PRODUCTION FUNCTION

1. PRODUCTION FUNCTION Mieczysław Dobija, Marcin Jędrzejczyk http://www.rigel.pl/ina http://swed.ae.krakow.pl mailto:jedrzejm@ae.krakow.pl

2. 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.

3. a* W Production function PR = W * WP Money Creation BANKS Human Capital (H) Equalising mechanism GDP – MK = 0 Assets MK = W * WK (1-a) * W W = u * H W = u * H

4. 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.

5. 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.

6. 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)

7. 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:

8. 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

9. 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!

10. 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.

11. PRODUCTION FUNCTION

12. PRODUCTION FUNCTION