# Managerial Economics

Autor:   •  October 19, 2015  •  Exam  •  445 Words (2 Pages)  •  611 Views

Page 1 of 2

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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