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Buying & Selling: Intertemporal Choice with Labor Supply, Uncertainty, and Applications

This model explores three applications of buying and selling: labor supply, intertemporal choice, and uncertainty. It covers topics such as cashflows, perpetuity, annuity, asset valuation, life cycle problems, and pension planning.

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Buying & Selling: Intertemporal Choice with Labor Supply, Uncertainty, and Applications

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  1. L10 Buying and Selling: Applications

  2. Three Applications Model with real endowments 1. Labor Supply (Labor-Leisure Choice) 2. Intertemporal Choice (Consumption-Savings Choice) 3. Uncertainty (Insurance) (Consumption across states of the world)

  3. Intertemporal Choice • Two periods: Today and Tomorrow • Goods: consumtion today and tomorrow • Endowment: income today and income tomorrow • Possibility of borrowing and lending

  4. Intertemporal Choice

  5. Many Periods • Cashflows

  6. Many Periods • Cashflow • E: T=3, r=100%. Choose: $1 in each of the three period or $8 in the third

  7. Important cashflow: Perpetuity • Gives constant payment x forever • Cashflow

  8. Perpetuity (Example) • You can rent an apartment for $1000 each month (r=0.5%=0.005) • You can buy it P=300.000 • Renting vs buying?

  9. Perpetuity (Example) • Valuate a consol that pays $10,000 per year. (r=5%=0.05) • You inherit $1000,000. How much monthly interest are you going to get ? (r=5%=0.05)

  10. Important cashflow: Annuity • “Tree” that gives constant payment in T following periods • Cashflow

  11. Leasing or Buying A Car • Leasing or buying a car? Lease T=3, x=$800, r=100% or buy P=750 • Take a loan (how much do you pay monthly) Loan=1000, T=3, r=100% and x=?

  12. Asset Valuation: Bonds • Treasury bill: Face, Coupon, Maturity • PV of T-bills (F, c, T) and r

  13. Asset Valuation: Example • T-bond (F=100, c=10, T=6) and r=5%

  14. Life cycle problems • Consumption – savings problem • Pension: • How much to put aside? • How much am I going to get?

  15. Consumption Smoothing • Income: m=100 in the first 40 years • Consumption C during 60 years, • Constant consumption! Find C if r=5%

  16. Pension Plan • You want C=100 when retired (61-80) • How much do you have to save if r=5%,

  17. Pension Plan • You save S=100 (21-60) • How much will you get (per year) if r=5%,

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