Page 119 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Mathematics for Economists

Note Therefore
wP
= DAL D 1 K E 1 u
wL

w P w / DL AL D 1 K E D u K
R= D E
w P w / K EAl K u E L

D § · K
= ¨ ¸
E © ¹ L
wR = DEw/ ( / )
KL
KL
K L
w KL / w(/ )/KL (/ )/ /
Therefore, σ =
w L /P K )/P L /P K w(P R /R
w(/ )/KL
KL
/
s= 1 It’s proved
w KL D(/ ) · /b
KL
(/ )· D /b
4. For production capital and laboXr are important requirements – If capital becomes Zero,
production will get into Zero
β β
Production function = P = AL K u
L =0
β
Assume P= A.B. K u = 0
K =0
α
Assume P= AL · O · u = 0
Thus, for production both the factors are essential.
β
α
5. If Production function P = AL K u is homogeneous and of a degree, then a and b reflects the
position of labour and capital in the production.
α
β
Production function is P = AL K u
Differentiating with respect to L and K separately
1 wP 1
P = wL D L

1 wP 1
PK = E. K
w
LR Labour
w
\ a = = × Marginal product of labour
PL product
w
Wage of labour
=
Product
K wP Capital
And b = × Marginal product of capital
PK Product
w
= Labour share of total production
= Share of capital in production.

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