Econ303 Homework 3B 1 1 4 points Adapted from Chapter 7 question 2 Country Healthy living in the Malthusian world has production function Y 560D0 4 N 0 6 where Y is measured in pounds of food and D acres of land a Suppose that the sustainable consumption is 600 pounds of food What is the country s population density b Suppose that an advance in medicine in country Healthy living makes its citizens healthier hence they could sustain life and reproduction at a lower level of consumption say 550 pounds What is the country s population density after the medical advance How would its standard of living as measured by GDP per capita change 2 5 points Chapter 8 question 2 In the Solow growth model suppose that the per worker production function is given by y zk 0 35 with s 0 22 d 0 07 and n 0 02 a Suppose that in country A z 50 Calculate per capita income and capital per worker in the steady state b Suppose that in country B z 100 Calculate per capita income and capital per worker in the steady state c As measured by GDP per capita how much richer is country B than country A What does this tell us about the potential for differences in total factor productivity to explain differences in standards of living across countries 3 8 points Page 265 Chapter 7 question 9 Consider a numerical example using the Solow growth model Suppose that F K N zK 0 4 N 0 6 with d 0 07 s 0 2 n 0 01 and z 20 and take a period to be a year a Determine capital per worker income per capita and consumption per capita in the steady state b Now suppose that the economy is initially in the steady state that you calculated in part a Then s increases to 0 3 Determine capital per worker in each of the 10 years following the increase in the savings rate c Determine capital per worker income per capita and consumption per capita at the new steady state d Discuss your results in particular comment on the speed of adjustment to the new steady state after the change in the savings rate and the paths followed by capital per worker worker income per capita ption per capita to z 1 for periods t 2 3 4 Calculate consumption investment savings and aggregate output for each period modify the Solow growth t 1 2 3 4 g long run technological c Repeat part b for the case where at t 1 ppose that z 1 for conveEcon303 Homework 3B 2 total factor productivity falls to z 0 9 and e is labor augmenting techthen stays there forever with a production function d data Discuss your 266 results in parts a c 13 shown below answer 4 3 points Using the on page Chapter 7 question F K bN the following 13 questions Suppose that thedata capital share is 40 hence the aggregate Consider the0 4following 0 6 production function is Y zK L number of units of human and bN is efficiency units enote future human capital Year Y billions K billions N millions that b 1 f b where f is of 2005 of 2005 uman capital dollars dollars ng run equilibrium has the K is a constant At 1995 9086 0 31438 0 124 9 bN aggregate output aggregate 1996 9425 8 32338 4 126 7 aggregate investment and 1997 9845 9 33307 7 129 6 me grow in this steady state 1998 10274 7 34428 0 131 5 1999 10770 7 35679 0 133 5 ect of an increase in f on 2000 11216 4 36999 0 136 9 per capita income Discuss 2001 11337 5 38164 0 136 9 the standard Solow growth 2002 11543 1 39233 9 136 5 2003 11836 4 40322 6 137 7 wth model so that the pros given by Y zK where Y 2004 12246 9 41471 4 139 2 al and z is total factor pro2005 12623 0 42609 9 141 7 put is produced only with 2006 12958 5 43836 6 144 4 2007 13206 4 44949 2 146 1 possible for income per ndefinitely an increase in the savings a Calculate the Solow residual for year 1995 and 2007 e growth rate in per capita 1 a Calculate the Solow residual for each b Calculate the annualyear average of output capital labor and TFP from growth 1995 torate 2007 during this time period c Determine the contribution of each factor Are there any surprises If so explain
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