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Understanding Time Value of Money: Utility Maximization and Decision-Making

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Chapter 19 explores the time value of money, illustrating how future and present values influence personal finance decisions. It delves into important concepts such as present value, future value with interest, and marginal utility per dollar spent on goods. Practical examples demonstrate how to make utility-maximizing choices with limited income while considering opportunity costs of leisure versus work. Real-world applications, such as mortgage refinancing and spending decisions, showcase how to assess costs comprehensively. The chapter contemplates preferences for cash versus non-cash gifts in maximizing personal utility.

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Understanding Time Value of Money: Utility Maximization and Decision-Making

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  1. Utility Maximization Chapter 19

  2. Time Value of $$$ • The value of money in the future, once interest has been considered • Ex- 2 options: A)You could have $10,000 now or B) $10,000 3 years from now. Which is better? • Present Value for both = $10,000 • Future Value A = 10,000 + interest • Future Value B = 10,000

  3. The Value of Time • Both production and consumption take time • By using an hour working, individuals can make $7, $10, $50 etc. • By using time for leisure activities, the individual incurs the opportunity cost of forgone income.

  4. Utility Maximization Rule • When buying 2 goods, the last dollar spent on each product yields the same amount of marginal (extra) utility • ***the consumer is in equilibrium and would be worse off (less total utility) if they altered purchases

  5. Marginal Utility Per Dollar • Used to make purchasing decisions • (Marginal Utility/Price) = MU/price • Choices are influenced by the MU that extra units of product A will yield but also by how many $$ (and how many units of alternative product B) must be given up to obtain added units of A

  6. (3) Product B: Price = $2 (2) Product A: Price = $1 (b) Marginal Utility Per Dollar (MU/Price) (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (a) Marginal Utility, Utils First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 10 8 7 6 5 4 3 24 20 18 16 12 6 4 12 10 9 8 6 3 2 Utility-Maximizing Combination of Products A and B Obtainable with an Income of $10 (1) Unit of Product Compare Marginal Utilities Then Compare Per Dollar - MU/Price Choose the Highest Check Budget - Proceed to Next Item

  7. (3) Product B: Price = $2 (2) Product A: Price = $1 (b) Marginal Utility Per Dollar (MU/Price) (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (a) Marginal Utility, Utils First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 10 8 7 6 5 4 3 24 20 18 16 12 6 4 12 10 9 8 6 3 2 (1) Unit of Product Again, Compare Per Dollar - MU/Price Choose the Highest Buy One of Each – Budget Has $5 Left Proceed to Next Item

  8. (3) Product B: Price = $2 (2) Product A: Price = $1 (b) Marginal Utility Per Dollar (MU/Price) (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (a) Marginal Utility, Utils First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 10 8 7 6 5 4 3 24 20 18 16 12 6 4 12 10 9 8 6 3 2 (1) Unit of Product Again, Compare Per Dollar - MU/Price Buy One More B – Budget Has $3 Left Proceed to Next Item

  9. (3) Product B: Price = $2 (2) Product A: Price = $1 (b) Marginal Utility Per Dollar (MU/Price) (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (a) Marginal Utility, Utils First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 10 8 7 6 5 4 3 24 20 18 16 12 6 4 12 10 9 8 6 3 2 ` (1) Unit of Product Again, Compare Per Dollar - MU/Price Buy One of Each – Budget Exhausted

  10. Do the Math • All $10 have been exhausted and the last dollar spent provides the same marginal utility (8 utils) • 2 units of A ($2) + 4 units of B ($8) = $10 • 2 units of A = 18 utils + 4 units of B (78 utils) • 96 utils

  11. Real World Example • Original mortgage = $140,000 over 30 years at 6.375% interest (fixed rate) • Payment: • Principal and interest= $875 • PMI= $68 • Homeowner’s insurance = $62 • Taxes= 328.34 • Total = 1333.34 • 1333.34 x 360 = $480,002.40

  12. Refinanced Mortgage • 15 years @ 3.3% fixed interest • Payment: • PMI= $68 • Homeowner’s insurance = $62 • Taxes= 337.34 • Principal and interest= 787.66 • Total Payment = $1255 • $1255 x 180 payments = $225,900

  13. Money Saved • If I didn’t refinance… • Still owe 26 years (312 payments @ 1333.34= $416,002.08) • By refinancing: $416,002.08 – 225,900 = • Savings of $190,102.08

  14. Example • Mary is considering a round of golf and a concert. She makes $10 per hour. Golf costs $30 (market price) and a concert costs $40 (market price). Golf takes 4 hours and a concert will take 2 hours. How much is the full price (market price + forgone income) of each event and which should Mary choose?

  15. Problem Solved • Full price of golf = $30 price + 4 hours X $10 • = $70 • Full price of a concert = $40 price + 2 hours x $10 • = $60 Mary should consume more concerts when time is considered and MU is assumed to be the same for both activities

  16. Cash v Noncash Gifts • People generally prefer cash to non-cash gifts because the non-cash gift may not match the recipient’s preferences which would not maximize utility

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