Econ 100A, Dr. Famulari, Practice Problems, Spring 2010
Week 1
See Calculus Appendix, CA.3 or Machina Handout
A.
Find the first and second derivatives for the following functions of x.
(1)
f(x) = a+bx+cx
2
+dx
3
(2)
f(x) = ln(4x
3
)
B.
Let z = 4x
4
y
3
5x
2
y+xy
2
(1) Derive the first and second partial derivatives for z.
What is true about the cross partials?
(2) Derive the total differential of z
C.
Calculate the slope and the elasticity of the following functions.
See Perloff
2.5 (Chpt 2,
section 5) for a review of elasticity.
(1)
f(x)=3+4x
(2)
f(x)=12+5x
(3)
f(x)=10x
2
(4)
f(x)=2x
3
(5)
What types of functions have constant slope?
constant elasticity?
D.
Solve the following :
2
2
max
x
yx
x

(1)
What is (are) the choice variable(s)?
(2)
What is the solution function?
(3)
What is the optimal value function (the maximal value of the function).
E.
A consumer is asked to rank order the commodity bundles below (see class notes):
X
Y
Bundle A
9
3
Bundle B
25
1
Bundle C
4
2
(1)
For the consumer’s preferences to be rational, what conditions MUST hold?
(2)
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 Spring '07
 fullterton
 Utility, indifference curves

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