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PracticeFinal_su11

# PracticeFinal_su11 - University of Minnesota Econ 3102...

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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 ° 0 . (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 0 . 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 0 > 0 . Assume that the household±s utility function is time-separable, and takes the form U ( C 0 ; C 1 ; :::; ‘ 0 ; ‘ 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 ( lim C t ! 0

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PracticeFinal_su11 - University of Minnesota Econ 3102...

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