Resources
Notes and handouts I write for my students at Sciences Po Paris, in Microeconomics and Mathematics. Free to use and share. If you spot a mistake, tell me. Practice sheets sit under the note they belong to, from starter to upper intermediate.
Microeconomics
Maths for Intermediate Microeconomics
Tutorial 1 companion: derivatives, logs, partials, optimisation, Lagrange, expectation and integrals, each with the essentials, a note and exercises, plus a study plan for the midterm.
Mathematics
Fractions and Exponents: The Algebra Behind Every Problem
The rules for fractions and powers in one place, how they combine, and how to use them to solve equations, take derivatives and work out a demand function.
- Fractions and Exponents Practice: Starter 50 calculations with numbers only: fractions, then powers, negative exponents and roots.
- Fractions and Exponents Practice: Intermediate 58 exercises with letters: algebraic fractions, exponent rules, single powers and solving equations.
- Fractions and Exponents Practice: Upper Intermediate 20 derivatives of fractions and roots, then 11 economics problems with every algebra step shown.
Derivatives: A Refresher
What a derivative measures, the rules you need, and how economists use them: marginal cost, elasticity, optimisation.
- Derivatives Practice: Starter 24 exercises on the definition and the basic rules.
- Derivatives Practice: Intermediate 100 exercises on the product and quotient rules, almost no chain rule.
- Derivatives Practice: Upper Intermediate 20 exercises with the chain rule and second derivatives.
Partial Derivatives and Optimisation in Two Variables
Treat the other variables as constants: marginal utility, MRS, second-order partials, the D test for maxima and minima, and the Problem Set 1 model as a derivative exercise.
- Partial Derivatives Practice 22 exercises in three levels, from first partials to classifying critical points and the redistribution model.
Lagrange Multipliers: Optimisation with Constraints
Tangency, the recipe, and what the multiplier really means: shadow prices, the envelope theorem and complementary slackness.
- Lagrange Multipliers: Practice 20 problems in three levels: numbers only, the standard economic problems, then two constraints, Kuhn-Tucker and the traps.