Question 1 Consider the following economy with production function: Y = AK L!-« where Y is total output; K is capital; L is labour force; A is the level of technology (exogenous); s is the saving rate; n is the population growth rate; 0
Question 1 Consider the following economy with production function: Y = AK L!-« where Y is total output; K is capital; L is labour force; A is the level of technology (exogenous); s is the saving rate; n is the population growth rate; 0
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Question 1
Consider the following economy with production function:
Y = AK"L-a
where Y is total output; K is capital; L is labour force; A is the level of technology
(exogenous); s is the saving rate; n is the population growth rate; 0 < a < 1. Assume
the rate of capital depreciation (5) to be zero. Hence, capital accumulation equation is:
K = sY
(a) Does this production function exhibitconstantreturns to scale to capital and labour?
Explain. Derive production function per worker.
(b) Derive an equation showing how the growth rate of capital per worker depends on
s, n, and A. Explain its growth implications and use a graph to support your answer.
(c) Find out the expression for the steady state capital per worker andoutputper worker.
How do they depend on s, n, and A? Explain.
(d) Instead of assuming saving rate (s) to be a constant, suppose we assume that "s"
depends on y,y =(equivalently on k, k = . In particular, s = e is constant. Find
the expression for the growth rate of capital per worker. Compare this expression with
the one obtained in part (b). Use graphs to support your answer.
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