Question

Problem 2 Consider two economies: San Escobar and New Ireland. Both are described by a neoclassical Cobb-Douglas production function: Y = KOS(A N.)0,5. In San Escobar the saving rate is s=0,5; the rate of population growth n=0,01; the depreciation rate is d 0,01 and the rate of technological progress is g=0,03. In New Ireland, the saving rate is s=0,6; the rate of population growth n=0; the depreciation rate is d=0,01 and the rate of technological progress is g=0,02 a) In which country the steady state level of output per effective worker is higher? Please, show all relevant calculations (4p). b) Assume that in San Escobar and in New Ireland, the current level output per effective worker is equal to 15. In which country the growth rate of output per effective worker will be higher in the short run? In which country the growth rate of output per effective worker will be higher in the long run? Shortly explain (5p). c) Assume that in San Escobar, the saving rate increases. Using a graph with time on horizontal axis, sketch the evolution over time of consumption per effective worker and output per worker. (4p)

Answer 1

1 - K 6.5 CAN) New Ireland, 0.5 K = 0.5 (AN) s.y = (&tu tgk 0.5 ANAN 0.5 -0.5 Y = y = K (AN) 8.6K = lot o.014 0.02K 0.6ks = 0.03k 06 - ? 0.03 2 5 = 20 19 = 20 output per worker и у 2 Escobar San sy = (stutgjok 0.5 6.5K = Cooltool+ 0.03).KL 6.58 -0.054 0.5 K = 10 107 1 = output per worker (6) San Escobar is operating below the steady state shes its growth rate over etre short rou would we higher relative to etre New Ireland which is above the steady state over the long run, eture will not be a grow.lt rate in effective ber worker. - Y=Afl 1) y sufic) there will be my iu Corruptiч and output per worker.