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Tutorial 7

Tutorial 7. Q1. Would either individual be prepared to swap their initial endowment for consumption of 85 in Period 1 and 121 in period 2? Individual 1: initial U = 19.0909... U(x 1A ,x 2A ) = √x 1A + (1/1.1)√x 2A U(x 1A ,x 2A ) = √85 + (1/1.1)√121 U(x 1A ,x 2A ) = 19.2195...

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Tutorial 7

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  1. Tutorial 7

  2. Q1 • Would either individual be prepared to swap their initial endowment for consumption of 85 in Period 1 and 121 in period 2? • Individual 1: initial U = 19.0909... • U(x1A,x2A) = √x1A + (1/1.1)√x2A • U(x1A,x2A) = √85 + (1/1.1)√121 • U(x1A,x2A) = 19.2195... • Individual 2: initial U = 16.6666... • U(x1A,x2A) = √x1A + (1/1.5)√x2A • U(x1A,x2A) = √85 + (1/1.5)√121 • U(x1A,x2A) = 16.5529...

  3. x1 100 B x2 Initial Endowment 100 X 100 x2 A x1 100

  4. x1 100 B x2 Equal consumption in both time periods 100 X 100 x2 A x1 100

  5. x1 100 B x2 100 X 100 UA x2 A x1 100

  6. x1 100 B x2 100 X 100 UA Slope = -1.1 x2 A x1 100

  7. x1 100 B x2 UB 100 X 100 x2 A x1 100

  8. x1 100 B x2 UB 100 X 100 Slope = -1.5 x2 A x1 100

  9. x1 100 B x2 100 X 100 UA x2 A x1 100

  10. x1 100 B x2 Both better off 100 X 100 UA x2 A x1 100

  11. Q1 revisited

  12. x1 100 B x2 Contract Curve 100 X 100 UA x2 A x1 100

  13. x1 100 B x2 Slope = -(1+ρA) = -1.1 100 X 100 UA Slope = -(1+ ρB) = -1.5 x2 A x1 100

  14. Preamble: Consider an inter-temporal choice problem with two periods where an individual's preferences over consumption, c1 and c2, in two periods 1 and 2 is given by U(c1, c2)=u(c1) + ρu(c2) where ρ is the individual's discount rate (which should lie between 0 and 1) and u(c) is the square root of c (that is, u(c) = √c).The first income stream gives 36 in the first period and 1 in the second; the second income stream gives 16 in the first period and 16 in the second. Question 21: What discount rate (if any between 0 and 1) would make the individual indifferent between these two streams of consumption? ⅔ 0.8 There is no discount rate between 0 and 1 which would make the individual indifferent 0.9 There is not enough information to tell

  15. Preamble: Consider an inter-temporal choice problem with two periods where an individual's preferences over consumption, c1 and c2, in two periods 1 and 2 is given by U(c1, c2)=u(c1) + u(c2)/(1+ ρ) where ρ is the individual's discount rate (which should lie between 0 and 1) and u(c) is the square root of c (that is, u(c) = √c).The first consumption stream gives 36 in the first period and 1 in the second; the second consumption stream gives 16 in the first period and 16 in the second. Question 21: What discount rate (if any between 0 and 1) would make the individual indifferent between these two streams of consumption? 0.5 0.8 There is no discount rate between 0 and 1 which would make the individual indifferent 0.9 There is not enough information to tell

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