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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