A growing collection of problems and interactive tools for students working towards graduate study in economics. Try each problem first, then open the worked solution.
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Latest problems
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Cournot duopoly with asymmetric marginal costs
A two-firm Cournot model with different marginal costs — find the equilibrium quantities, market price, and each firm’s profit.
Interactive tools
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Utility maximisation and expenditure minimisation under satiated preferences
An interactive tool for how UMP and EMP behave with satiated preferences: a bliss point, non-binding budgets, and the failure of Walras’ law.
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Utility maximisation and expenditure minimisation under convex preferences
An interactive tool for how UMP and EMP behave under convex preferences: set of optimal bundles is convex.
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Utility maximisation and expenditure minimisation under non-convex preferences
An interactive tool for how utility maximisation and expenditure minimisation behave under non-convex preferences: corner solutions, tied optima, and demand that jumps with prices.