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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(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...
A
B
X
x1
x1x2
x2
100
100
100 100
Initial Endowment
A
B
X
x1
x1x2
x2
100
100
100 100
Equal consumption in both time periods
A
B
X
x1
x1x2
x2
100
100
100 100
UA
A
B
X
x1
x1x2
x2
100
100
100 100
UA
Slope = -1.1
A
B
X
x1
x1x2
x2
100
100
100 100
UB
A
B
X
x1
x1x2
x2
100
100
100 100
UB
Slope = -1.5
A
B
X
x1
x1x2
x2
100
100
100 100
UA
A
B
X
x1
x1x2
x2
100
100
100 100
UA
Both better off
Q1 revisited
A
B
X
x1
x1x2
x2
100
100
100 100
UA
Contract Curve
A
B
X
x1
x1x2
x2
100
100
100 100
UA
Slope = -(1+ρA) = -1.1
Slope = -(1+ ρB) = -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
