(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).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 2CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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