Transcript PRODUCTION FUNCTION

PRODUCTION FUNCTION
Mieczysław Dobija, Marcin Jędrzejczyk
http://www.rigel.pl/ina
http://swed.ae.krakow.pl
mailto:[email protected]
PRODUCTION FUNCTION
PR = W * WP
Production (PR) is a composition of human work (W), Assets
and the coefficient WP (wage productivity).
Where:
PR – value of manufactured products,
W – cost of labour,
WP – wage productivity.
Equalising
mechanism
MK = W * WK
GDP – MK = 0
Production
function
Money
Creation
BANKS
PR = W * WP
a* W
(1-a) * W
Assets
W=u*H
Human
Capital (H)
W=u*H
PRODUCTION FUNCTION
C.W.Cobb i P.H.Douglas
Product X arises as a result of composition:
X = A·Nα · Cβ
where: N – number of employees, C – capital, A, α, β are
constants, that have to be estimated on the basis of empirical
data about production. Coefficient A can be equal to 1 for
a+b>1 or A>1 for a+b<1.
Second type cognition – does not explain the nature of the
problem.
PRODUCTION FUNCTION
Production function can be expressed as a sum of expenses:
PR = (W + zA – sA) (1 + r) (1 + I)
where:
PR – value of production expressed in realization prices,
W – labour costs,
A – Assets in historical value,
z – assets’ yearly waste indicator (composition to products),
s – assets waste in production process (losses),
r – appreciation of historical values to the market values,
I – value appreciation as a result of additional intellectual
capital in the company.
PRODUCTION FUNCTION
After reformulating previous equation we receive:
PR = W·[1 + A/W · (z - s)] (1 + r) (1 + I)
Because labour costs W are human capital derivatives:
W=u·H
where: u is a level of payment for conducted work and H
denotes the value of human capital. After adequate
substitution:
PR = W·[1 + A/H · (z - s)/u ] (1 + r) (1 + I)
PRODUCTION FUNCTION
Because coefficients r and I are close to zero, using the
relation:
1 + x = ex, we can reformulate the production function:
PR = W er eI [1 + A/H · [(z - s)/u] ] = W · WP
Therefore we can estimate the relation that represents
productivity ratio:
WP  e
rI
A zs
[1  
]
H
u
PRODUCTION FUNCTION
WP = PR/W
WP is wage productivity understood as multiplier of labour
costs that is generating the value of production and, at the
same time, the value of production that is distributed to one
money unit of labour cost.
The above equation can be seen from macroeconomic point
of view:
GDP = W · WP
PRODUCTION FUNCTION
Practical approach to this function requires some
simplification of the previous formulas:
PR = W· e
(A/H)·Z,
where synthetic coefficient Z denotes the level of
management Z = Z(z, s, u, r, I). Value of this coefficient is
measurable in terms of accounting and financial reporting!
PRODUCTION FUNCTION
We can see that accounting system generates the data
necessary to measure this very coefficient Z describing the
quantitative results of management level in the company.
The estimation of the Z coefficient has been shown in the
table below.
Period
PR
W
A
L
Z
1
3,0 mln
0,5 mln
2,0 mln
0,48 mln
5,37
2
3,5 mln
0,6 mln
2,5 mln
0,44 mln
3,88
3
4,0 mln
0,6 mln
2,5 mln
0,52 mln
4,93
PRODUCTION FUNCTION
PRODUCTION FUNCTION