Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is Yt+1 Ct+1 Ct+2 (1+r) (1+r)² (1+r) Ct + + +...+ Ct+T+1 T+11 (1+r) = Yt + + Yt+2 Yt+T+1 (1+r)² (1+r)ª 2+...+

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.3P
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Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is
Ct+2
Yt+2
Yt+1
(1+r) (1+r)²
(1 + r)²
Ct +
Ct+1
(1 + r)
+
2+...+
Ct+T+1
(1+r)²
\ T = Yt +
+
+...+
Yt+T+1
(1+r)
Transcribed Image Text:Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is Ct+2 Yt+2 Yt+1 (1+r) (1+r)² (1 + r)² Ct + Ct+1 (1 + r) + 2+...+ Ct+T+1 (1+r)² \ T = Yt + + +...+ Yt+T+1 (1+r)
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