Marginal productivity wages

The marginal productivity pay is a neoclassical theory , which deals with the demand of a company for additional work. The theory justifies the interdependent interaction of the demand for labor , depending on the wage rate and the demand for capital ( investments ), depending on the cost of capital (the interest rate ).

The entrepreneurial maxim of profit maximization requires that the marginal product of the factors of production corresponds to the marginal factor costs . In the case of marginal productivity wages for the production factors , the production elasticity of the factors determines the income distribution for society as a whole .

Sample calculation

The production function of a postal service company is given, where the number of working hours is: ${\ displaystyle L}$

{\ displaystyle f (L) = 1200 \ cdot L ^ {0 {,} 5}}

The demand for labor is obtained by equating the first derivative of the production function with the real wage:

{\ displaystyle f '(L) = {\ frac {W} {P}}}

This results in an hourly wage of 7.50 euros and a postage of 0.25 euros ${\ displaystyle W}$ ${\ displaystyle p}$

{\ displaystyle f '(L) = {\ frac {600} {\ sqrt {L}}} = {\ frac {7 {,} 50} {0 {,} 25}}}

,

so that one receives a labor demand from . ${\ displaystyle L = 400}$

Narrative formulation

According to the American economist John Bates Clark , marginal productivity remuneration is a reward for factors of production in accordance with their marginal productivity . It is based on the law of diminishing marginal products and presupposes perfect competition and completely mobile production factors. A company asks for additional work as long as the additional revenue ( marginal revenue from work ) is greater than or equal to the additional costs ( marginal cost of work ).

Mathematical formulation

{\ displaystyle P \ cdot \ partial Y / \ partial N = W \;}

thus marginal revenue (WGP) = nominal marginal costs

or

{\ displaystyle MPN = W / P \;}

thus marginal yield = real marginal costs

The factor productivities are determined from the capital intensity through the following Cobb-Douglas production function : ${\ displaystyle K / L}$

{\ displaystyle Y (t) = A \ cdot K (t) ^ {\ alpha} L (t) ^ {1- \ alpha}}

With

{\ displaystyle \ alpha \ in (0,1)}

The marginal product of the production factors can be determined from the partial derivatives of the production function:

Marginal product of labor: ${\ displaystyle {\ frac {\ partial F (K_ {t}, L_ {t})} {\ partial L_ {t}}} = (1- \ alpha) \ cdot A \ cdot (K_ {t} \ L_ {t}) ^ {\ alpha}> 0}$

Marginal product of capital: ${\ displaystyle {\ frac {\ partial F (K_ {t}, L_ {t})} {\ partial K_ {t}}} = \ alpha \ cdot A \ cdot (K_ {t} / L_ {t}) ^ {1- \ alpha}> 0}$

That is, a decision maker on the entrepreneurial side asks for additional work as long as the marginal value product of the work is greater than or equal to the wage rate ( ), i.e. until the marginal income of an additional employee ( ) corresponds to the real wage (real marginal costs). ${\ displaystyle W}$ ${\ displaystyle MPN}$

The following applies: better capitalization of jobs leads to higher labor productivity ; if more capital is used, which is capital productivity lower.

literature

John Bates Clark : The distribution of wealth: A theory of wages, interest and profits . Macmillan, New York, NY, 1899.

Individual evidence

↑ ^a ^b Employment and wage structures according to qualifications and age groups: an empirical analysis based on the IAB employee sample ( page no longer available , search in web archives ) Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice. , FITZENBERGER, Bernd, Alfred GARLOFF (both University of Mannheim , IFS and ZEW ), Karsten KOHN ( University of Mannheim ), contribution for the 2003 special issue of the communications from labor market and occupational research on “Wages and Employment” , University of Konstanz , November 2003, last accessed on December 1, 2017@1@ 2

^ Clark, JB, 1891, Distribution as determined by a law of rent , pp. 289-318 in: Quarterly Journal of Economics, April.

^ Clark, JB, 1908, The Distribution of Wealth , NY: Macmillan; First edition 1899.

↑ Fundamentals of Macroeconomics , Prof. Dr. Werner Smolny, Faculty of Mathematics and Economics, Ulm University from WS 09/10, last accessed on December 1, 2017

[konstanz-1] Employment and wage structures according to qualifications and age groups: an empirical analysis based on the IAB employee sample ( page no longer available , search in web archives ) Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice. , FITZENBERGER, Bernd, Alfred GARLOFF (both University of Mannheim , IFS and ZEW ), Karsten KOHN ( University of Mannheim ), contribution for the 2003 special issue of the communications from labor market and occupational research on “Wages and Employment” , University of Konstanz , November 2003, last accessed on December 1, 2017@1@ 2

[2] Clark, JB, 1891, Distribution as determined by a law of rent , pp. 289-318 in: Quarterly Journal of Economics, April.

[3] Clark, JB, 1908, The Distribution of Wealth , NY: Macmillan; First edition 1899.

[ulm-4] Fundamentals of Macroeconomics , Prof. Dr. Werner Smolny, Faculty of Mathematics and Economics, Ulm University from WS 09/10, last accessed on December 1, 2017