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Unformatted text preview: turns to scale. ,
) (iii)
( ( : (ii)
( ) ,
) (
( )
) Again, the higher is the ratio of K to L, the more units of capital we are able to give up in exchange for an
additional unit of labor, keeping production constant. Also, notice that this is also true the higher is
relative to : and summarize how productive is one factor of production relative to the other.
Now, since ( ), ( ) () ( ) ( )= ( () ( ) , so ) ( : for this production function there is always a 1% ) decrease in the ratio of capital to labor when we increase the MRTS 1%
(2) Suppose the production function is ( ) (a) What combination of capital and labor makes it cheapest to produce a given level of production Q if
wages are w and the rental rate of capital is r?
Here we need to set up the cost minimization problem: Since the marginal rate of technical substitution is decreasing, we can find the solution to this problem
using the Lagrangian function approach:
( ) ( ) The F.O.C. are given by:
() ( ) () ( ) () ( ) ( ) =0 ( ) =0 From (1) and (2) we obtain the optimality condition:
, or
Which...
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This note was uploaded on 08/22/2013 for the course ECON 11 taught by Professor Cunningham during the Summer '08 term at UCLA.
 Summer '08
 cunningham

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