ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Transcribed Image Text:Suppose Alex has the following utility function defined over goods x and y.
U (x, y) = xy+10x
a. Write out the expression for his indifference curve with y in terms of x and U.
b. Assume Alex's current level of utility is U = 80 and plot the indifference curve for this
level of utility for values of x between 2 and 12.
c.
Suppose Alex has $30 to spend on these two goods and x costs $5 per unit while y costs
$1.00 per unit. Add Alex's budget constraint to your graph. Visually determine the
combination of these two goods that Alex will purchase.
d. Write the expressions for the marginal utilities of each good and the marginal rate of
substitution between the two goods. Write out the expression for the slope of the
indifference curves. Does the MRSxy equal the negative of the expression for the slope?
e. Now suppose that the market conditions change, and the price of good y rises
dramatically to py = $5, while all else remains unchanged. Add this budget line to your
graph.
f.
Since Alex is faced with a higher price for y, we know that he will not be able to enjoy
the same level of utility as he did before the price increase. How do we know this?
g. Suppose you are told that after the price increase, the highest level of utility Alex can
enjoy is U = 60. Plot the indifference curve for this level of utility for values of x between
2 and 12.
h. What combination will Alex choose now? What causes this outcome and is it correct that
under the current conditions the highest level of utility Alex can enjoy is U = 60.
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