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Econ 441
Alan Deardorff
Problem Set 1
International Equilibrium
Page 1 of 1
Problem Set 1
International Equilibrium
1.
a.
Explain how it is possible for a production function to have the property of
constant or increasing returns to scale and still satisfy the Law of Diminishing
Returns.
b.
If a production function has only one input, say labor, and displays constant
returns to scale, does it then violate the Law of Diminishing Returns?
c.
Suppose that a production function has two inputs,
K
and
L
, and that, contrary to
the Law of Diminishing Returns, an increase in
L
alone always causes output to
rise by the same proportion that
L
has increased.
Show that the production
function must therefore display increasing returns to scale.
d.
Differentiate the definition of “Homogeneous of Degree
k
“ with respect to λ, and
evaluate the result at λ=1.
Then use this result to show that, if factors of
production are paid the value of their marginal products as assumed under
perfect competition, then factor payments will exactly equal the value of output
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 Spring '09
 GUAN

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