Problem Set 4

From: Mash-Erdene Ganbold (1154248)

1.

(a)

y = ALf(k) = A L fI KAL

, 1M = A L fHk, 1L

r = MPK =Y

K=

y

K

r =IALf I K

AL,1MM

K= A L f ' I K

AL, 1M 1

AL

= f ' Hk, 1L = f ' HkL

Using chain rule:

f(g(x)) = f(g(x))g(x), where

fHgHxLL = fI KAL

, 1MgHxL = K

AL

(b)

y = ALf(k) = A L fI KAL

, 1M

w = MPL =Y

L=

y

L

w =IALf I K

AL,1MM

L= A f ' I K

AL, 1M - K

AL2 L+A fI KAL , 1M

= Af ' I KAL

, 1M - KAL+A fI K

AL, 1M

= AA f ' I KAL

, 1M - KAL+ fI K

AL, 1ME

= A[f(k)-kf(k)]

Using product & chain rule:

(fg) = fg+fg where fHxL = A fI K

AL, 1M

gHxL = L