1
AEM 4150
Price Analysis
Fall Semester 2009
Homework Assignment 3
Suggested Solutions
Problem 1
(a) (1 point) Profit maximization for the monopolist implies that MC = MR
TC = 4,000 + 20Q
MC = dTC/dQ
= 20
At profit max MC = MR
Therefore, 20 = 300 – 0.4Q
=>
Q* = 700
From demand curve P = 300  0.2Q
= 300  0.2(700)
P*= 160
Profit = TR – TC
at P = 160 and Q = 700
= PQ – (4,000 + 20Q)
= (160x700) –
[4,000 + 20(700)]
=
94,000
Graph (2 points for monopoly and perfect competition)
(b)
(1 point) In perfect competition the firm takes the price as given, in this case profit
maximization implies that:
P = MC
P = 300  0.2Q = 20
P
PC
= 20
D
MR
P
P
M
=160
Q
M
= 700
Q
PC
= 1400
MC=20
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
=>
Q* = 1,400
and
P* = 20
Profit = TR – TC
at P = 20 and Q = 1,400
= PQ – (4,000 + 20Q)
= (20x1,400) –
[4,000 + 20(1,400)]
=
4,000
=
Loss
See graph in part (a)
Problem 2
(a)
(1 point) Calculation of the MC of milk production:
TC = 8 + 2Q
MC =
dTC/dQ =
2
(b) Fluid milk market
(1 point)
At profit max. MR = MC
Therefore
15 – 4Q
f
= 2 or
Q
f
*= 3.25
P
f
*= 15 – 2(3.25) =
8.5
Processing milk market (1 point)
At profit max. MR = MC
Therefore
10 – 1Q
p
= 2 or
Q
p
*= 8
P
p
*= 10 – 0.5(8) =
6
They should therefore sell 3.25 units of milk at $8.5 per unit in the Fluid Milk Market and 8 units
of milk at $6 per unit in the Processing Market.
(c) Fluid milk buyers are paying more for their milk ($8.50  $6.50 =
This is the end of the preview.
Sign up
to
access the rest of the document.
 '07
 KAISER,H.M.
 Price Discrimination, Supply And Demand, price inverse form

Click to edit the document details