Long Exercise Solutions
Ramon manages a branch office of a large financial ser ices firm He uses
computers capital K and people labour L to produce consulting ad ice Q
according to the production function Q K L
Emplo ing people costs the age rate
hile renting computers costs the
rental rate r Suppose computers cost t ice hat people do i e r
For
no the number of computers in the branch is fi ed at K 0
A Ho much labour does Ramon emplo if he needs to produce output
Q Sho that short run total cost is SRTC Q
Q 0
0
Ans er
Gi en he a mp ion ha capi al i con an a K k
e ha e ha o p i
Q K L 0 L F om hi fo a gi en le el of o p Q e need o emplo L Q
Sho
n o al co no ice ha SRTC
L K
Q 0
0
0 Q 0
B Deri e short run a erage and marginal costs Ho do short run
a erage and marginal cost ar ith the output Dra a diagram
Ans er
The ho
n SR a e age co i ATC SRTC Q
0
Q
Q
0
0
Q
0
The ma ginal co i hen MC
0 No ice ha SR a e age co decline
o p b SR ma ginal co i con an
He e i a diag am ill
a ing he a e age and ma ginal co c
e
ih
0
C Assume that Ramon decides to optimall choose capital Deri e the
long run total cost function a erage cost function and marginal cost
function
Ans er
The long n o al co i gi en b he minim m co o p o ide a pecific le el of
o p b op imall choo ing bo h inp
In o ca e e need o choo e k o
minimi e he ho
n co fo each le el of o p To minimi e he SRTC e
ake he de i a i e i h e pec o 0 and eq ali e i o
R C
0
Which implie
LR C = 2
and he long
0
Q
2
Q
2
=
+Q
2
Q
Q
=0 ⇒ 2
We can
b i
= 2 2Q The long
n ma ginal co i LRMC
2
( 0)
= 0.
e hi in o he SRTC o ge he
n a e age co i hen LRTC Q
2
Q
2 2Q
Q