Page 128 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Unit 7: Homogeneous Function and Euler’s Theorem

Self Assessment Note
2. Multiple Choice Quesitons:
6. Who has been credited to devise the Cobb-Douglas Production Function?
(a) C W Cobb and D H Douglas (b) Cobb and Marshal
(c) Douglas and Arastu (d) Above all
7. Production function is
E
(a) P AL K u (b) P AL K u
D
E
D
E
D
(c) P L K E (d) P AK u
8. Marginal production of CES is always –
(a) negative (b) cubic
(c) positive (d) None of them
7.5 Summary

z Maximum use of special production is referred to as Homogeneous function.
z Euler’s Theorem states that all factors of production are increased in a given proportion
resulting output will also increase in the same proportion each factor of production (input) is
paid the value of its marginal product, and the total output is just exhausted.
z Euler’s Theorem has an important place in economic area especially in marketing area.
Production is made in conjugation with many means.
z Cobb-Douglas Production Function is used widely in economic area. This production function
was developed by C W Cobb and D H Douglas.
z If Production function is homogeneous and of a degree, it means that production will come
under constant formula.
z Cobb Douglas Production Function has a very important role in economic area. At present
many economists are using Cobb Douglas Production Function in various economic areas.
z Although Cobb Douglas Production Function is used widely in economic areas and its use is
increasing in especially in various industries and agriculture, but some economists criticize
this production function.
z In the Cobb-Douglas Production Functions it has already been discussed that elasticity of
substitution is always a unit in it.
z Compared to Cobb-Douglas Production Function, CES Production Function brings more
general technique.

7.6 Keywords

z Homogeneous: Undifferentiated, similar
z Theorem: practically which can be proved

7.7 Review Questions

1. Define homogeneous function with example.
2. Explain Euler’s Theorem with realistic example.
3. Write down the mathematical solution of Euler’s Theorem.

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