a. Express the production function in per worker. b. Assuming closed economy with no government, A = 1, labor growth rate being constant (GL) and depreciation rate is positive 8 > 0, show the step by step derivation of the fundamental equation of growth (using per worker capital, k) c. Find the steady-state values of capital per labor (kss), output per labor (yss) and consumption per labor (Css). Note: Take kss = 0 as given, you don't have to show that it is true.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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ECO 4218 – Economics of Growth
Solow Model Exercise
Suppose that the production function of an economy is characterized by the following Cobb-
Douglas production technology Y = AK“L²-«, where Y is the aggregate output, A is the level of
technology, K is the capital stock, L is the labor and 0 < a < 1.
a. Express the production function in per worker.
b. Assuming closed economy with no government, A = 1, labor growth rate being constant
(gL) and depreciation rate is positive 8 > 0, show the step by step derivation of the
fundamental equation of growth (using per worker capital, k)
c. Find the steady-state values of capital per labor (kss), output per labor (yss) and
consumption per labor (Css). Note: Take kss = 0 as given, you don't have to show that it is
%3D
true.
d. What would be the effect of s, 91, 8 and a on yss?
e. What is the golden rule of saving rate? Hint: Use css you found on part (c)
f. Find steady-state values of k ss, Yss and css if s = 0.2, gı = 0.01, a = 0.5 and 8=0.04
Transcribed Image Text:ECO 4218 – Economics of Growth Solow Model Exercise Suppose that the production function of an economy is characterized by the following Cobb- Douglas production technology Y = AK“L²-«, where Y is the aggregate output, A is the level of technology, K is the capital stock, L is the labor and 0 < a < 1. a. Express the production function in per worker. b. Assuming closed economy with no government, A = 1, labor growth rate being constant (gL) and depreciation rate is positive 8 > 0, show the step by step derivation of the fundamental equation of growth (using per worker capital, k) c. Find the steady-state values of capital per labor (kss), output per labor (yss) and consumption per labor (Css). Note: Take kss = 0 as given, you don't have to show that it is %3D true. d. What would be the effect of s, 91, 8 and a on yss? e. What is the golden rule of saving rate? Hint: Use css you found on part (c) f. Find steady-state values of k ss, Yss and css if s = 0.2, gı = 0.01, a = 0.5 and 8=0.04
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