Consider the dynamic choice of consumption with in-period utility given by u(c) = ln(c). • It's fairly easy to show that a person with this per-period utility flow who judges a stream (C₁, C2, C3) by U(C1, C2, C3) Au(c₁) + Bu(c₂) + Cu(c3) and faces consumption prices P1, P2, and p3 will split a total budget of S such that = C1= B S A+B+C P2 S A+B+C P3 • If there are only two periods, the results is similar, just replace with C = 0. 1. In(c) is an interesting utility function. Let's talk about it. (a) What shape does it have? (b) When 0 < c < 1, ln(c) is negative. Is that a problem? Is there anything special about negative utility? - C2 = - S A A+B+C P1 C3 = (c) What is it about In(c) that means you'll consume something in all periods (Assuming A, B, C > 0)
Consider the dynamic choice of consumption with in-period utility given by u(c) = ln(c). • It's fairly easy to show that a person with this per-period utility flow who judges a stream (C₁, C2, C3) by U(C1, C2, C3) Au(c₁) + Bu(c₂) + Cu(c3) and faces consumption prices P1, P2, and p3 will split a total budget of S such that = C1= B S A+B+C P2 S A+B+C P3 • If there are only two periods, the results is similar, just replace with C = 0. 1. In(c) is an interesting utility function. Let's talk about it. (a) What shape does it have? (b) When 0 < c < 1, ln(c) is negative. Is that a problem? Is there anything special about negative utility? - C2 = - S A A+B+C P1 C3 = (c) What is it about In(c) that means you'll consume something in all periods (Assuming A, B, C > 0)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the dynamic choice of consumption with in-period utility given by
u(c) = ln(c).
• It's fairly easy to show that a person with this per-period utility flow who
judges a stream (C₁, C2, C3) by U(C₁, C2, C3) = Au(c₁) + Bu(c₂) + Cu(c3)
and faces consumption prices P₁, P2, and p3 will split a total budget of S
such that
S
C1 =
A
A+B+C P1
S
- C₂ = A+B+C P²₂
P2
S
- C3 = A+B+C P3
. If there are only two periods, the results is similar, just replace with C = 0.
1. In(c) is an interesting utility function. Let's talk about it.
(a) What shape does it have?
(b) When 0 < c < 1, ln(c) is negative. Is that a problem? Is there
anything special about negative utility?
(c) What is it about In(c) that means you'll consume something in all
periods (Assuming A, B, C > 0)
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