Chapter3_BasicModel_011309

Chapter3_BasicModel_011309 - The Basic Model Juan...

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The Basic Model Juan Rubio-Ram°rez Duke University and Federal Reserve Bank of Atlanta January 13, 2009 Juan Rubio-Ram°rez (DUKE) Basic Model January 13, 2009 1 / 26

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Agents Households and ±rms: 1 Households represent the families in the economy. They decide: 1 how much to consume, 2 how much to save, 3 how much to work. 2 Firms represent the production side of the economy: 1 they hire labor and rent capital from households, 2 they use these inputs to manufacture goods, 3 they sell these goods back to the households. For the moment, we ignore the government sector and the relations of the economy with the rest of the world ( closed economy) . Juan Rubio-Ram°rez (DUKE) Basic Model January 13, 2009 2 / 26
Dynamics We want to study evolution of the economy over time. Thus, we need to specify how time moves. Time evolves in discrete periods (a month, a quarter, or a year, etc...). Concrete choice of period will depend on the particular question that we are interested in. The economy lasts for T periods. Later we allow for T = . A typical time period is denoted by t . First, we will deal with deterministic models. Juan Rubio-Ram°rez (DUKE) Basic Model January 13, 2009 3 / 26

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Representative Household Households live for T periods. All households are completely identical. Why? 1 Simpli±es the analysis. 2 Provides insightful answer to many questions. 3 Necessary ±rst step to understand models with heterogeneous households. 4 Justi±cation: complete ±nancial markets+some form of the utility function (CRRA). Then, we will call the household the representative household since it stands in for (²represents³) all other households in the economy. Juan Rubio-Ram°rez (DUKE) Basic Model January 13, 2009 4 / 26
Number of Households There is large number of households in the economy. Each household perceive itself as small relative to the rest of the economy. Households behave competitively. 112 million households in the United States. Bill Gates´net worth \$59 billions in 2008, only around 0.18 percent of the total wealth of households in the U.S.. Probably even less in consumption terms. For convenience we normalize the total number of households to 1 . With our assumption economy-wide and per-capita variables coincide. Juan Rubio-Ram°rez (DUKE) Basic Model January 13, 2009 5 / 26

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Household Preferences Households decide how much to consume and save out of their income. No labor supply decision. Household does not value leisure and hence it works all of its 1 unit of time. c t : household´s consumption at time t . f c t g T t = 0 : paths of consumption. Preferences of households over di/erent paths of consumption f c t g T t = 0 can be represented by a utility function: U ( c 0 , c 1 , . . . , c T ) = u ( c 0 ) + β u ( c 1 ) + β 2 u ( c 2 ) + . . . + β T u ( c T ) = T t = 0 β t u ( c t ) Juan Rubio-Ram°rez (DUKE) Basic Model January 13, 2009 6 / 26
Discount Factor β 2 ( 0 , 1 ) is the time discount factor.

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