Economics (9708) | Types of cost, revenue and profit, short-run and long-run production

Welcome to Production Theory: Costs, Revenue, and Profit!

Hi there! This chapter might seem like it's full of confusing formulas, but don't worry. We are essentially learning the fundamental business rules of economics:

How do firms decide how much stuff to make, and how much money do they need to cover their operations?

Understanding costs, production, and profit is absolutely essential because it explains why businesses exist, how they grow, and why they behave the way they do in different markets. Let's break it down!

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Section 1: Production and the Concept of Time (Short Run vs. Long Run)

The Crucial Distinction: Time Periods

In economics, "time" isn't measured by the clock or calendar. It's measured by whether a firm can change its inputs. The two main time periods are:

1. The Short Run (SR)

• Definition: A time period where at least one factor of production is fixed (unchangeable).
• Example: A bakery decides to increase output by hiring more staff (variable factor) but cannot immediately build a new, larger oven (fixed factor).
• Fixed Factors of Production: Inputs that cannot be changed quickly (e.g., factory size, machinery, land).
• Variable Factors of Production: Inputs that can be changed easily (e.g., labour, raw materials, electricity).

2. The Long Run (LR)

• Definition: A time period where all factors of production are variable. There are no fixed costs. (Syllabus 7.5.3)
• Example: The bakery owner can now sell the old oven, buy a bigger one, or lease a completely new factory.

Analogy: Think of a student studying for an exam. In the short run, the size of their textbook (capital) is fixed. In the long run, they can buy new books, change courses, or even switch schools. Everything is flexible!

Short-Run Production Function (Syllabus 7.5.1)

The production function describes the relationship between inputs (factors of production) and output (product). We focus on three types of product when adding variable factors (like labour) to a fixed factor (like capital):

A. Product Definitions

• Total Product (TP): The total volume of output produced by a given number of inputs.
• Average Product (AP): Output per unit of the variable factor (usually labour).
  Formula: \[ AP = \frac{TP}{L} \] (where L = quantity of labour)
• Marginal Product (MP): The extra output generated by adding one more unit of the variable factor.
  Formula: \[ MP = \frac{\Delta TP}{\Delta L} \] (The change in Total Product divided by the change in Labour)

B. The Law of Diminishing Returns (LDR)

(Also called the Law of Variable Proportions) (Syllabus 7.5.1)

Definition: In the short run, if a firm increases the quantity of a variable factor while holding at least one other factor fixed, eventually the marginal product of the variable factor will decline.

The Stages of LDR:

1. Increasing Marginal Returns: MP rises initially (e.g., adding the first few workers allows for specialisation).
2. Diminishing Marginal Returns: MP starts to fall (e.g., adding more workers causes crowding and less efficient use of the fixed machinery).
3. Negative Marginal Returns: MP becomes negative (e.g., adding too many workers causes chaos, and total output actually falls).

Key Takeaway: The Law of Diminishing Returns is a short-run phenomenon because it relies on the existence of a fixed factor.

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Section 2: Short-Run Cost Functions (Syllabus 7.5.2)

Now that we know how output is related to inputs, we can calculate the costs associated with that output.

A. Total Costs

• Total Fixed Costs (TFC or FC): Costs that do not change with the level of output (e.g., rent, insurance premiums). They exist even if output is zero.
• Total Variable Costs (TVC or VC): Costs that change directly with the level of output (e.g., wages, raw materials, fuel).
• Total Cost (TC): The sum of fixed and variable costs.
  Formula: \[ TC = TFC + TVC \]

B. Average and Marginal Costs

Average costs help a firm determine the cost per unit of production.

• Average Fixed Cost (AFC): Fixed cost per unit of output.
  Formula: \[ AFC = \frac{TFC}{Q} \] (Q = quantity of output). The AFC curve always slopes downwards as TFC is spread over more units.
• Average Variable Cost (AVC): Variable cost per unit of output.
  Formula: \[ AVC = \frac{TVC}{Q} \]
• Average Total Cost (ATC or AC): Total cost per unit of output.
  Formula 1: \[ ATC = \frac{TC}{Q} \] Formula 2: \[ ATC = AFC + AVC \]
• Marginal Cost (MC): The extra cost incurred by producing one additional unit of output.
  Formula: \[ MC = \frac{\Delta TC}{\Delta Q} \] (Since TFC doesn't change, MC is also equal to \(\frac{\Delta TVC}{\Delta Q}\))

Understanding the Shapes of the SR Cost Curves

The shape of the short-run average and marginal cost curves (the U-shape) is directly caused by the Law of Diminishing Returns.

• MC and AVC/ATC: The MC curve intersects the AVC and ATC curves at their minimum points.
• Why the U-Shape?
  1. At low output, average costs fall: AFC is falling rapidly, and specialization keeps AVC low.
  2. At high output, average costs rise: The Law of Diminishing Returns kicks in. Marginal Product (MP) falls, meaning we need more and more variable input (like labour) to produce one extra unit. This makes Marginal Cost (MC) rise, pulling the AVC and ATC curves up with it.

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Section 3: Long-Run Costs and Scale (Syllabus 7.5.3, 7.5.4, 7.5.5-7.5.7)

In the long run, firms can change all inputs, including their scale (size). This leads to the concept of Returns to Scale.

A. Returns to Scale (RTS)

RTS refers to what happens to output when a firm increases all inputs proportionately in the long run.

1. Increasing Returns to Scale (IRS): Output increases by a greater percentage than the increase in inputs. (Example: Doubling inputs leads to triple the output.)
2. Constant Returns to Scale (CRS): Output increases by the same percentage as the increase in inputs. (Example: Doubling inputs leads to double the output.)
3. Decreasing Returns to Scale (DRS): Output increases by a smaller percentage than the increase in inputs. (Example: Doubling inputs leads to only 50% more output.)

B. Long-Run Average Cost (LRAC) Curve

The LRAC curve shows the lowest possible average cost of production achievable at any level of output when all factors are variable.

• The LRAC curve is derived by finding the minimum point on a series of short-run average cost (SRAC) curves, representing different plant sizes.
• The LRAC curve is U-shaped due to economies and diseconomies of scale.

C. Economies and Diseconomies of Scale

These are the factors that cause the LRAC curve to fall or rise. (Syllabus 7.5.5)

Internal Economies of Scale (Syllabus 7.5.6)

These are cost savings that happen inside the firm as output increases. They lead to falling LRAC (IRS stage).

• Technical Economies: Using larger, more efficient machinery (specialized capital) or benefiting from the "Law of Bulk Buying" (a 100-litre tank doesn't cost 10x a 10-litre tank).
• Managerial Economies: Larger firms can afford specialized managers (e.g., hiring an HR specialist instead of the owner doing everything).
• Financial Economies: Larger firms can borrow money at lower interest rates because they are seen as less risky.
• Marketing Economies: Buying inputs in bulk (quantity discounts) and spreading advertising costs over higher sales volumes.

Internal Diseconomies of Scale (Syllabus 7.5.7)

These are cost increases that happen inside the firm as output increases beyond a certain point. They lead to rising LRAC (DRS stage).

• Management and Coordination Problems: As the firm gets huge, communication lines lengthen, decision-making slows down, and management becomes inefficient.
• Worker Alienation: Workers become isolated or bored doing repetitive tasks, leading to decreased motivation and productivity.

External Economies of Scale (Syllabus 7.5.6)

These are cost savings that occur outside the firm but benefit all firms in a particular industry or location, usually as the industry grows.

• Example: The government builds a new road (infrastructure) that benefits all logistics companies in the region, lowering their transport costs.
• Example: Specialized training institutions open near an industrial hub, providing a better pool of skilled labour for all local firms.

External Diseconomies of Scale (Syllabus 7.5.7)

These are cost increases that occur outside the firm but negatively affect all firms in an industry as the industry grows too large.

• Example: Increased traffic congestion in an industrial area raises delivery times and costs for all firms.
• Example: Intense competition for scarce, specialized labour drives up the price (wages) of that labour across the industry.

D. Minimum Efficient Scale (MES) (Syllabus 7.5.4)

Definition: The lowest level of output at which a firm achieves the minimum long-run average cost (the bottom of the LRAC curve).

At MES, the firm has exhausted all possible internal economies of scale. Firms aiming for optimal efficiency will target production at or beyond the MES.

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Section 4: Revenue Concepts (Syllabus 7.5.8)

Revenue is the money a firm earns from selling its output.

A. Total Revenue (TR)

Definition: The total amount of money received by the firm from the sale of a given quantity of goods.
Formula: \[ TR = P \times Q \] (Price times Quantity)

B. Average Revenue (AR)

Definition: Revenue per unit sold. In all market structures, Average Revenue is exactly the same as the price of the good (P).
Formula: \[ AR = \frac{TR}{Q} = \frac{P \times Q}{Q} = P \] Importance: The AR curve is the firm's Demand Curve.

C. Marginal Revenue (MR)

Definition: The extra revenue generated by selling one additional unit of output.
Formula: \[ MR = \frac{\Delta TR}{\Delta Q} \]

Quick Tip: AR vs. MR Relationship

For a firm operating in a market where it faces a normal, downward-sloping demand curve (i.e., it must lower the price to sell more—like a monopoly or oligopoly), the MR curve always lies below the AR curve.

Why? To sell the next unit, the firm must drop the price not only on that unit but on ALL previous units sold. The extra revenue gained (price of the new unit) is offset by the revenue lost (the discount on all previous units).

Did you know? In Perfect Competition, the firm is a price taker, meaning it can sell all it wants at the market price. Therefore, for a perfectly competitive firm, P = AR = MR.

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Section 5: Profit Concepts (Syllabus 7.5.9, 7.5.10)

Profit is the primary objective of most firms and is the difference between total revenue and total cost.

Formula: \[ Profit = TR - TC \]

A. Economic Cost vs. Accounting Cost

When calculating profit in Economics, we use Economic Cost.

• Accounting Costs (Explicit Costs): Actual payments made to outsiders (wages, rent, materials).
• Implicit Costs (Opportunity Costs): The value of the inputs owned by the firm that are used in production (e.g., the income the owner could have earned working elsewhere).
• Economic Cost = Explicit Costs + Implicit Costs.

B. Types of Profit

1. Normal Profit (NP) (Syllabus 7.5.9)

Definition: The minimum level of profit required to keep the factors of production (especially enterprise/entrepreneurship) in their current use in the long run. It is considered an implicit cost of production.

• It is equal to the firm's total implicit costs (i.e., the opportunity cost of the owner's time and capital).
• If a firm only earns Normal Profit (\(TR = TC\)), it is covering all its explicit costs and its implicit costs, meaning the owner is earning just enough to justify staying in this business instead of moving to the next best alternative.

2. Supernormal Profit (SNP) (Syllabus 7.5.9)

(Also called Abnormal Profit or Economic Profit)

Definition: Any profit earned above normal profit. This happens when Total Revenue (TR) is greater than Total Cost (TC, which includes implicit costs).

Calculation: \[ SNP = TR - Economic\ Cost \]

3. Subnormal Profit (Loss) (Syllabus 7.5.9)

Definition: A situation where Total Revenue (TR) is less than Total Cost (TC), meaning the firm is not even covering its normal profit. The firm is making an economic loss.

C. The Short-Run Shutdown Decision

When a firm is making a subnormal profit, should it close immediately?

Rule: A firm should continue operating in the short run if Total Revenue covers Total Variable Costs (TVC).

• If \(\mathbf{TR \ge TVC}\): The firm covers all variable costs and contributes something towards its fixed costs. It's better to continue producing and minimize losses than shut down, where losses would equal the entire TFC.
• If \(\mathbf{TR < TVC}\): The firm cannot even afford the materials and labour needed to produce. It should shut down immediately, as the additional loss from production is greater than its fixed costs.