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ECON 256: Intermediate Microeconomics
Long Assignment: 3
1
Answer Key
Due Date: Thursday, October 21, 2010
1. Marilyn spends her entire monthly income of $600 on champagne (C) and perfume (F).
The price of a bottle of champagne is $30 and the price of an ounce of perfume is $10. If she
consumes 12 bottles of champagne and 24 ounces of perfume, her MRS
CF
is 1. Is her choice
optimal? If yes, mention why. If not, explain what she ought to change in her consumption.
Explain your answer with a diagram labeling everything clearly.
The budget constraint has a slope of 3. To put it another way, the ratio of the prices of the
goods on the X and Y axis is 3. So for optimal consumption, Marilyn should consume a
bundle that generates MRS of Perfume for Champagne of 3. At her current consumption
point
B
, her MRS
CF
is 1. As we know that there is a diminishing MRS along an indifference
curve, so we will have an MRS
CF
of 3 to the left of an MRS of 1 implying Marilyn needs to
alter her consumption towards consuming more perfumes and less champagne to reach
optimal consumption. Of course, what the final optimal bundle will be is not known to us
unless we are given more information. All we know is that the budget constraint and an
indifference curve has to be tangent to one another at the optimal bundle. I have denoted
that optimal bundle with
A
.
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View Full DocumentECON 256: Intermediate Microeconomics
Long Assignment: 3
2
2. (Textbook p. 78; Problem Question 10) For Alexi coffee and tea are perfect substitutes:
One cup of coffee is equivalent to one cup of tea. Suppose Alexi has $90/month to spend on
these beverages and coffee costs $0.90/cup while tea costs $1.20/cup. Find Alexi’s best
affordable bundle of tea and coffee.
Explain your answer succinctly.
Label the axes and
graph clearly (use the graph space provided in the next page). Place cups of coffee/month
on the horizontal axis and cups of tea/month on the vertical axis.
Alexi's budget constraint (BC) is
°
= 75
−
3
4
±
, with a slope of
−
3
4
.
Her perfect substitute preferences yield linear indifference curves with slope equal to 1,
such as T = 75 – C (IC
0
) and T = 100 – C (IC
1
).
By consuming 90/0.90 = 100 cups of coffee each month, she reaches a higher indifference
curve than consuming 90/1.20 = 75 cups of tea (or any affordable mixture of coffee and
tea). [Indeed, as we know when MRS
XY
is greater than the price ratio of X and Y, we buy
only X.]
Thus at the optimal consumption bundle Alexi buys 100 cups of coffee and no tea (point
A
).
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 Fall '05
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 Microeconomics

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