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 = – 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 ) = Individual 2: initial U = – U(x 1A,x 2A ) = √x 1A + (1/1.5)√x 2A – U(x 1A,x 2A ) = √85 + (1/1.5)√121 – U(x 1A,x 2A ) =

A B X x1x1 x1x1 x2x2 x2x2 100 Initial Endowment

A B X x1x1 x1x1 x2x2 x2x2 100 Equal consumption in both time periods

A B X x1x1 x1x1 x2x2 x2x2 100 UAUA

A B X x1x1 x1x1 x2x2 x2x2 UAUA Slope = -1.1

A B X x1x1 x1x1 x2x2 x2x2 100 UBUB

A B X x1x1 x1x1 x2x2 x2x2 UBUB Slope = -1.5

A B X x1x1 x1x1 x2x2 x2x2 100 UAUA

A B X x1x1 x1x1 x2x2 x2x2 UAUA Both better off

Q1 revisited

A B X x1x1 x1x1 x2x2 x2x2 100 UAUA Contract Curve

A B X x1x1 x1x1 x2x2 x2x2 100 UAUA Slope = -(1+ρ A ) = -1.1 Slope = -(1+ ρ B ) = -1.5

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? A.⅔ B.0.8 C.There is no discount rate between 0 and 1 which would make the individual indifferent D.0.9 E.There is not enough information to tell

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? A.0.5 B.0.8 C.There is no discount rate between 0 and 1 which would make the individual indifferent D.0.9 E.There is not enough information to tell