Cost Theory Problems, answer guide
1. &n=
bsp; C
=3D 190 + 53 Q
a. &n=
bsp; FC
=3D 190
b. =
; at
Q =3D 100,000, VC =3D 5,300,000; AVC =3D VC/Q =
=3D 53
c. MC =3D 53
d. AFC
=3D FC/Q =3D 190/Q
e. &n=
bsp; C’
=3D 240 + 45 Q + 30 I
2. &n=
bsp; Desktop:
Cd &=
nbsp; =3D
200 + 0.035 Q
&nbs=
p; Larger: Cl =3D 400 + =
0.02 Q
&nbs=
p; for Q =3D 15,000; Cd =3D $=
725 and Cl =3D $ 700
&nbs=
p; hint for last part: set two equations equal to each ot=
her
and/or graph.
3. &n=
bsp; franchise fee: treat as a FIXED COST, doesn’t af=
fect
operating costs
MC and AVC unchangedl
ATC up
&nbs=
p; tax on output: increases cost of each unit produced
&nbs=
p;
all three change
&nbs=
p; 4.
Set MRTS =3D w/r; sol=
ve
for K and substitute into production function
&nbs=
p;
L =3D 50 and K =3D 200
&nbs=
p;
C =3D wL + r K =3D 4=
(50) +
1(200) =3D 400 so C/q =3D 400/200 =3D 2
&nbs=
p;
Function exhibits CRS so for q =3D400; L=3D 100 and K =3D 400
&nbs=
p;
Solve as a short run cost model using capital FIXED at 200
&nbs=
p;
q =3D 400 =3D 2 =
L
1/2 (200) 1/2
&nbs=
p;
400 =3D 28 L1/2
&nbs=
p;
L 0.5 =3D 14 --> L =3D 200
so SR cost will be C =3D 4 (200) + 1 (200) =3D 900