Economics 4808
Problem Set 5
1.
Assume Wilbur’s utility function is
3
2
1
x
x
x
U
=
.
Further assume that the law dictates that Wilbur
consume two units of
2
x
for every unit of
1
x
.
Determine Wilbur’s demand function for good 1.
Explain, in words, all the steps in your derivation of his demand function for good 1.
Now derive
Wilbur’s demand functions for goods 2 and 3.
How many units of the three goods will he choose to
purchase if his income is $72.00, p
1
= $1.00, p
2
= $0.50 and p
3
= $7.00.
2.
Suppose a legislator applies price regulation on a natural monopoly to garner votes.
Votes are a
function of producer utility (U
R
) and consumer utility (U
C
).
The legislator’s vote/utility function is V =
V(U
R
, U
C
).
U
R
= R, and U
C
= K – R – L where R and L are shown in the typical monopoly versus
competitive market outcome below.
$
P
m
R
L
P
c
MC
Q
MR
D
Obviously, both U
R
and U
C
are affected by the eventual price (P) set by the legislator because both R and L
are affected by that price.
a.
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 '06
 EDWARDMOREY
 Economics, Supply And Demand, Utility, Wilbur, Uncle Bob, fruit punch

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