Statistics 103: Lab 1
LAB PROBLEMS
1. Suppose that the tax
t
i
paid by individual
i
is the
following function of his or her income
x
i
:
t
i
= 0
.
1(
x
i

2000)
(i.e. , there is a flat tax of 10% on all income over
$2000). You know that total income in a geograph
ical area containing 500 individuals is $5
,
000
,
000.
What will the total tax revenue be?
answer: 400,000
2. In a particular geographical area, the demand func
tion for each person
i
for a particular good is
q
d
i
= 100 +
.
2
x
i

9
p
where
q
d
i
is quantity demanded for person
i
,
x
i
is
person
i
’s income and
p
is the commodity’s price.
For firms in this area the supply function for this
good is
q
s
j
=

50 + 20
p
where
q
s
j
is the quantity supplied of the good by
firm
j
. There are 5 firms and 100 consumers. Total
income of the consumers is $100
,
000. Equilibrium
occurs where
100
X
i
=1
q
d
i
=
5
X
i
=1
q
s
j
(i.e. , market demand equals market supply). Find
the equilibrium price.
answer:
$
30.25
3. Suppose
x
1
= 2,
x
2
=

1 and
x
3
= 0.
Compute
∑
3
i
=1
5
x
i
+ 2 and
∑
3
i
=1
1
x
i
+2
answer: 11; 1.75
4. Suppose ¯
x
= 11 and define
y
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 '09
 Drake
 Statistics, Supply And Demand, Suppose, deﬁne yi

Click to edit the document details