earning just enough to cover all expenses, including what they could have earned elsewhere (their opportunity cost).

Supernormal Profit (Abnormal Profit)

Definition: Any profit earned above and beyond normal profit.

• Supernormal profit is achieved when Total Revenue > Total Cost (TR > TC) or Average Revenue > Average Cost (AR > AC).

Calculation (7.5.10):
\(\text{Supernormal Profit} = (P - \text{AC}) \times Q\)

Subnormal Profit (Loss)

Definition: When the firm fails to cover all its costs, including implicit costs (normal profit).

• Subnormal profit (a loss) occurs when Total Revenue < Total Cost (TR < TC) or Average Revenue < Average Cost (AR < AC).

Calculation (7.5.10):
\(\text{Subnormal Profit (Loss)} = (\text{AC} - P) \times Q \quad (\text{If positive, it is a loss})\)

Memory Trick: Think of Normal Profit as a necessary wage for the owner. Supernormal Profit is the bonus payment on top of that wage. If you make subnormal profit, you aren't even covering your required wage (opportunity cost).