Lesson Plan

• Describe the utility‑maximisation problem and its budget constraint.
• Apply the Lagrangian method to obtain first‑order conditions for optimal consumption.
• Derive Marshallian demand functions for a Cobb‑Douglas utility specification.
• Interpret how a change in price shifts the individual demand curve while holding income constant.
• Analyse the graphical relationship between indifference curves, the budget line, and the optimal bundle.

• Projector and screen
• Whiteboard and markers
• Printed worksheet with utility‑maximisation problems
• Graph paper and calculators for each pair
• Slide deck containing equations and the Cobb‑Douglas example
• Student response clickers (or online poll)

Begin with a quick poll: “What everyday decision reflects a trade‑off between two goods?” Connect responses to the idea of a budget constraint. Review the definition of utility and remind students of the marginal rate of substitution. State that by the end of the lesson they will be able to derive an individual demand curve from first principles.

1. Do‑now (5'): short quiz on budget constraints and basic utility concepts.
2. Mini‑lecture (10'): introduce the utility maximisation problem and the Lagrangian formulation.
3. Guided derivation (15'): work through the first‑order conditions and MRS on the board, checking for understanding.
4. Group activity (15'): students solve the Cobb‑Douglas example, derive \(x_1^*\) and \(x_2^*\) and complete the worksheet.
5. Visualisation (10'): each group sketches indifference curves and the budget line, identifies the tangency point, and labels the resulting demand curve.
6. Formative check (5'): exit‑ticket question – “Explain in one sentence how a price increase affects the derived demand function.”

Summarise the steps from utility maximisation to the Marshallian demand function and emphasise the economic intuition behind the slope of the demand curve. Collect exit tickets and highlight a common misconception to address next class. Assign homework: derive the demand functions for a CES utility function with given parameters.