The Use of Economic and Mathematical Methods When Analyzing the Activities of Enterprises



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303-Article Text-1070-1-10-20210913 (1)

Volume 9, 2021
Page: 34 
Academic Journal of Digital Economics and Stability 
Volume 9, 2021 
 
at the optimal point, the final product corresponding to the resource unit is equal to the price. 
tity of products without changing production costs is written as follows: 
This problem is a problem of variables that have a linear limit of linear programming. Following 
Then we find the maximum value without the variables being negative. To do this, we fulfill the 
Douglas function, we consider the problem of maximizing the profit of a 
For example. If the firm allocates 150 thousand soums for rent and wages, maximize the amount 
If so, find the limit of the final exchange of stock and labor at the optimal point? 
in the optimal solution. 


 
ISSN 2697-2212 Online: 
ISSN 2697-2212 (online), Published under Volume 9 in September
Copyright (c) 2021 Author (s). This is an open
under the terms of Creative Commons Attribution License (CC BY).To view a 
copy of this license, visit https://creativecommons.org/licenses/by/4.0/
Dividing the first equation by the second, we find:
L
K
w
w
K
L
=
*
*
2
Putting it under the following condition, we find 
5
,
20
150
3
2
*
*
=
=

=
L
w
K
K
The solution can be expressed geometrically. In Figure 1, the isocosta line (constant cost line for 
S = 50,100,150 s) and isoquants (constant X = 25.2; 37.8 gross product line).
Isocosts are written by the following equation:
const
C
L
K
=
=
+
10
5
Isoquants are explained by the following equations:
const
X
L
K
=
=
3
/
1
3
/
2
3
At the optimal point 
*
=
K
are 










L
F
K
F
,

)
,
(
L
K
w
w
collinear.
Optimal point stock and labor exchange:
1
*
*



=
=
L
K
L
K
F
L
F
S
K
α




This means that one worker can be replaced by two unit fun
maximizing the firm's profit, we find the resource demand 
*
*
wx
C
=
. Now we find the production of the product without changing the cost. The optimal 
solution in the above neoclassical production function is the 
K
30
C=150
20
C=100
10
C=50

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