Eco 401, J. Sandford, spring 2009
February 26, 2009
Homework 4
Answers
Problem 1
Nadia likes spare ribs, R, and fired chicken, C. Her utility function is
U
= 10
R
2
C
(1)
Her marginal utilities are
MU
R
= 20
RC
and
MU
C
= 10
R
2
. Her weekly income is $90, which she spends
on only ribs and chicken.
a. If she pays $10 for a slab of ribs and $5 for a chicken, what is her optimal consumption bundle? Show
her budget line, indifference curve, and optimal bundle,
e
1
in a diagram.
C
*
= 6,
R
*
= 6
b. Suppose the price of a chicken doubles to $10. How does her optimal consumption of chicken and ribs
change? Show her new budget line and optimal bundle,
e
2
, in your diagram.
C
*
= 3,
R
*
= 6
c. Solve for Nadia’s demand for chicken when the price of a chicken is
p
c
, for any
p
c
.
C
*
=
30
p
c
Problem 2
The cost function for John’s shoe repair is
c
(
q
) = 100 + 10
q

q
2
+
1
3
q
3
, so that marginal cost
is
c
0
(
q
) = 10

2
q
+
q
2
. Shoe repair is a perfectly competitive industry.
a. Suppose the price of shoes is $80. Solve for John’s profitmaximizing quantity of shoes repaired. What
is John’s profit in this case?
The profitmaximizing quantity
q
solves 80 = 10

2
q
+
q
2
, or
q
= 9
.
43.
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 Fall '10
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 Economics, Microeconomics, Supply And Demand, Utility, producer, J. Sandford

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