Economics is multivariable: output depends on labour and capital, utility on every good at once. The partial derivative is how you isolate one effect while holding the rest fixed. A complete guide: marginal products and utilities, the marginal rate of substitution, second-order and cross-partials, multivariable optimisation, the chain rule, and what the cross-partial says about automation and wages.
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How to Interpret Log Coefficients in Regression: The Four Rules
Log-log, log-level, level-log, level-level — what each regression coefficient actually means, why economists take logs of everything, and when the ×100 shortcut breaks. With worked examples and practice questions.
Hypothesis Testing: A Complete Step-by-Step Guide with Examples
Hypothesis testing only clicks once you've run the five steps yourself, repeatedly, on new scenarios. The Statistics Made Simple Practice Questions workbook has dozens of worked hypothesis tests with full mark schemes. Statistics · Hypothesis Testing Hypothesis Testing A complete step-by-step guide — from stating your hypotheses to reaching a conclusion, with worked examples from economics and...
The Cobb-Douglas Production Function: Returns to Scale, Elasticity and Cost Minimisation
The exponents in Q = AL^α K^β are not just parameters — they are output elasticities, they sum to the returns to scale, and under competition they equal income shares. A complete guide to the Cobb-Douglas production function: marginal products, diminishing returns vs returns to scale, cost minimisation, Solow’s growth accounting, and the declining labour share — with worked examples and exam technique.
Confidence Intervals Explained: Definition, Formula and How to Interpret Them
The interpretation trap in this post catches almost every student at least once. The Statistics Made Simple Practice Questions workbook has interval-construction and interpretation questions with full worked answers. Statistics · Estimation Confidence Intervals Explained Point estimates give you one number — confidence intervals tell you how much to trust it. Here's exactly what they mean and...
Game Theory and Nash Equilibrium: Strategic Decision-Making in Economics
Game theory explained simply — dominant strategies, Nash equilibrium, the Prisoner’s Dilemma, and why OPEC keeps cheating on oil quotas. A beginner-friendly guide with real examples, payoff matrices, the OPEC case study, and practice questions.
Consumer Surplus and Producer Surplus: Integration, Welfare Triangles and Policy Applications
Every time you would have happily paid more than you did, you pocketed consumer surplus. A complete guide to measuring welfare with integration: consumer and producer surplus, total surplus and market efficiency, deadweight loss, why tax loss grows with the square of the rate, and non-linear demand curves — with worked examples and exam technique.
What is Game Theory? Definition, Examples and Applications in Economics
Mathematical Economics · Game TheoryWhat is Game Theory?A complete guide to strategic decision-making — how economists model the choices of rational players when outcomes depend on what everyone else does.Think about the last time you negotiated a price, chose a lane on the motorway, or decided whether to study harder than your classmates. In each situation, the best choice for you depended not...
P-Value Explained: What It Means and How to Interpret It Correctly
P-values are the most tested, most misread concept on any statistics exam. The Statistics Made Simple Practice Questions workbook has over a hundred hypothesis-testing questions built to catch every one of the classic misreadings. Statistics · Hypothesis Testing The P-Value Explained The most misunderstood concept in all of statistics — what p-values actually mean, what they don't mean, and how...
Normal Distribution Explained: Properties, Z-Scores and Real-World Examples
Z-scores and the normal table look intimidating the first time and become completely mechanical by the tenth. The Statistics Made Simple Practice Questions workbook has a full chapter of normal distribution problems to get you there. Statistics · Probability Distributions Normal Distribution Explained Why the bell curve appears everywhere in nature, economics and social science — and how to use...
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