Production, Cost and Revenue: Concepts and Formulas
Notes on production, cost and revenue for exams: production function, law of variable proportions, returns to scale, cost curves, revenue concepts and break-even point.
By GK24 Editorial Team· Published · 4 min read
Every firm faces the same three questions: how much output the inputs will yield, what that output costs, and what it earns. The answers are the theory of production, the theory of cost and the theory of revenue, and together they explain why a firm stops expanding at a particular level of output. Exams treat this chapter as a formula chapter, so the safest preparation is to learn each definition with its formula and the shape of its curve.
Production and the factors of production
Production is the creation of utility by combining the four factors of production: land, which earns rent, labour, which earns wages, capital, which earns interest, and enterprise, which earns profit. The relation between physical inputs and physical output is the production function. Output is measured in three ways. Total product is the whole output of a given quantity of the variable factor. Average product is total product divided by the units of the variable factor. Marginal product is the addition to total product from one more unit of the variable factor. Two identities are asked directly: total product is the sum of the marginal products, and marginal product is zero when total product is at its maximum.
The law of variable proportions
In the short run at least one factor, usually plant and machinery, is fixed, so only the proportions of the factors can be changed. The law of variable proportions says that as more units of a variable factor are applied to a fixed factor, marginal product first rises, then falls, and finally becomes negative. This gives three stages: increasing returns, where better utilisation of the fixed factor helps; diminishing returns, where the fixed factor is crowded; and negative returns, where additional units get in each other way. A rational producer stops in the second stage. In the long run every factor can be changed, and the corresponding idea is returns to scale, which may be increasing, constant or decreasing.
The cost concepts
| Concept | Formula | Behaviour as output rises |
|---|---|---|
| Total fixed cost | Cost of the fixed factors | Constant at every level of output, even at zero output |
| Total variable cost | Cost of the variable factors | Zero at zero output, then rises |
| Total cost | TC equals TFC plus TVC | Starts at the level of fixed cost and rises |
| Average fixed cost | AFC equals TFC divided by output | Falls continuously, never touching the output axis |
| Average variable cost | AVC equals TVC divided by output | U shaped: falls, reaches a minimum, then rises |
| Average cost | AC equals TC divided by output, or AFC plus AVC | U shaped, with its minimum to the right of the AVC minimum |
| Marginal cost | MC equals the change in TC divided by the change in output | U shaped; unaffected by fixed cost |
Two properties of marginal cost are examined again and again. Marginal cost depends only on variable cost, because fixed cost does not change with output. And the marginal cost curve cuts both the average variable cost curve and the average cost curve at their lowest points, from below. Beyond the arithmetic, costs are also classified as explicit, which are actual money payments, and implicit, which are the imputed value of the owner own factors, such as rent on his own building or the salary he could have earned elsewhere. Economic cost is the sum of the two, and opportunity cost is the value of the next best alternative given up. A sunk cost is one already incurred and not recoverable, and it should be ignored in a fresh decision.
The revenue concepts
Total revenue is price multiplied by quantity sold. Average revenue is total revenue divided by output, and since that equals the price, the average revenue curve is the demand curve facing the firm. Marginal revenue is the addition to total revenue from selling one more unit. Under perfect competition the firm is a price taker, so price, average revenue and marginal revenue are all equal and the curve is a horizontal line. Under monopoly and monopolistic competition the firm must lower the price to sell more, so average revenue falls and marginal revenue falls faster and lies below it. In cost accounting the same ideas appear as contribution, which is sales minus variable cost, and the profit volume ratio, which is contribution expressed as a percentage of sales.
Equilibrium, break-even and shut-down
A producer is in equilibrium where marginal revenue equals marginal cost and marginal cost is rising at that point; these two conditions together are asked as the condition of producer equilibrium. The break-even point is the output at which total revenue equals total cost, so profit is zero and the firm earns only normal profit. A firm shuts down in the short run when price falls below average variable cost, because then it cannot even cover the cost of the variable factors, and in the long run when price falls below average cost.
Exam Point of View
The questions are definitional and formula based. Expect which cost does not change with output, the shape of the average fixed cost curve, where the marginal cost curve cuts the average cost curve, the formula for marginal cost and marginal revenue, the relation between average revenue and price, and the condition of producer equilibrium. Numerical questions give a cost or sales schedule and ask for marginal cost, average cost, contribution, the profit volume ratio or the break-even output. Banking and state service papers also ask the cost accounting terms: direct and indirect cost, sunk cost, explicit and implicit cost. The traps are treating fixed cost as part of marginal cost, confusing the short-run law of variable proportions with the long-run returns to scale, and assuming marginal revenue equals price in a monopoly, where it is always lower.
Important Facts
| Total cost | TC equals TFC plus TVC |
|---|---|
| Average cost | AC equals TC divided by output, also AFC plus AVC |
| Marginal cost | MC equals change in TC divided by change in output |
| Marginal revenue | MR equals change in TR divided by change in output |
| Average revenue | AR equals TR divided by output, which is the price |
| Perfect competition | Price equals AR equals MR, a horizontal revenue curve |
| Producer equilibrium | MR equals MC, with MC rising at that output |
| Break-even point | Output where total revenue equals total cost |
| Short-run shut-down | Price falls below average variable cost |
| Law of variable proportions | Short-run law; stages of increasing, diminishing and negative returns |
| Returns to scale | Long-run concept; increasing, constant or decreasing |
| Contribution | Sales minus variable cost |
| Profit volume ratio | Contribution divided by sales, in per cent |
| Implicit cost | Imputed value of the owner own factors, such as rent of his own premises |
Practice MCQs on this topic
Which of the following costs remains the same at every level of output in the short run?
- A.Total variable cost
- B.Total fixed cost
- C.Marginal cost
- D.Average cost
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Fixed cost is the payment for factors that cannot be varied in the short run, such as the rent of the factory building, insurance and the salary of permanent staff, and it has to be met even when output is zero, which is why it is also called supplementary or…
Read the full explanation →As the level of output increases, the average fixed cost of a firm
- A.remains constant
- B.rises continuously
- C.falls continuously but never becomes zero
- D.first falls and then rises
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Average fixed cost is total fixed cost divided by output; the numerator is unchanged, so a larger output spreads the same fixed cost over more units.
Read the full explanation →The marginal cost curve cuts the average cost curve at
- A.the minimum point of the average cost curve
- B.the maximum point of the average cost curve
- C.the point where average cost equals average fixed cost
- D.no point at all
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The reason is arithmetic rather than economic: so long as marginal cost is below average cost, each extra unit pulls the average down, and once marginal cost rises above average cost the average must rise, so the two can only be equal where the average is at its lowest.
Read the full explanation →The law of variable proportions operates in which situation?
- A.When all factors of production are increased in the same proportion
- B.When one factor is varied and the others are held fixed
- C.Only in the long run
- D.Only when the firm is in equilibrium
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This is the defining condition of the short run, where plant and machinery cannot be changed, so only the proportion between the variable factor and the fixed factor alters.
Read the full explanation →Under perfect competition, the average revenue of a firm is equal to
- A.total cost
- B.marginal cost only
- C.price and marginal revenue
- D.half the price
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A firm in perfect competition is a price taker because its output is a negligible part of the market, so it can sell any quantity at the ruling price.
Read the full explanation →A producer is in equilibrium when
- A.marginal revenue equals marginal cost and marginal cost is rising
- B.average revenue equals average fixed cost
- C.total revenue is at its maximum
- D.marginal cost is at its minimum
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Both conditions are needed. If marginal revenue exceeds marginal cost the firm gains by producing more, and if marginal cost exceeds marginal revenue it gains by producing less, so profit can be highest only where they are equal; and the equality must occur on the rising part of the marginal…
Read the full explanation →The break-even point of a firm is the level of output at which
- A.total revenue equals total cost
- B.total revenue equals total variable cost
- C.average cost is at its minimum
- D.marginal cost equals average fixed cost
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At that output the firm makes neither profit nor loss in the economic sense and earns only normal profit, since normal profit is already counted in cost as the reward of enterprise.
Read the full explanation →Marginal cost is correctly defined as
- A.total cost divided by total output
- B.the change in total cost divided by the change in output
- C.total fixed cost divided by total output
- D.the change in total revenue divided by the change in output
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Marginal cost is the addition to total cost from producing one more unit, so for a one unit change it is simply the difference between successive values of total cost.
Read the full explanation →Which of the following is an example of an implicit cost?
- A.Wages paid to hired workers
- B.Electricity bill of the factory
- C.Rent of the owner own building used by the firm
- D.Interest paid on a bank loan
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An implicit cost is the imputed value of a factor supplied by the entrepreneur himself, for which no payment leaves the firm; the rent he could have earned by letting out his own premises, the interest on his own capital and the salary he could have drawn elsewhere are the…
Read the full explanation →Returns to scale is a concept that applies to
- A.the short run, when one factor is fixed
- B.the long run, when all factors can be changed
- C.the market period, when output is fixed
- D.only to agriculture
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Returns to scale asks what happens to output when every input is increased in the same proportion, which is possible only in the long run, when the firm can build a bigger plant as well as hire more labour.
Read the full explanation →Indirect cost is that cost incurred by the firm which ________.
- A.has already been incurred and cannot be avoided
- B.can be easily traceable to a product
- C.are common to several products
- D.are aggregate of variable cost
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Costs are classified as direct or indirect by traceability. A direct cost can be attributed wholly to one product, job or process, such as the raw material in a shirt or the wages of the worker who stitches it.
Read the full explanation →A firm has total sales of Rs. 4,00,000 and variable cost of Rs. 2,00,000. If the firm has made profit of Rs. 50,000, then the profit volume ratio of the firm is _______.
- A.50%
- B.30%
- C.20%
- D.40%
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The profit volume ratio measures contribution as a percentage of sales, and contribution is sales minus variable cost.
Read the full explanation →Frequently Asked Questions
What is the difference between fixed cost and variable cost?
Fixed cost is the cost of factors that cannot be changed in the short run, such as rent of the plant, and it stays the same at every output including zero. Variable cost is the cost of factors like raw material and wages of casual labour, and it is zero when output is zero.
Why does the average fixed cost curve never touch the output axis?
Because average fixed cost is total fixed cost divided by output. However large the output, dividing a positive number by it leaves a positive result, so the curve keeps falling towards the axis without ever reaching zero; its shape is a rectangular hyperbola.
Where does the marginal cost curve cut the average cost curve?
At the minimum point of the average cost curve, cutting it from below. The same is true of the average variable cost curve, and the reason is arithmetic: average cost falls while marginal cost is below it and rises once marginal cost is above it.
How is marginal revenue related to price under perfect competition?
They are equal. A firm in perfect competition is a price taker and can sell any quantity at the ruling price, so total revenue rises by exactly the price for each extra unit, which makes price, average revenue and marginal revenue identical.
What is the law of variable proportions?
It is the short-run law that when more units of a variable factor are applied to a fixed factor, the marginal product of the variable factor first increases, then diminishes and finally becomes negative, giving the three stages of increasing, diminishing and negative returns.
What is the break-even point of a firm?
The level of output at which total revenue is exactly equal to total cost, so the firm makes neither profit nor loss and earns only normal profit. In cost accounting it is found by dividing fixed cost by the contribution per unit.
Sources
- Introductory Microeconomics (Class XII), Chapter on Production and Costs — NCERT
- Introductory Microeconomics (Class XII), Chapter on the Theory of the Firm under Perfect Competition — NCERT
