CE_notes - Econ 3102 - Competitive Equilibrium Notes John...

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Econ 3102 - Competitive Equilibrium Notes John Seliski 6/19/11 1 The Economic Agents in our Economy 1.1 Consumers Suppose that there exists a representative consumer in this economy whose preferences over consumption ( C ) and leisure ( ) are represented by the utility function U : R + & 0 ; h ± ! R Assume that: ± C and are both normal goods ± U is continuous, twice-di±erentiable, strictly concave (consumers prefer variety), and U C > 0 ; U > 0 U CC < 0 ; U ‘‘ < 0 In words, the marginal utility of consumption and leisure are assumed to be positive and strictly decreasing. That is, there is diminishing returns to consuming more of the consumption good and leisure. From the above, we can also conclude that U is strictly increasing (consumers prefer more to less) in both its arguments. ± U lim C ! 0 U C = + 1 ; lim ! 0 U = + 1 Both the factor and output markets are assumed to be competitive , so the representative consumer will be a price-taker. That is, the representative consumer will take the price of the consumption good and wages as will be distributed back to the consumer (think of our circular ²ow diagram). In other words, the consumer owns the consumer³s budget constraint in this economy (letting the consumption good be the numeraire) is: C ² wn + ( ³ T ) where C : Consumption good n : Labor units supplied to the factor market w : Real wage rate (consumption units per labor unit) : T : Lump-sum taxes 1
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Thus, given wages w , and taxes T , the problem of the representative consumer is: max C;‘;n U ( C;‘ ) s.t. C wn + ( ± T ) + n h C ² 0 ;‘ ² 0 ;n ² 0 (Non-negativity constraints) where h > 0 is a parameter that determines the upper bound on how much labor/leisure the consumer can feasibly choose. For example, I cannot feasibly work more than 24 hours in one day. Similarly, I cannot enjoy more than 24 hours of leisure time in one day. Note that this problem would make no sense if w h + ( ± T ) < 0 , since that would imply that consumption would always be negative. Also, I assume that
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CE_notes - Econ 3102 - Competitive Equilibrium Notes John...

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