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Unformatted text preview: Econ 3102: Intermediate Macroeconomics Homework #3 Answer Key 1 Problems (65 points) Exercise 1 (30 points) Consider a two-period economy where we have a representative consumer, a representative &rm, and a gov- ernment. The representative consumer derives utility from a consumption and leisure in period 1 (denoted by C 1 , ‘ 1 , respectively), and consumption and leisure in period 2 ( C 2 , ‘ 2 ), according to the utility function U ( C 1 ;‘ 1 ;C 2 ;‘ 2 ) . The consumer¡s time endowment consists of & h hours each period, which she can devote either to work or leisure. If she decides to work, she supplies labor to the representative &rm and earns wage rates w 1 (for period 1 labor) and w 2 (for period 2 labor) per hour worked. She also enjoys a dividend income & t and has to pay a lump-sum tax to the government of size ¡ t , where t = 1 ; 2 . The representative consumer can save in the form of physical capital and government bonds. The representative consumer rents capital to the representative &rm. Capital depreciates at the rate ¢ 2 [0 ; 1] after use. The consumer is endowed with & k 1 > units of capital in the &rst period. The representative &rm rents capital and hires labor to produce output according to a time-invariant pro- duction function given by Y t = z t F ( K t ;N t ) where z t is total factor productivity, K t denotes capital input and N t denotes labor input. Finally, the government collects T t in taxes and issues bonds B in the &rst period to &nance expendi- tures measured by G t , for t = 1 ; 2 . Government expenditures do not enter the representative consumer¡s utility function nor the representative &rm¡s production function (i.e., it¡s a ¢throw-in-the-ocean£governmentutility function nor the representative &rm¡s production function (i....
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