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Leo Spornstarr
TA: Bridget Hoffman
Microeconomics
January 17, 2010
Econ Homework, Problem Set I
1a. there are a few general properties of all utility functions.
That there are always increasing at
a decreasing rate, yet it is impossible to accurately define how much it increases each time as it is
a personal preference of how much an individual likes something.
Doing some calculations can
help us determine a few restrictions that we can put on U(2).
It must be greater than 48 and less
than 124.
However, it cannot be 96 (48*2) because the first time it increased that much and the
U function decreases as the x function increases, this is the upper limit.
We also can determine
that it must be greater than 86 though because 12448 = 76/2 = 38 and since the U needs to be
decreasing between increasing values; this finds us the lower limit.
Therefore, 96 >U(2)>86.
The same logic can be applied U(5).
Since the difference between 152124 = 28, U(5)> (196
28), as once again the U function decreases as x increases.
And then the difference between U(5)
and 196 must be less than half of the difference between 196152=44 44/2=22 in order to
guarantee that U Is decreasing as x is increasing.
Then 152+22=174, which is the lower limit.
Therefore 180 > U(5) > 174.
1b. To figure out the price of coconuts we have to use the simple formula that when the utility is
maxed out completely.
MU(coconuts)/P(coconuts) = MU(muffins)/P(muffins).
Using the
numbers we know of mu(c)=42 (given), Mu(muffins) (M(u(4)U(3))=28, P(m)=4.
We substitute
in 28/4 = 42/x.
Do some algebra and we get the price of one coconut equal to $6.
1c. Biggie’s income level is equal to P(coconut)*#of coconuts bought + P(muffins)*#of muffins
bought = Income.
Doing some simple substitution and addition 6*3 + 4*4 = $34.
His income
level is equal to $34.
2a.
The first thing to note is that we should note is that Income = Price of 1 * amount of 1 +
price of 2 * amount of 2.
Here we have waffles (x) and eggs (y).
So we substitute what we
know into the equation.
30 = P(y)*A(y) + P(x)*A(x).
P(y)=2 and P(x)=3.
30 = 3A(x)+2A(y).
To find out the opportunity cost of consuming an additional egg, we must find the equation of the
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 Spring '11
 ZELDER
 Microeconomics, Utility

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