The highest steady state level of consumption occurs if workers save half of the
ID: 3220803 • Letter: T
Question
The highest steady state level of consumption occurs if workers save half of their income each period (i.e. s=0.5). Let us check this. Consider a simplified version of the Solow Growth Model. Assume per capita output is given by q=k^(alpha). Assume depreciation, , is 10 percent (i.e. = 0.1) and alpha is 0.5.
a)What is consumption per capita in the steady state if s=0.25?
b)What is consumption per capita in the steady state if s=0.75?
c)What is consumption per capita in the steady state if s=0.5?
d)What savings level gives the highest level of steady state consumption?
s=0.25? s=0.75? s=0.5?
Explanation / Answer
Let n = 0.2 the population growth
s, savings rate = 0.5
d, depreciation rate = 0.1
alp, alpha = 0.5
k, kapital
c, consumption
q, (denoted usually as y), per capita output
as per solow's model at steady state
q or y = [ s /(n+d) ] ^ (alp/1-alp)
c = (1-s) * y
a) c = (1-0.25) * (0.25/(0.2+0.1))^ (1/1-0.5)
= 0.63
b) similarly for s = 0.5, c = 0.83
c) for s = 0.75, c = 0.63
consumption per capita is maximum at s =0.5
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