Managerial Economics
Autor: Kiama • October 19, 2015 • Exam • 445 Words (2 Pages) • 1,019 Views
Question 1
Q=0.1K0.5L0.5
MPL = ∂Q/∂L =0.05K0.5L-0.5
MPK = ∂Q/∂K=0.05K-0.5L0.5
0.05K0.5L-0.5=0.05K-0.5L0.5
4 1
L=4K
Q=0.1(4K)0.5K0.5
=0.1XK0.5XK0.5
= 0.2K
K=Q/0.2 = 5Q
Q=0.1L0.5X1/2XL0.5
Q=0.05L
L=20Q
T.C=wL+rK
=1(20Q) +4(5Q)
=40Q
b)
TC=40Q
MC=∂Q/∂L
=40
AC=T.C/Q
=40Q/Q
=40
c)
Q=0.1K0.5L0.5
Q2=0.01KL
Q2=0.1L
L=Q2/0.1
L=10Q2
TC=wL+rK
10Q2+4O
d)
MC = ∂Q/∂L
= 20Q
At equilibrium M.C=P
P=20Q
Q = 0.05P
e)
Producer surplus (profit)
π = T.R – T.C
= (P*Q) – (10Q2 + 40)
= (P*Q) – (10Q2 + 40) Q=0.05P
Π = 0.025P2 - 40
Question 2
Q=0.1K0.5L0.5
MPL = ∂Q/∂L =0.05K0.5L-0.5
MPK = ∂Q/∂K=0.05K-0.5L0.5
0.05K0.5L-0.5=0.05K-0.5L0.5
9 1
L=9K
Q=0.1(9K)0.5K0.5
=0.1X3K0.5XK0.5
= 0.3K
K=Q/0.3
Q=0.1(1/9L)0.5L0.5
Q=1/30L
L=30Q
T.C=wL+rK
=1(30Q) +9(Q/0.3)
=60Q
TC=60Q2
MC=∂Q/∂L
=60
AC=T.C/Q
=60Q2/Q
=60
b)
Q=0.1K0.5L0.5
MPL = ∂Q/∂L =0.05K0.5L-0.5
MPK = ∂Q/∂K=0.05K-0.5L0.5
0.05K0.5L-0.5=0.05K-0.5L0.5
4 4
L=K
Q=0.1(K)0.5K0.5
=0.1K0.5K0.5
= 0.1K
K=Q/0.1 = 10Q
Q=0.1L0.5L0.5
Q=0.1L
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