2010
Econ Spring 320 Intermediate Microeconomic Analysis
Yoichi Otsubo
4. Consider the single-good utility function
U ( y) = 2 y .
a. What are this consumers utility for y = 1, y = 4, y = 5? Sketch the utility function.
(You may use
xz = x z , 2 = 1.1, 3 = 1.7, 5 = 2.2, 6 = 2.5)
Ans.
U (1) = 2 = 1.1, U (4 ) = 8 = 2 2 = 2.2, U (5) = 10 = 2 5 = 2.32
(Graph will be shown in class)
b. Does this consumers preferences satisfy transitivity assumption? Explain.
Ans.
Yes. Let A, B and C denotes the consumption basket y=1, y=4 and y=5 respectively.
B A and C B since U(4)>U(1) and U(5)>U(4). To satisfy transitivity condition, this
consumers preferences has to be C
preferences are transitive.
A . Since U(5)>U(1), C
A . Hence her
c. Does this consumers preferences satisfy more the better assumption? Explain.
Ans.
Yes. Since U(5)>U(4)>U(1), C B A . And basket C contains most the units, B the
second, and A the least.
d. Derive this consumers marginal utility using derivative. What are this consumers
marginal utility for y = 1, y = 4, y = 5? Sketch the marginal utility.
(You may use
1
x = x x)
Ans.
MU y = 2 (2 y )
(Graph will be shown in class)
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Spring 2010
Econ 320 Intermediate Microeconomic Analysis
Yoichi Otsubo
5. Suppose David purchases only Pepsi and Pizza. Let x be the number of units of Pepsi,
and y be the units of Pizza he purchases per month. Also suppose that his utility function
is measured by U =
xy , and his monthly income is I. Each unit of Pepsi costs Px and
each unit of Pizza costs Py. Write a statement of the constrained optimization problem.
Which variables are exogenous? Which variables are endogenous?
Ans.
max xy
( x, y )
subject to : Px x + Py y I
Exogenous variables: I, Px, Py.
Endogenous variables: x, y.
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