ECO202: Tutorial Worksheet 12
1.
Suppose that the economy’s production function is given by Y = K
α
N
1
α
. Assume
that
α
= 1/3.
a.
Is this production function characterized by constant returns to scale?
Explain.
b.
Are there decreasing returns to capital?
c.
Are there decreasing returns to labor?
d.
Transform the production function into a relation between output per
worker and capital per worker.
e.
For a given savings rate (s) and depreciation rate (
δ
), given an expression
for capital per worker in the steady state.
f.
Give an expression for output per worker in the steady state.
g.
Solve for the steady state level of output per worker when
δ
= 0.08 and s =
0.32.
h.
Suppose that the depreciation rate remains constant at
δ
= 0.08, whereas
the saving rate is reduced by half to s = 0.16. What happens to the steady
state level of output per worker?
2.
Suppose that the economy’s production function is Y = K
1/3
N
2/3
and that both the
saving rate (s) and the depreciation rate (
δ
) are equal to 0.10.
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 Spring '11
 Wolfson
 depreciation rate, worker, Yt

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