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Unformatted text preview: University of Minnesota Econ 3102: Intermediate Macroeconomics Practice Final 1 De&nitions (10 points) 2 Short Answers (15 points) 3 Solow Growth Model (15 points) Consider the Solow growth model studied in Chapter 6, with technology given by Y t = zF ( K t ;N t ) = zK 1 = 4 t N 3 = 4 t . Capital depreciates after use at the rate & 2 (0 ; 1) . Assume that each agent is endowed with one unit of time & & h = 1 and supplies their labor inelastically. Additionally, each agent saves a fraction s 2 (0 ; 1) of their total income. The population evolves according to N t +1 = (1 + n ) N t , where n & . (a) Find an expression that relates capital per worker tomorrow k t +1 and capital per worker today k t . (b) What is the steady-state value of capital per worker in terms of exogenous variables. (c) Suppose that the economy is initially in a steady-state and suddenly TFP decreases permanently from z to z . What happens to steady-state output per capita y & , capital per worker k & , and consumption per capita c & ? Plot the evolution of capital per worker from the old to the new steady-state. (d) Suppose that TFP only decreases temporarily . Plot the impulse reponse function for the per capita capital stock k as a function of time. 4 Neoclassical Growth Model (25 points) Consider the in&nite horizon one-sector growth model. The representative household (consumer) enjoys consumption and leisure time in all periods t = 0, 1,.... The household has no exogenous income but she has a &xed time endowment & h in each period to split between labor and leisure. The household is endowed with the initial capital stock & k > . Assume that the households utility function is time-separable, and takes the form U ( C ;C 1 ;:::; ; 1 ;::: ) = 1 X t =0 t u ( C t ; t ) where C t and t denote consumption and leisure in period t , u ( ; ) is the period utility function which is strictly in- creasing, strictly concave, twice-di/erentiable and sati&es the Inada conditions (...
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This note was uploaded on 09/21/2011 for the course ECON 3102 taught by Professor Econ during the Summer '10 term at University of Minnesota Crookston.
- Summer '10