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Utility Maximization

Utility Maximization . Chapter 19. 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

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Utility Maximization

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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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