wk2 practice questions ans - The Colorado College...

1
The Colorado College
Department of Economics and Business
Block 7
Econ 207
Practice Question set 2 ans.
1. (a) c bQ aQ
dQ
TC d
MC + + = = 2 3
) (
2
(b) To obtain the level of output for which MC is minimum we set
0
) (
=
dQ
MC d
0 2 6
) (
= + = b aQ
dQ
MC d
a
b
a
b
Q
3 6
2 -
=
-
=
(c) The minimum value of MC at this level of output is:
a
b ac
c
a
b
a
b
c
a
b
b
a
b
a MC
3
3
3
2
3
)
3
( 2 )
3
( 3
2 2 2
2
min
-
= + - = +
-
+
-
=
2. (a) TR = P.Q = 70Q-5Q
2
Q
dQ
TR d
MR 10 70
) (
- = =
Q
dQ
TC d
MC 20 10
) (
+ = =
(b) The Profit maximizing condition is MR=MC
Using this we obtain the optimal quantity
70-10Q = 10+20Q
60 = 30Q
Q* = 60/30 = 2
(c) The maximum level of profit (
π
) for the firm is given by
π =TR – TC
= P.Q – TC
= 2(70-5Q) – [10Q+10Q
2
+10]
= 2(70-10) – [20+40+10]
= 120 – 70
= 50 .
3. (a) We first obtain the MC for Happy Valley Supply Inc.

2
Q
dQ
TC d
MC 2 . 0 5
) (
+ = =
Now since the firm is perfectly competitive its equilibrium is obtained as P=MC.
55 = 5+0.2Q
0.2Q = 50
Q* = 50/0.2 = 250 .
Profit for Happy Valley Supply Inc. is given as:
π = TR –TC
= P.Q. – TC
= 55(250) – 4000 - 5(250) – 0.1(250)
2
= $2250 .