# Hw4ak - Sonoma State University ECONOMICS 304 Department of...

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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 find saving rate to produce this as a steady state, use steady state condition: s f(k* gold ) = ( δ ) k* gold s (6.09) 1/3 = 0.10 * 6.09 so s = 0.33 Countries with this production function should have a saving rate of 33 percent, if they want to enjoy the maximum level of consumption in steady state. Clearly,
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