Every time a textbook says “marginal”, it means “derivative”. A complete guide to differentiation in economics: deriving marginal cost and marginal revenue, why MC cuts AC at its minimum, the MR = MC profit maximisation rule and the second-order condition everyone forgets, elasticity as a derivative, and why airlines sell seats below average cost.
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Mean, Median and Mode: Definitions, Differences and Examples
Statistics · Descriptive StatisticsMean, Median and ModeThe three measures of central tendency — what they are, how to calculate them, and which one to use depending on your data.When economists analyse income data or teachers review exam scores, they need a single number that summarises a whole dataset. That number is called a measure of central tendency — and there are three of them: the mean,...
Type I vs Type II Errors: A Way to Never Confuse Them Again
A false positive and a false negative — everyone mixes them up. The “boy who cried wolf” mnemonic that runs Type I then Type II in order, the trade-off nobody explains, why power = 1−β, and why which error to fear is a values judgement, not a formula.
What a P-Value Actually Means (And the Three Things It Doesn’t)
The p-value is the probability of data this extreme assuming the null is true — not the probability the null is true, not the chance your result was luck, not the probability the alternative holds. The one correct definition, the three seductive wrong ones, and why significant doesn’t mean important.
Standard Deviation vs Standard Error: What’s the Difference?
Standard deviation describes your data; standard error describes your estimate. Here’s the difference, the SE = SD/√n formula that connects them, why only one shrinks with sample size, and the error-bar trap that catches everyone.
Hypothesis Testing in Economics: t-Tests, p-Values, and Statistical Significance
Hypothesis testing explained simply — like a friendly tutor, not a textbook. Learn what t-tests, p-values, and Type I/II errors actually mean, with the Card-Krueger minimum wage case study and worked practice questions for beginners.
Net Present Value (NPV) and Present Value in Economics: Formula, Examples and Investment Decisions
A pound today is worth more than a pound tomorrow — and NPV is the machinery that turns that observation into a decision rule. A complete guide to present value, discounting, the NPV formula, IRR and why it fails, payback period, perpetuities and annuities, the discount rate debate in climate policy, and exam technique for AP and Cambridge A-Level.
How to Read Regression Output: Every Number Explained
Software prints about forty numbers. Roughly six of them matter. Here’s what every number in a regression table actually means — coefficients, standard errors, t-stats, p-values, R², F-stat — with annotated output from R, Stata and Excel, plus the six questions to ask any result.
Compound Interest Formula: Simple vs Compound vs Continuous Compounding with Worked Examples
Einstein probably never called compound interest the eighth wonder of the world — but the mathematics is remarkable enough without the quote. A complete guide to simple interest, compound interest, compounding frequency, the number e, continuous compounding, the Rule of 72, and effective annual rates, with worked examples and exam technique for AP and Cambridge A-Level.
Lagrange Multipliers in Economics: Shadow Prices, the Envelope Theorem, and Kuhn-Tucker Conditions
Every proposition in microeconomics is the solution to the same problem: optimise subject to a constraint. A complete guide to Lagrange multipliers, the envelope theorem, why λ is a shadow price, Kuhn-Tucker conditions, and the duality between utility maximisation and cost minimisation.
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