ECON 400
Hartman
Winter 2011
PROBLEM SET I
(for Monday, January 10)
1.
(This is problem 8 in Chapter 1 of the text.)
A monopolist faces the demand function
x
ab
p
where
x
is
the quantity sold,
p
is the price (to buyers), and
a
and
b
are given parameters.
The monopolist's production
costs are given by
2
Ck
x
where
k
is a given parameter.
There is also a
per unit
tax on the monopolist's
sales at the rate
t
.
The monopolist's objective is the maximization of profit.
a.
What restrictions on the values of the parameters
a
,
b
, and
k
would you be inclined to assert,
a priori
?
b.
Find the monopolist's output as a function of
t
,
*( )
x
xt
.
Confirm that
*( )/
0
dx
t
dt
for the
restricted values of
a
,
b
, and
k
from part a,
i
.
e
., show that output decreases as the tax rate increases.
c.
What restrictions does the hypothesis of profit maximization place on the parameters
a
,
b
, and
k
?
How
do these restrictions compare with those from part a?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Ellis,G
 Economics, marginal utilities, Utility Functions

Click to edit the document details