Eco 300, Spring 2011, Homework 2
Professor Rui Zhao
Due Thursday, 02/17
1.
(20 points) Suppose a consumer has the utility function U(x, y) = 2xy. The
marginal utilities are MU
x
= 2y, MU
y
= 2x. Suppose price of x is P
x
= 1, price of y
is P
y
= 2, and the consumer’s income is $12.
a.
In a clearly labeled graph draw the budget line and several indifference
curves. Indicate where the optimal choice is. (You don’t need to draw the
curves precisely for the equations, just illustrate the idea of the tangency
condition.)
b.
Using algebra (the tangency equation and the budget equation) to find the
optimal choice.
c.
At the optimal choice that you found, what is the marginal rate of
substitution between x and y, i.e. MRS
x,y
?
d.
Suppose the consumer decides to buy 4 units good x and 4 units y. What is
the marginal utility per dollar spent on x (MU
x
/P
x
)? What is the marginal
utility per dollar spent on y (MU
y
/P
y
)? What does this tell you about how
the consumer should substitute one good for the other?
(Hint: Compare to Learningbydoing exercise 4.2)
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 Spring '11
 zh
 Utility, $1, $2, $1.5

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