Notes · EconomicsUK · A-Levels

Production, costs and revenue

This chapter connects a firm's inputs to its costs, revenues and profit. It covers production and productivity and the law of diminishing returns in the short run, the shape of the short-run cost curves, economies and diseconomies of scale and the long-run average cost curve, and the revenue concepts and the meaning of normal and supernormal profit that prepare the ground for the theory of the firm.

4 sections~18 min reading time4 competenciesLevel Foundation 1 · Standard 3

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Exam profile

AO1 · Define the short and long run, diminishing returns, the cost and revenue concepts and normal and supernormal profitAO2 · Calculate average, marginal and total cost, revenue and profit from dataAO3 · Analyse why short-run cost curves are U-shaped and how economies of scale shape the LRAC curveAO4 · Evaluate the significance of economies of scale and the role of profit in a market economy

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basic level

AS-Level requires production and productivity, fixed and variable costs, average and marginal cost, and the distinction between normal and supernormal profit.

higher level

The full A-Level expects the link between diminishing returns and the U-shaped cost curves, economies of scale and the LRAC, and the revenue-elasticity relationship.

Depth

Text

Contents · 4 sections

Production, costs and revenue

Production, productivity and the law of diminishing returns#

FoundationAQA 7136 4.1.4DfE GCE Economics - production and productivity

Total product and diminishing marginal returns

Fig. 1As more of the variable factor is added to a fixed factor, total product rises but at a diminishing rate - the marginal product is falling (diminishing marginal returns).

Production is the process of converting inputs (the factors of production) into outputs of goods and services. Productivity measures output per unit of input over a period; the most common measure is labour productivity, output per worker or per hour worked. Higher productivity means more output from the same inputs, which lowers unit costs, and it is the key long-run driver of a country's living standards. It is vital not to confuse the two: production is the total amount produced, whereas productivity is the efficiency with which inputs are turned into output.

The distinction between the short run and the long run is defined by whether factors of production can be varied. In the short run, at least one factor is fixed (typically capital - the size of the factory), so output can only be increased by adding more of the variable factor (typically labour) to the fixed factor. In the long run, all factors are variable - the firm can change the scale of its entire operation, including its capital. This distinction is not about calendar time but about the ability to vary all inputs, and it separates the analysis of diminishing returns (a short-run idea) from returns to scale (a long-run idea).

The law of diminishing returns (more precisely the law of diminishing marginal returns) is a short-run law. It states that as successive units of a variable factor are added to a fixed factor, the marginal product of the variable factor will eventually fall. At first, adding workers to a fixed amount of capital may raise marginal product (as specialisation and better use of the capital take hold), but beyond some point each additional worker adds less to output than the last, because they have less and less of the fixed factor to work with - eventually workers get in each other's way. Note it is the MARGINAL product that falls first; total product still rises, but at a diminishing rate.

Diminishing marginal returns is the reason short-run costs eventually rise, which is developed in the next section, so it underpins the U-shape of the short-run cost curves. It also has evaluative significance: the point at which diminishing returns sets in depends on the state of technology and the flexibility of the fixed factor, and firms can postpone it by investing in more capital - but that is a long-run decision. Do not confuse diminishing marginal returns (a variable factor added to a FIXED factor, in the short run) with diseconomies of scale (all factors varied, in the LONG run); this is one of the most common and costly confusions at A-Level.

\text{Labour productivity} = \frac{\text{Total output}}{\text{Number of workers}}

Labour productivity

Output per worker (or per hour). Rising productivity lowers unit costs and raises living standards; it is distinct from total production.

Worked example

Identifying where diminishing returns set in

In a small bakery with one fixed oven, total output (loaves) with 1, 2, 3, 4 and 5 bakers is 10, 24, 42, 54 and 60. Find the marginal product of each baker and state when diminishing marginal returns begin.

Compute marginal product
MP is the change in total output from each extra baker: 1st = 10; 2nd = 24-10 = 14; 3rd = 42-24 = 18; 4th = 54-42 = 12; 5th = 60-54 = 6.
Find the turning point
Marginal product rises to a peak of 18 at the 3rd baker, then falls to 12 and 6 - so diminishing marginal returns set in from the 4th baker onwards.
Explain the cause
With only one oven (the fixed factor), extra bakers beyond the third have less capital to work with and begin to get in each other's way, so each adds less to output than the last.

Result: Marginal product peaks at the 3rd baker (18 loaves); diminishing marginal returns begin with the 4th baker.

Typical mistakes

Confusing diminishing marginal returns (a short-run law with a fixed factor) with diseconomies of scale (a long-run phenomenon with all factors variable).
Saying total product falls under diminishing returns - total product keeps rising while marginal product is positive; only the RATE of increase falls.

Active revision

Explain, using the law of diminishing marginal returns, why adding more and more workers to a fixed-size kitchen eventually raises output by smaller and smaller amounts.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for economics (Department for Education) · AQA A-level Economics 7136 specification (AQA)

Short-run costs: fixed, variable, average and marginal#

StandardAQA 7136 4.1.4DfE GCE Economics - costs of production

Short-run cost curves

Fig. 2MC cuts AVC and ATC at their minimum points. AVC reaches its minimum before ATC because average fixed cost falls throughout, narrowing the gap between the two averages.

In the short run, a firm's total costs split into fixed and variable costs. Total fixed costs (TFC) do not vary with output - rent, insurance, loan interest, salaried management - and must be paid even if output is zero. Total variable costs (TVC) vary directly with output - raw materials, energy, wages of hourly workers - and are zero when output is zero. Total cost is their sum, TC = TFC + TVC. From these come the average concepts: average fixed cost (AFC = TFC/Q) falls continuously as output rises because a fixed sum is spread over more units ('spreading the overheads'); average variable cost (AVC = TVC/Q); and average total cost (ATC = TC/Q = AFC + AVC), the cost per unit of output.

Marginal cost (MC) is the addition to total cost of producing one more unit, MC = change in TC / change in Q. Because fixed costs do not change with output, marginal cost depends only on variable cost. Marginal cost is the single most important cost concept in the theory of the firm, because a profit-maximising firm decides how much to produce by comparing marginal cost with marginal revenue.

The short-run average and marginal cost curves are U-shaped, and the reason is diminishing marginal returns. At low output, adding variable factors raises marginal product, so each extra unit of output requires less additional input and marginal cost falls; once diminishing marginal returns set in, marginal product falls, so each extra unit requires more input and marginal cost rises - the MC curve turns upward. The average variable and average total cost curves are U-shaped for the same underlying reason, and AFC falls throughout, so the gap between ATC and AVC (which equals AFC) narrows as output rises.

A precise geometric relationship links the curves and is frequently tested. The marginal cost curve cuts both the average variable cost curve and the average total cost curve at their lowest points. The logic is the marginal-average rule: while marginal cost is below average cost it is pulling the average down; while marginal cost is above average cost it is pulling the average up; so the average is at its minimum exactly where marginal cost equals it. Because AFC falls continuously, AVC reaches its minimum at a lower output than ATC, so MC cuts AVC to the left of where it cuts ATC. Drawing this relationship correctly - MC through the minima of AVC and ATC - is essential.

ATC = \frac{TC}{Q} = AFC + AVC, \qquad AFC = \frac{TFC}{Q}

Average costs

Average total cost is total cost per unit and equals average fixed plus average variable cost. AFC falls continuously as fixed costs are spread over more output.

MC = \frac{\Delta TC}{\Delta Q}

Marginal cost

The cost of producing one more unit. Because fixed costs do not change with output, MC reflects only variable cost, and it cuts AVC and ATC at their minima.

Worked example

Building the cost table

A firm has total fixed costs of 60 pounds. Its total cost at outputs of 0, 1, 2, 3 and 4 units is 60, 90, 110, 138 and 180 pounds. Find the marginal cost of each unit and the ATC at 4 units.

Marginal cost
MC is the change in total cost per unit: 1st = 90-60 = 30; 2nd = 110-90 = 20; 3rd = 138-110 = 28; 4th = 180-138 = 42. MC falls then rises - the U-shape.
Average total cost at 4 units
ATC = TC/Q = 180/4 = 45 pounds per unit.
Check the split
At 4 units, TVC = TC - TFC = 180 - 60 = 120, so AVC = 120/4 = 30 and AFC = 60/4 = 15; indeed ATC = AFC + AVC = 15 + 30 = 45.

Result: Marginal cost is 30, 20, 28 and 42 pounds (U-shaped); ATC at 4 units is 45 pounds, split into AFC 15 and AVC 30.

Typical mistakes

Drawing MC cutting the averages anywhere other than at their minimum points.
Forgetting that AFC falls continuously - it never turns up, which is why ATC and AVC converge as output rises.

Active revision

A firm's total fixed cost is 200 pounds. Complete a short cost analysis: at 100 units of output with total variable cost of 300 pounds, calculate AFC, AVC and ATC, and explain what happens to AFC as output rises.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for economics (Department for Education) · AQA A-level Economics 7136 specification (AQA)

Long-run costs, economies and diseconomies of scale#

StandardAQA 7136 4.1.4DfE GCE Economics - economies and diseconomies of scale

The long-run average cost curve

Fig. 3Economies of scale pull LRAC down; beyond the minimum efficient scale (MES) it flattens. Diseconomies, if present, would eventually turn it up.

In the long run all factors are variable, so the firm can change the scale of its whole operation. The long-run average cost (LRAC) curve shows the lowest average cost at which each level of output can be produced when the firm is free to choose the best combination and scale of all its factors; it is drawn as an envelope beneath a series of short-run ATC curves, one for each possible plant size. Its shape is governed not by diminishing returns (a short-run idea) but by returns to scale - what happens to output when ALL inputs are increased together.

Economies of scale are the cost advantages that a firm gains as it increases its scale of output, causing long-run average cost to fall. Internal economies (arising within the firm as it grows) are conventionally grouped as: technical (larger, more efficient capital and the specialisation of labour and machinery); purchasing or bulk-buying (discounts on large orders); managerial (employing specialist managers); financial (borrowing more cheaply); marketing (spreading advertising costs over more units); and risk-bearing (diversifying products or markets). External economies arise from the growth of the whole industry rather than the individual firm - a skilled local labour pool, specialist suppliers or shared infrastructure - and lower costs for all firms in the industry.

Diseconomies of scale are the cost disadvantages of becoming too large, causing long-run average cost to rise beyond some point. They are usually managerial and behavioural: coordination and communication become harder in a very large organisation, control is weakened, and workers may become alienated and demotivated, lowering productivity. The minimum efficient scale (MES) is the lowest level of output at which the firm exhausts its economies of scale and reaches the minimum LRAC; its size relative to the market matters greatly for market structure, because a large MES relative to demand means only a few firms can operate efficiently, tending towards oligopoly or monopoly.

The LRAC curve is therefore typically drawn U-shaped or, more realistically for many industries, L-shaped - falling as economies of scale are reaped, then flattening out over a long range of output once the MES is reached, with diseconomies of scale (the upturn) often weak or absent. The significance is evaluative: substantial economies of scale can make large firms more cost-efficient than small ones, which is a key argument in the monopoly debate (large firms may pass lower costs on as lower prices), but the size of these economies varies enormously by industry, and diseconomies set a limit. Whether growth lowers average cost 'depends on' the industry's cost structure and the MES.

Worked example

Economies of scale in numbers

A firm doubles all its inputs from 10 to 20 units and finds output rises from 100 to 240 units, while total cost rises from 500 to 900 pounds. Does it enjoy economies of scale?

Check returns to scale
Inputs doubled (x2) but output more than doubled (100 to 240, x2.4) - the firm shows increasing returns to scale.
Compute average cost before and after
Before: ATC = 500/100 = 5 pounds per unit. After: ATC = 900/240 = 3.75 pounds per unit.
Conclude
Average cost has fallen from 5 to 3.75 pounds as scale increased, so the firm is enjoying economies of scale over this range of output.

Result: Yes - output more than doubles when inputs double and average cost falls from 5 to 3.75 pounds, showing economies of scale.

Typical mistakes

Confusing economies of scale (a long-run, all-factors-variable fall in average cost) with increasing marginal returns (a short-run idea).
Attributing diseconomies of scale to diminishing returns - diseconomies are managerial/coordination problems in the long run, not a fixed factor.

Active revision

Explain why a large supermarket chain can achieve a lower average cost than a small independent shop, and evaluate whether growth always lowers a firm's average costs.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for economics (Department for Education) · AQA A-level Economics 7136 specification (AQA)

Revenue, elasticity and the concept of profit#

StandardAQA 7136 4.1.4DfE GCE Economics - revenue and profit

Average and marginal revenue for a firm with market power

Fig. 4For a downward-sloping demand curve, MR lies below AR and falls twice as steeply. Total revenue is maximised where MR = 0, which is where demand is unit elastic.

Revenue is the money a firm receives from selling its output. Total revenue (TR) is price times quantity, TR = P x Q. Average revenue (AR) is revenue per unit, AR = TR/Q, which equals the price - so the demand curve facing a firm is also its average revenue curve. Marginal revenue (MR) is the addition to total revenue from selling one more unit, MR = change in TR / change in Q. For a firm that can sell as much as it likes at the going price (a price taker in perfect competition), AR and MR are equal and constant (a horizontal line). For a firm facing a downward-sloping demand curve (one with market power), MR lies below AR and falls twice as steeply, because to sell an extra unit the firm must lower the price on all units.

There is a precise relationship between marginal revenue, total revenue and the price elasticity of demand along a straight-line demand curve. Where demand is price elastic (the upper part of the curve), MR is positive and cutting price raises total revenue; where demand is unit elastic, MR is zero and total revenue is at its maximum; where demand is inelastic (the lower part), MR is negative and cutting price lowers total revenue. A profit-maximising firm will therefore never knowingly produce where demand is inelastic, because it could raise revenue and cut costs by producing less.

Profit is the reward to enterprise and the difference between total revenue and total cost, profit = TR - TC. Economists define costs to include the opportunity cost of all resources, including a normal return to the entrepreneur, so 'total cost' includes normal profit. This leads to the crucial distinction between normal and supernormal profit. Normal profit is the minimum reward required to keep the entrepreneur supplying their enterprise in this industry - just enough to cover the opportunity cost of not using their resources elsewhere; it is treated as a cost of production. Supernormal (or abnormal) profit is any profit above normal profit - the excess of total revenue over total cost including normal profit.

The distinction is central to the theory of the firm because supernormal profit is the signal that attracts new entrants to a competitive market and, where entry is possible, competes the supernormal profit away in the long run. Profit performs vital functions in a market economy: it is a signal that guides resources towards products consumers value (the signalling role), an incentive to enterprise, risk-taking and efficiency, and a source of retained earnings to finance investment and innovation. The role and the level of profit are, however, contested - very high supernormal profits may indicate market power and be criticised on equity grounds - which links directly to the analysis of market structures and of monopoly.

TR = P \times Q, \qquad AR = \frac{TR}{Q} = P, \qquad MR = \frac{\Delta TR}{\Delta Q}

Revenue concepts

Average revenue equals price, so the demand curve is the AR curve. For a downward-sloping demand curve, MR lies below AR.

\text{Profit} = TR - TC

Profit

Since economic cost includes normal profit, supernormal (abnormal) profit is any profit above normal - the excess of TR over TC including the entrepreneur's opportunity cost.

Worked example

Revenue maximisation and profit

A firm faces demand P = 12 - Q and has total costs TC = 10 + 2Q. Find the output that maximises total revenue and the profit at that output.

Total and marginal revenue
TR = P x Q = (12 - Q)Q = 12Q - Q^2, so MR = 12 - 2Q. Total revenue is maximised where MR = 0, that is 12 - 2Q = 0, giving Q = 6.
Compute TR at Q = 6
P = 12 - 6 = 6, so TR = 6 x 6 = 36 pounds; this is the maximum total revenue, where demand is unit elastic (PED = 1).
Compute profit at Q = 6
TC = 10 + 2(6) = 22 pounds. Profit = TR - TC = 36 - 22 = 14 pounds. Note this is the revenue-maximising output, not necessarily the profit-maximising one.

Result: Total revenue is maximised at Q = 6 (TR = 36 pounds, PED = 1); profit there is 14 pounds - a reminder that revenue maximisation and profit maximisation differ.

Typical mistakes

Treating normal profit as zero profit - normal profit is the opportunity-cost reward that is included in total cost.
Drawing MR with the same slope as AR - for a linear demand curve MR falls twice as steeply and hits zero at half the quantity.

Active revision

A firm's demand curve is P = 12 - Q. Derive its total and marginal revenue, find the output that maximises total revenue, and state the price elasticity of demand at that output.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for economics (Department for Education) · AQA A-level Economics 7136 specification (AQA)

References & sources

Sources

Department for Education

GCE AS and A level subject content for economics

AQA

AQA A-level Economics 7136 specification

Production, costs and revenue

4 sections~18 min reading time4 competenciesLevel Foundation 1 · Standard 3

Production, costs and revenue

Key points

Identifying where diminishing returns set in

Key points

Building the cost table

Key points

Economies of scale in numbers

Key points

Revenue maximisation and profit

Sources

Production, costs and revenue

Key points

Identifying where diminishing returns set in

Key points

Building the cost table

Key points

Economies of scale in numbers

Key points

Revenue maximisation and profit

Sources