325_Lecture6_Feb9

325_Lecture6_Feb9 - CONSUMPTION-SAVINGS FRAMEWORK...

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1 C ONSUMPTION- S AVINGS F RAMEWORK (C ONTINUED ) F EBRUARY 9, 2011 February 9, 2011 2 B ASICS Model Structure ± Timeline of events ± Notation ± c 1 :c o n s u m p t i o n i n p e r i o d 1 ± c 2 o n s u m p t i o n i n p e r i o d 2 ± P 1 :n o m i n a l p r i c e o f c o n s u m p t i o n i n p e r i o d 1 ± P 2 o m i n a l p r i c e o f c o n s u m p t i o n i n p e r i o d 2 ± Y 1 o m i n a l i n c o m e i n p e r i o d 1 ( f a l l s f r o m t h e s k y ) ± Y 2 o m i n a l i n c o m e i n p e r i o d 2 ( f a l l s f r o m t h e s k y ) ± A 0 o m i n a l w e a l t h a t t h e b e g i n n i n g o f p e r i o d 1 / e n d o f p e r i o d 0 ± A 1 o m i n a l w e a l t h a t t h e b e g i n n i n g o f p e r i o d 2 / e n d o f p e r i o d 1 ± A 2 o m i n a l w e a l t h a t t h e b e g i n n i n g o f p e r i o d 3 / e n d o f p e r i o d 2 ± i o m i n a l i n t e r e s t r a t e b e t w e e n p e r i o d s ± r :r e a l i n t e r e s t r a t e b e t w e e n p e r i o d s ± Ⱥ 2 e t i n f l a t i o n r a t e b e t w e e n period 1 and period 2 ± y 1 e a l i n c o m e i n p e r i o d 1 ( = Y 1 / P 1 ) ± y 2 e a l i n c o m e i n p e r i o d 2 ( = Y 2 / P 2 ) 21 2 2 11 1 PP P PP S §· ± ± ¨¸ ©¹
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2 February 9, 2011 3 U TILITY Model Structure ± Preferences u ( c 1 , c 2 ) with all the “usual properties” ± Lifetime utility function ± Strictly increasing in c 1 ± Strictly increasing in c 2 ± Diminishing marginal utility in c 1 ± Diminishing marginal utility in c 2 ± Plotted as indifference curves ± Utility side of consumption-savings framework identical to Chapter 1 framework c 1 u(c 1 ,c 2 ) c 2 u(c 1 ,c 2 ) c 2 c 1 February 9, 2011 4 B UDGET C ONSTRAINT(S) ± Suppose again Y “ falls from the sky” ± Y 1 in period 1, Y 2 in period 2 ± Need two budget constraints to describe economic opportunities and possibilities ± One for each period ± Period-1 budget constraint ± Period-2 budget constraint 11 1 1 0 (1 ) P cAY i A ± ±± Total expenditure in period 1: period-1 consumption + wealth to carry into period 2 Total income in period 1: period-1 Y + income from wealth carried into period 1 (inclusive of interest) 22 2 2 1 ) P i A Total expenditure in period 2: period-2 consumption + wealth to carry into period 3 Total income in period 2: period-2 Y + income from wealth carried into period 2 (inclusive of interest) 1 0 1 0 P cAAYi A ± ² ± 2 1 2 1 P A ± Savings during period 1 (a flow) Savings during period 2 (a flow) Asset income during period 1 (a flow) Asset income during period 2 (a flow) DEFINITION: A consumer’s savings during a given period is the change in his wealth during that period can rewrite as can rewrite as
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3 February 9, 2011 5 B UDGET C ONSTRAINT(S) Model Structure ± Adopt a lifetime view of the budget constraint(s) ± All analysis conducted from perspective of beginning of period 1 ±
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This document was uploaded on 11/01/2011 for the course ECON 325 at Maryland.

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325_Lecture6_Feb9 - CONSUMPTION-SAVINGS FRAMEWORK...

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