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M16.L01 — Intertemporal Choice: Saving and Borrowing

Module: Module 16 — Applications of Consumer Theory Lesson: L01 of 05 Duration: ~30 minutes Level: Intermediate Provenance: Intermediate Microeconomics with Excel (Barreto) | Principles of Microeconomics (Curtis and Irvine)

Learning Objective

Analyze consumption decisions across time periods using the two-period budget constraint.

Intertemporal Budget Constraint

The two-period budget constraint shows the tradeoff between present (c₁) and future consumption (c₂):

c₁ + c₂/(1+r) = m₁ + m₂/(1+r)

Where: - r = interest rate - m₁, m₂ = income in periods 1 and 2

In Australia (RBA cash rate target 4.35% as of March 2024), this means $1 saved today becomes $1.0435 next year. The slope of the budget line is -(1+r), showing the opportunity cost of current consumption.

Worked Example

Australian context: Suppose an Australian worker earns $50,000 this year (m₁) and $55,000 next year (m₂) with r=5%.

  1. Maximum c₁ if they borrow against all future income: c₁ = m₁ + m₂/(1+r) = 50,000 + 55,000/1.05 ≈ $102,381

  2. Maximum c₂ if they save all current income: c₂ = m₁(1+r) + m₂ = 50,000*1.05 + 55,000 = $107,500

  3. Optimal choice where MRS = (1+r)

Common Misconception

"Higher interest rates always make people save more"

Actually, for borrowers, higher rates may reduce saving as the cost of current consumption rises. In Australia, household saving ratio fell to 3.2% in Q3 2023 (ABS 5206.0) despite rate rises.

Key Takeaways

  • The endowment point (m₁,m₂) shows income without borrowing/saving
  • Interest rates represent the price of current vs future consumption
  • Borrowers and savers are affected differently by rate changes
  • Revealed preference can show time consistency in choices

Practice

  1. Derive the slope of the budget line from c₁ + c₂/(1+r) = m₁ + m₂/(1+r)
  2. Calculate maximum c₁ and c₂ for m₁=\(40k, m₂=\)45k, r=4%
  3. Graph how a rate rise affects a borrower vs saver

Further Resources

Provenance: Intermediate Microeconomics with Excel (Barreto) | Principles of Microeconomics (Curtis and Irvine)