Econ 365
M. Muniagurria
Answer Key Problem Set 1
(I)
In the Solow
model without population growth or technological change:
(1)
)
k = i
*
k ,
where k is capital per worker, i investment per worker and
*
the rate of depreciation of the capital
stock. Since investment per worker equals savings per worker, we have that
(2)
)
k = s f(k) 
*
k ,
where s is the savings rate and f(k) output per worker (equal to income per worker).
Let k* be the level of capital per worker along a BGP. Since
at the BGP :
)
k=0, using
(2) we
have that:
(3)
s f(k*) =
*
k*
Notice that at the BGP
the function s f(k) crosses the function
*
k. Both functions are increasing
(see Figure 44, page 82 in RP1).
As the savings rate increases, the function s f(k) increases for positive values of k so the
intersection occurs at a higher level of k. Since output or income per worker (f(k) ) is increasing
in k, the
level of income per worker at the BGP increases
(see Figure 45 , page 86 in RP1).
At the BGP, the growth rate of capital per worker is zero and therefore the growth rate of income
per worker is zero. Since this is independent of the level of k,
the savings rate has no influence
on the growth rate of output/income per worker along a BGP
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 Spring '07
 Muniagurria
 Economics, Stock and flow, Capital accumulation, worker, Mankiw.

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