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+...+
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+...+
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7810ab07-6748-4d32-b0d1-a5d0d459c5f8%2Fd7dab187-9c7b-42d0-83e4-cf165347db86%2Fsohgcro_processed.png&w=3840&q=75)
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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