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(a) u(c) u" (c(t)) c'(t) = (B − y) u'(c(t)). For the remainder of this question, the utility function u(c) is given, for c > 0, by = c¹-0 differential equation in c(t): - 0' 1 where 0 << 1 is a constant and 3 = (1 - 0)y. (b) Show that the differential equation found in part (a) may be written as c'(t)= k c(t), where k = (7-3)/0, and solve this equation for the stationary path c(t).

(a) u(c) u" (c(t)) c'(t) = (B − y) u'(c(t)). For the remainder of this question, the utility function u(c) is given, for c > 0, by = c¹-0 differential equation in c(t): - 0' 1 where 0 << 1 is a constant and 3 = (1 - 0)y. (b) Show that the differential equation found in part (a) may be written as c'(t)= k c(t), where k = (7-3)/0, and solve this equation for the stationary path c(t).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) u(c) u" (c(t)) c'(t) = (3-y)u'(c(t)). For the remainder of this question, the utility function u(c) c > 0, by differential equation in c(t): = c²-0 given, for ·0' where 0 << 1 is a constant and 3 ‡ (1 - 0)y. (b) Show that the differential equation found in part (a) may be written as c'(t) = к c(t), where ‹ = (y − ß)/0, and solve this equation for the stationary path c(t).
Transcribed Image Text:(a) u(c) u" (c(t)) c'(t) = (3-y)u'(c(t)). For the remainder of this question, the utility function u(c) c > 0, by differential equation in c(t): = c²-0 given, for ·0' where 0 << 1 is a constant and 3 ‡ (1 - 0)y. (b) Show that the differential equation found in part (a) may be written as c'(t) = к c(t), where ‹ = (y − ß)/0, and solve this equation for the stationary path c(t).
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