Utility, Wealth, Production: formula sheet

Key formulas

Opportunity cost

Opportunity cost = value of the next best alternative given up

It is the best forgone option only, not the total of all options not chosen.

Central economic problems

What to produce | How to produce | For whom to produce

These three arise in every economy because of scarcity of resources.

Micro vs macro

Micro = individual units | Macro = economy as a whole

Use this to classify any example, such as price of one product (micro) or national income (macro).

Nature of business economics

Science + art; micro in character; pragmatic; mainly normative

It also uses positive analysis, but the normative side is the main focus.

Total utility

TU = MU₁ + MU₂ + ... + MUₙ

TU is the running sum of marginal utilities of all units consumed.

Marginal utility

MUₙ = TUₙ − TUₙ₋₁

For one extra unit. For larger changes use MU = ΔTU ÷ ΔQ.

Relation of MU and TU

MU > 0: TU rises | MU = 0: TU maximum | MU < 0: TU falls

This is the most tested rule in MCQs.

Types of utility

Form, Place, Time, Possession

Match each type with its example: production, transport, storage, transfer of ownership.

Cardinal vs ordinal

Cardinal: measured in utils | Ordinal: ranked by preference

Cardinal is linked with Marshall. Ordinal is linked with Hicks and Allen.

Marginal utility from total utility

MUₙ = TUₙ − TUₙ₋₁

Use when a table of TU is given. For the first unit, MU = TU.

Marginal utility for a large change

MU = ΔTU ÷ ΔQ

Use when quantity changes by more than one unit.

Total utility from marginal utility

TUₙ = MU₁ + MU₂ + … + MUₙ = ΣMU

Add MU values to rebuild TU.

Satiety point

MU = 0 ⇒ TU is maximum

After this point MU is negative and TU falls.

Law in short

Quantity ↑ ⇒ MU ↓ (other things constant)

MU falls first; TU rises at a decreasing rate while MU > 0.

Three features of wealth

Wealth = Utility + Scarcity + Transferability

Under the strict definition, a thing must pass all three tests. Missing any one means it is not wealth. Skills and health fail transferability.

National wealth

National wealth = Personal wealth + Social (collective) wealth

National wealth is the aggregate of what individuals own and what the community or State owns within a country.

Stock vs flow

Wealth = stock (at a point of time); Income = flow (over a period)

Use this to separate wealth from income in questions.

Wealth and welfare

Wealth is a means; welfare is the end

Wealth does not automatically guarantee welfare.

Land and its reward

Land → Rent

Gift of nature, supply fixed for the economy as a whole, passive factor, no cost of production.

Labour and its reward

Labour → Wages

Human effort for payment, active factor, perishable, inseparable from the labourer.

Capital and its reward

Capital → Interest

Man-made wealth used for further production. Supply can be increased by saving and investment.

Entrepreneur and its reward

Entrepreneur → Profit

Organises factors and bears risk. Profit is a residual and can be negative.

Production

Production = creation of utility

Includes form, place, time and service utility.

Production function

Q = f(L, K, ...)

Output depends on inputs and technology. Short run: some inputs fixed. Long run: all variable.

Average product

AP = TP ÷ units of variable input

Output per unit of the variable factor.

Marginal product

MP = change in TP ÷ change in variable input = TPn − TPn−1

Extra output from one more unit of the variable input.

Total product from MP

TP = Σ MP

TP is the running total of all MP values.

Relation of AP and MP

MP > AP: AP rises. MP = AP: AP is at maximum. MP < AP: AP falls.

MP cuts AP at AP's highest point.

Three stages of variable proportions

Stage I: from start to where AP is maximum. Stage II: from max AP to where MP = 0. Stage III: MP < 0.

TP is maximum where MP = 0.

Returns to scale

Increasing: output rises by a larger %. Constant: same %. Decreasing: smaller %.

Compare % rise in output with % rise in all inputs.

Quick revision

• Utility is the want-satisfying power of a good or service.
• Total utility is the sum of satisfaction from all units consumed.
• Marginal utility = change in total utility from one extra unit.
• As you consume more units, marginal utility falls, and this is the law of diminishing marginal utility.
• When marginal utility is zero, total utility is at its maximum.
• Wealth needs utility, scarcity and transferability.
• Factors of production are land, labour, capital and organisation (entrepreneurship).
• Rewards are rent, wages, interest and profit respectively.
• Production function shows the relation between inputs and maximum output.
• Returns to a factor apply when one input varies and others stay fixed.
• Read the question carefully for words like total, marginal, short run and long run.

Common mistakes

• Calling business economics purely macroeconomic. Fix: Remember it is micro in character because it focuses on the firm. Macro is only the background environment.
• Mixing up positive and normative. Fix: Positive states facts ('Inflation is 5%'). Normative gives a judgement or advice ('The firm should cut price').
• Confusing total utility with marginal utility. Fix: TU is the whole satisfaction from all units. MU is only the extra from the last unit. Say it as 'total' versus 'extra'.
• Saying TU falls whenever MU falls. Fix: TU falls only when MU is negative. When MU is positive but falling, TU still rises, at a slower rate.
• Treating TU as falling when MU falls Fix: TU keeps rising as long as MU is positive. It falls only when MU is negative.
• Calculating MU as TU ÷ units Fix: MU is the change in TU for one more unit. TU ÷ units is average utility.
• Treating wealth as only money. Fix: Remember wealth includes all useful, scarce, transferable goods such as land, buildings and machines.
• Calling air or sunlight wealth. Fix: They are not scarce, so they are free goods and not wealth.
• Treating land and capital as the same because both are passive. Fix: Ask if it is a gift of nature or man-made. Nature means land. Made by effort means capital. A tractor is capital, the field is land.
• Saying the supply of land is fixed for every user. Fix: Land is fixed for the economy as a whole. One firm or use can get more land by paying more, taking it from another use.

Exam tips

• Expect direct definition and classification MCQs. Learn the micro vs macro split with one example of each.
• Learn the three central problems (what, how, for whom) in that order, and link each to scarcity.
• For opportunity cost sums, pick only the best forgone alternative, never the total.
• Watch the words 'only', 'always' and 'never'. They often mark wrong options in nature-of-subject questions.
• Expect at least one table question where you must find a missing TU or MU. Practise the subtraction and addition until it is automatic.
• Learn the three-way rule: MU positive, zero and negative, and what each does to TU.
• Memorise one example for each of the four types of utility. Questions usually give a situation and ask you to name the type.
• For cardinal vs ordinal, remember the names: Marshall for cardinal, Hicks and Allen for ordinal.