Q=180LK0.8L=5 K=10
1.
MPL=dLdQ=2L180K0.8=L90K0.8
MPK=dKdQ=180×0.8L K−0.2MPK=144LK−0.2
2.
Q=180LK0.8
APL=LQ=L180LK0.8=L180K0.8
APL=5180(10)0.8=80.49845(10)0.8
APL=507.9
APK=KQ=K180LK0.8
APK=K0.2180L=100.21805=100.2402.49
APK=1.5848932402.49=253.9554
3.
Q(K,L)=180LK0.8
Scaling both factors of production by t>t
Q(tK,tL)=180tL(tK)0.8
=180(t)21L(t)0.8(K)0.8=180L(K)0.8(t)0.8=180L(K)0.8(t)0.5+0.8=(t)1.3180L(K)0.8
Q(tK,tL)=Q(K,L)(t)1.3
(t)1.3>(t) implies increasing returns to scale
4.
MRTS=MPKMPL=L90(K)0.8×144L(K)−0.21
=14490LK0.8(K)0.2
=14490LK
=1610LK
MRTS=85LK
5.
Cross partial effects
MPL=L90(K)0.8
dKdMPL=90L(0.8)(K)−0.2=L72(K)−0.2>0
MPK=144L(K)−0.2
dLdMPK=2L144(K)−0.2=L72(K)−0.2>0
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