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M16.L02 — Labour-Leisure Choice and Labour Supply

Module: Module 16 — Applications of Consumer Theory Lesson: L02 of 05 Duration: ~30 minutes Level: Intermediate Provenance: University of Utah Intermediate Microeconomics | MIT OCW 14.01

Learning Objective

Derive an individual's labour supply curve from utility maximization under time constraints.

The Labour-Leisure Tradeoff

Assume a worker has T total hours (e.g., 168/week) to allocate between: - Leisure (R) - Labour (L = T - R)

The budget constraint is: wL + V = wT + V Where: - w = hourly wage (e.g., Australia's $23.23 minimum wage) - V = non-labour income

The slope -w shows the opportunity cost of leisure in forgone wages.

Worked Example

Australian context: Consider a worker with: - T = 100 hours/fortnight - V = $200/fortnight (Centrelink payment) - w = $25/hour

  1. If they work 60 hours: Income = 25*60 + 200 = $1700 Leisure = 40 hours

  2. Optimal choice where MRS = w: Maximize U(R, C) s.t. C = w(T-R) + V

At current Australian tax rates (19% above $18,200), the after-tax wage becomes critical.

Common Misconception

"Higher wages always increase labour supply"

Actually, when income effects dominate (at high wages), labour supply may decrease as people "buy" more leisure. Australia's workforce participation rate was 66.6% in Feb 2024 (ABS 6202.0).

Key Takeaways

  • The wage rate is the price of leisure
  • Labour supply curves can bend backward
  • Taxes create a wedge between gross and net wages
  • Australian Fair Work Act sets minimum conditions

Practice

  1. Derive the labour supply curve for U(R,C) = R^0.4*C^0.6
  2. Calculate optimal L for w=\(30, V=\)300, T=80
  3. Graph how a tax rate increase affects labour supply

Further Resources

Provenance: University of Utah Intermediate Microeconomics | MIT OCW 14.01