problem set 4.1 solutions

Problem Set 4 From: Mash-Erdene Ganbold (1154248) 1. (a) y = A·L·f(k) = A L f I K AL ,1M = A L f Hk,1L r = MP K = ΔY ΔK = Δy ΔK r = ΔIAL f I K AL ,1MM ΔK = 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 f HgH xLL = f I K AL ,1M gH xL = K AL (b) y = A·L·f(k) = A L f I K AL ,1M w = MP L = ΔY ΔL = Δy ΔL w = ΔIAL f I K AL ,1MM ΔL = A f ' I K AL ,1M - K AL 2 L + A f I K AL ,1M = A· f ' I K AL ,1M - K AL + A f I K AL ,1M = AA f ' I K AL ,1M - K AL + f I K AL ,1ME = A[f(k)-kf’(k)] Using product & chain rule: (f·g)’ = f’·g+f·g’ where f H xL = A f I K AL ,1M gH xL = L

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Solutions to Problems Set 4.1 for Macroeconomics course at University of Vienna

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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