The Ohio State University
Department of Economics
Econ 501.02—Prof. James Peck
Homework #1
(due Wednesday, April 11)
1.
Suppose we have the utility function,
U
=
x
2
y
3
.
(a)
Find the function for the marginal rate of substitution.
(b)
Show that this utility function satis
fi
es the
fi
rst 3 axioms of consumer
preference.
(Hint:
For example, the completeness axiom is satis
fi
ed if for
any two bundles A and B, either bundle A gives more utility than B when
evaluated according to the function U, or B gives more utility than A, or the
utility numbers of A and B are the same.)
2.
Suppose we have the utility function,
U
= 2
xy
+
x
+
y.
(a)
Find the function for the marginal rate of substitution.
(b)
If prices are
p
x
= $2
and
p
y
= $4
, and if income is
M
= $17
,
fi
nd the
utility maximizing consumption bundle.
3.
Suppose we have the utility function,
U
=
x
+ 3
y.
(a)
Find the function for the marginal rate of substitution.
(b)
If prices are
p
x
= $2
and
p
y
= $4
, and if income is
M
= $200
,
fi
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 Spring '08
 YANG
 Economics, Microeconomics, Utility, Neoclassical economics, Ohio State University Department of Economics Econ

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