Sonoma State University ECONOMICS 304 Department of Economics Florence Bouvet Assignment 4 –Chapter 7- Answer Key 1a) Defining y = Y/L, and k = K/L, the production function can be written: y = k 1/3 . b) At steady state k*, the following condition will hold: s f(k*) = ( δ ) k* or s k* 1/3 = ( δ ) k* or k* = (s/( δ )) 3/2 steady-state capital per worker: country A: k* A = (0.2 / 0.10) 3/2 = 2.83 country B: k* B = (0.3 / 0.10) 3/2 = 5.20 c) steady-state output per worker: country A: y* A = (k* A ) 1/3 = (2.83) 1/3 =1.41 country B: y* B = (k* B ) 1/3 = (5.20) 1/3 = 1.73 steady-state consumption per worker: country A: c* A = (1–s A ) y* A = (1-0.2)(1.41)= 1.13 country B: c* B = (1–s B ) y* B = (1-0.3)(1.73)= 1.21 So country B has a higher consumption level (although it spends a smaller fraction of its income on consumption). This means country B is closer to the golden rule. d) Golden rule: (1/3) k* gold-2/3 = 0.01 k * gold= 6.09: golden rule of capital stock
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This note was uploaded on 03/08/2011 for the course ECON 304 taught by Professor Eyler during the Spring '07 term at Sonoma.