Practical question for midterm
1)
The utility function for a consumer is given by U(X, Y) =XY.
The price of goods X and Y
are $5.
The consumer has $200 of income. Hint you have to use first derivative to get MRS
=MUx/MUy.
a)
Derive the demand bundle
(X*, Y*) and
the utility level at
(X*, Y*), Ū.
b)
Now suppose that the price of good
X
increases to $10.
Solve for the new demand
bundle
(X**, Y**)
and the utility level at
(X**, Y**), Ū.
c)
Draw a diagram in
XY
space clearly labeling all optimal bundles, indifference curves,
budget lines, slopes, and intercepts.
d)
On your graph, show the income and substitution effects of the price change.
e)
Under the new pricing scheme, the amount of income needed to make the consumer just
as well off as he was
before
prices changed is called the compensating variation.
Calculate the compensating variation for this consumer and label it on your graph.
f)
How much income would the consumer need to be compensated so that she could afford
her original bundle?
Is this more or less than the compensating variation?
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 Winter '09
 bandy
 Utility, $5, $10, $20, Slutsky Equation, utility level

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