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tutorial3questions

# tutorial3questions - optimal consumption and leisure...

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EC2102 Macroeconomic Analysis I Tutorial 3, Week 6 (February 14-18, 2011) Question 1 Consider an economy with a two-period lived representative agent. This agent has h units of time each period, which can be either spent working or on leisure, and this agent°s utility function is u ( C t ; l t ) , where C t and l t are consumption and leisure in time period t , t = 1 ; 2 : Let w t denote the real wage rate at time period t , t = 1 ; 2 , and let r denote the real interest rate between time periods 1 and 2. ( i ) Write down the per-period budget constraints of the representative agent. Now rewrite the two per-period budget constraints to obtain the representative agent°s lifetime budget constraint. ( ii ) Express C 1 as a function of ( C 2 ; l 1 ; l 2 ) , and set up the representative agent°s utility maximization problem. ( iii ) Derive the First Order Conditions to the representative agent°s utility maxi- mization problem laid out in part ( ii ) . ( iv ) Manipulate the First Order Conditions to show that the representative agent°s optimal consumption and leisure choices are such that the following conditions hold:

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Unformatted text preview: optimal consumption and leisure choices are such that the following conditions hold: & u 1 ( C & 1 ; l & 1 ) &u 1 ( C & 2 ; l & 2 ) = & (1 + r ) ( I ) & u 2 ( C & 1 ; l & 1 ) u 1 ( C & 1 ; l & 1 ) = & w 1 ( II ) & u 2 ( C & 2 ; l & 2 ) u 1 ( C & 2 ; l & 2 ) = & w 2 ( III ) ( v ) Explain the economic interpretations of equations ( I ) to ( III ) ? 1 Question 2 (This is a past-year &nal exam question) You are eating your breakfast and reading the newspaper one morning when you came across this sentence which made you thoughtful: ±For a fully-funded social security system, either it does not bind and does not make any di/erence, or it binds and people are worse o/.² Explain what this sentence means with the aid of a graph. ( Hint : First explain what a fully-funded social security system is, and then explain how people³s consumption decisions are a/ected.) 2...
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