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Notes on Competition and the Distribution of Product
In macro the aggregate production function is typically used and it is assumed that
the competitive equilibrium aggregates will satisfy it. Further, it is assumed that the rental
price of a factor of production is equal to the partial derivative of the aggregate
production function. The purpose of these notes is to provide some justifications for these
assumptions.
Proposition:
If factor markets are competitive, the competitive equilibrium output is the
maximum output F(K,N). Further, factor payments exhaust total product; that is
Y
′
= r K + w N
where Y
′
is the competitive equilibrium aggregate output, r is the equilibrium rental price
of capital and w is the equilibrium rental price of labor.
Proof:
Let z
′
= {z
′
kn
} be a competitive equilibrium production plan.
For all plant
technologies,
(1)
f
kn
– r k – w n
≤
0.
If this were not the case there would be a profit opportunity, which is inconsistent with
equilibrium. If the inequality is strict for some (k,n) type plant, z
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This note was uploaded on 04/13/2011 for the course ECON 509 taught by Professor Villamil during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Villamil

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