Problem Set 1 -
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Problem Set 1 -
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 to scale refers to what happens to output when all inputs are expanded
in the same proportion, while the Law of Diminishing Returns refers to
expansion of one input holding another input fixed.
Thus, the Law of
Diminishing Returns says that expansion of the labor input, say, holding the
capital input fixed, causes output to rise by smaller and smaller amounts,
that at least eventually the rise in output is smaller than proportional to the
expansion of labor.
But if that increase in labor were instead accompanied by
an increase in capital also, the latter would increase output by more.
would make it possible for output to rise by an equal or greater proportion than
the increase in both inputs, thus displaying constant or increasing returns to
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?
With constant returns to scale and only labor as an input, output is simply
proportional to the amount of the input.
It is true, therefore, that the marginal
product of labor is then constant and does not diminish as more and more labor
Whether that is a violation of the Law of Diminishing Returns,
however, is debatable, since we are not fixing the input of any other factor,
there not being any other factor available to fix.
Suppose that a production function has two inputs,
, and that, contrary to
the Law of Diminishing Returns, an increase in
alone always causes output to
rise by the same proportion that
Show that the production
function must therefore display increasing returns to scale.
If K and L both rise by some proportion λ, we can break the effect into two