Lecture_6_February 18A

# Lecture_6_February 18A - CONSUMPTION-SAVINGS...

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C ONSUMPTION- S AVINGS M ODEL (C ONTINUED ) F EBRUARY 18, 2010

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February 18, 2010 2 C ONSUMER O PTIMIZATION The Graphics of the Consumption-Savings Model Consumer’s decision problem: maximize lifetime utility subject to lifetime budget constraint bring together both cost side and benefit side Choose c 1 and c 2 subject to Plot budget line Superimpose indifference map At the optimal choice 2 2 2 1 1 1 11 P c Y Pc Y ii  c 1 c 2 slope = -(1+ i )/(1+ π 2 ) optimal choice ** 1 1 2 2 1 2 2 ( , ) 1 ( , ) 1 u c c i u c c CONSUMPTION-SAVINGS OPTIMALITY CONDITION - A key building block of modern macro models MRS (between consumption in consecutive time periods) price ratio (across consecutive time periods) Derive consumption-leisure optimality condition using Lagrange analysis
February 18, 2010 3 L AGRANGE A NALYSIS The Mathematics of the Consumption-Savings Model Apply Lagrange tools to consumption-savings optimization Objective function: u ( c 1 , c 2 ) Constraint: Step 1: Construct Lagrange function Step 2: Compute first-order conditions with respect to c 1 , c 2 , λ Step 3: Solve (with focus on eliminating multiplier) 2 2 2 1 2 1 1 1 ( , ) 0 11 Y Pc g c c Y ii  2 2 2 1 2 1 2 1 1 1 ( , , ) ( , ) Y P c L c c u c c Y     ** 1 1 2 2 1 2 2 ( , ) 1 ( , ) 1 u c c i u c c CONSUMPTION-SAVINGS OPTIMALITY CONDITION MRS (between consumption in consecutive time periods) price ratio (across consecutive time periods)

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February 18, 2010 4 S AVINGS AND A SSET P OSITIONS Macro Fundamentals Definition: A consumer’s savings during a given time period is the change in his wealth during that time period Assets/wealth (whether positive or negative) are a means for “transferring income over time” c 1 c 2 slope = -(1+ i )/(1+ π 2 ) Y 1 / P 1 Y 2 / P 2 (continuing to assume A 0 = 0) optimal choice Optimal c 1 > Y 1 / P 1 thus consumer is in debt at the end of period 1 (i.e., period-1 savings is negative) c 1 c 2 slope = -(1+ i )/(1+ π 2 ) Y 1 / P 1 Y 2 / P 2 optimal choice OR Optimal c 1 < Y 1 / P 1 thus consumer has positive wealth at the end of period 1 (i.e., period-1 savings is positive) Consumer borrowed during period 1 Consumer saved during period 1
February 18, 2010 5 A SSESSING THE C REDIT C RUNCH Current Events c 1 c 2 slope = -(1+ i )/(1+ π 2 ) Y 1 / P 1 Y 2 / P 2 (continuing to assume A 0 = 0) optimal choice Optimal c 1 > Y 1 / P 1 thus consumer is in debt at the end of period 1 (i.e., period-1 savings is negative) c 1 c 2 slope = -(1+ i )/(1+ π 2 ) Y 1 / P 1 Y 2 / P 2 optimal choice OR Optimal c 1 < Y 1 / P 1 thus consumer has positive wealth at the end of period 1 (i.e., period-1 savings is positive) Consumer borrowed during period 1 Consumer saved during period 1 Use this framework to analyze the channel by which financial market problems have been affecting consumption activity

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February 18, 2010 6 F ISHER E QUATION Macro Fundamentals Nominal interest rate measured in dollars Real interest rate
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## This note was uploaded on 03/08/2011 for the course ECON 602 taught by Professor Chugh during the Spring '11 term at Johns Hopkins.

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Lecture_6_February 18A - CONSUMPTION-SAVINGS...

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