Homework 2
Additional Questions:
1.
Utility and Indifference Curves
A.
Suppose a consumers utility function is given by U(x,y)=sqrt(xy), where sqrt denotes
the power (1/2) or the square root function.
Plot the indifference curve for a utility level
equal to 10.
Plot at least 3 points on this indifference curve.
B.
Does this indifference curve for a utility level of 10 ever intercept the x or y axis?
Do
any of the indifference curves intercept the axis (excluding the indifference curve for a
utility level of 0)?
C.
What does the slope of this indifference curve tell us?
D.
Does this utility function, U(x,y)= sqrt(xy), satisfy the more is better property which
we expect consumer’s preferences to exhibit?
2.
Consumer’s Utility Maximizing Bundle
Suppose our consumer’s utility function is given by U(x,y)=sqrt(xy).
Therefore, the
MU
x
=(1/2)*sqrt(y/x)
and MU
y
=(1/2)*sqrt(x/y).
You will never have to work these
marginal utilities out, they will be given.
A.
What is the slope of the indifference curve for a utility level of 4, at the point
(x,y)=(2,8)?
At the point (x,y)=(4,4)?
At the point (x,y)=(8,2)?
Why do we see this
pattern in the slope as we move along this indifference curve from the left to right?
B.
Suppose the prices of good x and y are equal to 1 and 2 respectively.
What is the
slope of this consumer’s budget line (with x on the horizontal axis, y on the vertical
axis)?
C.
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 Fall '08
 Williams
 Economics, Supply And Demand, Utility

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