Cornell University
Economics 3130
Problem Set 1 Solutions
1. What is Nechyba’s interpretation of what Friedman meant when he said that no one
knows how to make a pencil? That no one person knows how to make a pencil from
scratch.
2. What are the three basic insights Nechyba attributes to economics? 1) There are many
situations in which everyone can win–just because there is a winner does not mean
there is a loser, 2) People’s actions are often based on incentives rather than inherent
dispositions, and 3) Order can emerge spontaneously without someone designing it.
3. Compute
f
x
(that is,
∂f
∂x
),
f
y
,
f
xy
(that is,
∂
2
f
∂x∂y
),
f
xx
, and
f
yy
for the following functions:
(a)
f
(
x,y
) = 10
x
1
5
y

1
2
.
f
x
= 2
x

4
5
y

1
2
,
f
y
=

5
x
1
5
y

3
2
,
f
xy
=

x

4
5
y

3
2
,
f
xx
=

8
5
x

9
5
y

1
2
,
f
yy
=
15
2
x
1
5
y

5
2
(b)
f
(
x,y
) = 4
e
3
x
ln
(2
y
).
f
x
= 12
e
3
x
ln
(2
y
),
f
y
= 4
e
3
x
y

1
,
f
xy
= 12
e
3
x
y

1
,
f
xx
=
36
e
3
x
ln
(2
y
),
f
yy
=

4
e
3
x
y

2
(c)
f
(
x,y
) =
2(2
x

1)
4
y

2
.
f
x
=
16(2
x

1)
3
y

2
,
f
y
=

2(2
x

1)
4
(
y

2)
2
,
f
xy
=

16(2
x

1)
3
(
y

2)
2
,
f
xx
=
96(2
x

1)
2
y

2
,
f
yy
=
4(2
x

1)
4
(
y

2)
3
(d)
f
(
x,y
) =
x
3
y
.
f
x
= 3
y
,
f
y
=
x
(
ln
3)3
y
,
f
xy
= (
ln
3)3
y
,
f
xx
= 0,
f
y
=
x
(
ln
3)
2
3
y
4. Suppose that there are two goods: