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Handout 1 - University of Minnesota Department of Economics...

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University of Minnesota Department of Economics Econ 3102: Intermediate Macroeconomics Handout 1 In this handout I would like to go in more detail into the ups and downs of Chapter 4. Specifically, I’ll go over the representative consumer’s problem; the representative firm will be analyzed later on ... 1 The representative consumer’s problem In class we described the representative consumer’s optimization problem as maximizing some utility function U ( C, ‘ ) subject to the budget constraint C = w ( h - ) + π - T. We would certainly like to have C 0. (What would a negative consumption mean, anyway?) Also, we have to abide by the restriction 0 h . Formally, our optimization problem is: max C,‘ U ( C, ‘ ) (1.1) subject to C = w ( h - ) + π - T C 0 0 h. Note that (1.1) is a standard optimization problem. To avoid corner solutions (which are messy and, in my opinion, add too little economics, too much algebra) we will usually assume the Inada conditions hold, which are: U C (0 , ‘ ) = + (1.2) U ( C, 0) = + , (1.3) where U C ( · , · ) and U ( · , · ) are the partial derivatives of the utility function with respect to C and , respectively (i.e., the marginal utilities). It can be shown that under (1.2) and (1.3),
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